Complete Garfield help file

Garfield input is subdivided in sections:

• the &CELL section: chamber layout, ANSYS, Maxwell and Tosca interfaces;
• the &MAGNETIC section: setting the magnetic field;
• the &GAS section: transport and ionisation properties of the gas and the interfaces to Heed and Magboltz;
• the &OPTIMISE section: modification of the layout, space charge and improving the field uniformity;
• the &FIELD section: visualisation of the field;
• the &DRIFT section: drifting of electrons and ions;
• the &SIGNAL section: induced currents;
• top level input can be entered after a &MAIN command;
• program execution ends when &STOP is entered.

Garfield input can also contain rudimentary scripting:

• Calling procedures;
• Do loops to repeatedly execute statements;
• Global and Vector to manipulate variables;
• If_line and If_block for conditional execution of statements;
• Parse to obtain terminal input while running an input file;
• Say for simple output.

Occasionally, you may wish to use the various utilities:

• background to the algebra used to evaluate formulae;
• comment in input files;
• use of the control_keys;
• error_handling in program library procedures;
• enhanced control of graphics;
• input from, output to and manipulation of datasets;
• OPTIONS valid in all sections;
• recording terminal input;
• issuing shell commands;
• translation of characters in input statements.

Chapter 1: introduction

It is a program that can be run both interactively and in batch on a wide variety of computers without significant change in outwards appearance. The program is fully command driven but if you desire to add some pieces, you'll find no major obstacles (the program has been written in Fortran-77 and uses Patchy as pre-processor).

Section 1.1: getting_started

Although Garfield can be run in batch mode, it is easier to run it from a workstation or graphics terminal. You should be able to issue any combinations of commands without causing core dumps, abends etc. (please contact me if this nevertheless happens !).

A simple example:

&CELL
plane x -1
plane y -1
rows
S 5 * i i 1000*i

&FIELD
plot-field surface V, contour V

There is one special header: &STOP (or &QUIT or &EXIT if you prefer) which will stop program execution. End-Of-File on input will have the same effect.

The instructions within the sections are free format lines. Input files can be both fixed and variable record length. The maximum record length is large, about 500\ characters.

An ellipsis (...) at the end of one physical line indicates that the instruction continues on the next. There can be only 1 instruction per input line.

The first word on each line is the command proper. The other words can be viewed as a set of parameters, with sometimes a value assigned to them.

The elements on the input are separated from each other by a blank ( ), a comma (,), a colon (:) or an equal sign (=). There is no difference in meaning between these separators. You may if you wish place several between the words.

Case is irrelevant in commands. Strings of which the case matters, such as file names on Unix systems and also in identifiers, should be delimited by double quotes.

Here is an example of a cell description:

&CELL
plane x=10, V=1000
plane x -10 ...
      V 1000
periodicity y 3
rows
S * * 0 0 5000

cell-identifier "Test cell"

PLANE V=1000 X=10

The ROWS command has a slightly different syntax from the rest: apart from having arguments of its own (not shown in the example), it is followed by a series of lines (1 in this example) that contain the actual data. The end of the list is signalled by a blank line. There is one more such command in the cell section (SOLIDS) and there are also a few commands of this type in the gas section (CLUSTER and TABLE).

Nearly all words in the input may be abbreviated to some extent in each of the 'segments':

E-MOST-PROBABLE    & CELL      PLANE
E-MOST-PROB        &CELL       PLAN
E-M-PROB           &C          PL

Global ok False
Until ok Do
   Say "Please enter an integer number"
   Parse Terminal n
   If n<0 Then
      Say "The number you entered, {n}, is negative."
      Iterate
   Elseif entier(n)#n Then
      Say "The number you entered, {n}, is not an integer"
      Iterate
   Endif
   Global fac=1
   For i From 1 To n Do
      Global fac=fac*i
   Enddo
   Say "Factorial of {n} is {fac}."
   Global ok True
Enddo

After a little practice, you should become aware of the utility commands. They can be used to change the graphics settings, to issue commands to the shell (Aegis, DCL, Unix or VM/CMS), to take input from and to output data to files etc.

Section 1.2: command_descriptions

{ a | b ... }

One, and only one, of the items between the brackets must be present. If the item is omitted, the command as a whole will be declared as not valid. The curly brackets are not part of the command, they are only typed when substitution of expressions of global variables is desired.

[ a | b ... ]

You may select one, and not more than one. item from the list between brackets, but you don't have to. A default value will be used if you omit this item. The square brackets are not part of the command, such brackets are only typed when indexing a Matrix.

[ a ]

The contents of the brackets is an optional part of the command, you may use it but don't have to. The square brackets are not part of the command, they are only used when indexing a Matrix.

CAPITALS

Are used for things that should be typed as-is.

lower case

Is used for things that should be replaced by some value (values can be numeric, strings and Booleans).

Section 1.3: input_elements

abbreviations

Abbreviations are usually permitted, those words that contain hyphens (-) may be abbreviated in each each of the hyphen-separated segments independently.

brackets

Garfield uses 3 kinds of brackets which serve entirely different purposes.

case

Matters for file names on Unix and VM/CMS systems. By default all input is converted to upper case when reading the command, but this can be avoided by using quotes.

defaults

Default arguments are chosen by typing an asterisk.

long commands

A line that is to be continued on the next line should end in ... (ellipsis), there is no limit on the number of continuation lines by itself but the total length of a line shouldn't exceed some fixed number (at present 500).

separators

Words in the input lines must be separated by one or more of the separators.

quotes

Like with brackets, care should be taken to use the various quotes correctly.

Section 1.4: special_characters

Some characters have a special meaning when used inside commands:

Section 1.5: brackets

• Round brackets "( ... )": Used in formulae, for arguments of functions and procedures, and also around sub-expressions that need to be evaluated first.

  Examples:

  Global a=cos(2*pi/3)
  Call print(1+2*(3+4))
  

• Square brackets "[ ... ]": Used in formulae, when indexing a Matrix.

  Example:

  Global a=number(b[3;3])
  

• Curly brackets "{ ... }": Form the bridge between normal statements and Global variables. Curly brackets request evaluation of what is between the brackets followed by substitution of the result in the input statement.
  Curly brackets must not be used in control statements.
  Example:

  Global argon=80
  Global co2=20
  Global gas_file=`Ar`/string(argon)/`CO2`/string(co2)
  Call inquire_file(gas_file, exist)
  If exist Then
     get {gas_file}
  Else
     magboltz argon {argon} co2 {co2}
     heed argon {argon} co2 {co2}
     add mobility 1.5e-6
     write {gas_file}
  Endif
  

  Please note that curly brackets are used only in the GET, WRITE, MAGBOLTZ and HEED statements - these are commands, not control statements. Curly brackets are not used when the global variable GAS_FILE is used as argument of the INQUIRE_FILE procedure. Similarly, EXIST is not enclosed in curly brackets in the If-condition. When ARGON and CO2 are used without brackets in the Global statement, but with curly brackets in MAGBOLTZ and Heed.

Section 1.6: quotes

• Double quote ("): Is used in normal input statements, around strings that need to form a single input word but that contain special characters such as spaces, equal signs, commata, double quotes etc. Case is preserved between double quotes.

  Examples:

  Say "Hello, how are you doing ?"
  arrival dataset "arrival.dat"
  

• Single quote ('): Are like double quotes, but the text between single quotes is converted to upper case.

  Example:

  Call threshold_crossing(1,-0.02,`rising,linear`,n,t1,t2)
  If 'n=0' Then
     Say "Warning: No crossing found."
     Iterate
  Endif
  

  In earlier versions of Garfield, the condition of If_lines and If_blocks had to be a single word in upper case. In the example, an equal sign is used in the condition. Since equal signs are separators, like commata and blanks, the condition without quotes would be read as 2 words: "N" and "0".

• Reverse quote (`): Are used to delimit Strings. They appear only in control statements such as Call, Global, If_line, If_block, Do and Parse.

  Example:

  Global argon=80
  Global co2=20
  Global gas_file=`Ar`/string(argon)/`CO2`/string(co2)
  

  A file name is constructed from the percentages of Ar and CO\<SUB\>2\</SUB\>.

Section 1.7: separators

• comma: ","
• blank: " "
• equal sign: "="
• colon: ":"

Text strings, such as formulae, that should not be broken up but which contain a word separator, should be put between single or double quotes. The string is converted to upper case when single quotes are used, while the case is preserved with double quotes.

Section 1.8: trouble

Garfield is a fairly large drift chamber simulation program, it is a one person enterprise and the program changes rapidly. This has the advantage for the user that the program tries to track changes in the design considerations of gas detectors. The drawback is a lack of (complete) backwards compatibility of input files.

Please contact the author in case of trouble and if you need further information, have suggestions for extensions etc. In case you suspect an error, send the following:

• a complete copy of the input, not just the relevant part
• a complete copy of the output, not just the relevant part
• a description of the system you are running on plus version indication of the program.

A common source of problems is the use of a manual that is out of date. As a rule, it is better to consult the help file via WWW for up to date information concerning the commands:

http://cern.ch/garfield/cnl       for modifications
http://cern.ch/garfield/examples  for examples
http://cern.ch/garfield/files     for the files
http://cern.ch/garfield/help      for help

Section 1.9: authors

Magboltz is the work of Steve Biagi.

The TRIM interface has been contributed by James Butterworth.

Most of Garfield has been written by Rob Veenhof (referred to as 'I' or 'me' in the documentation). The best way to contact me is by electronic mail.

If you prefer more traditional means:

Rob Veenhof            Rob Veenhof
CERN / PH department   2, Rue du Reculet
CH-1211 Gen\ève 23      F-01630 St Genis-Pouilly
Suisse                 France
tel: + 41 22 7673222   tel: + 33 4 50421784

For technical questions and remarks about the control-C mechanism and other typical Vax features, please contact Carlo Mekenkamp directly (cmekenkamp@vx8000.nl).

G.A. Erskine contributed key ideas but he should not be called in case of problems. Please contact me in case of questions about his parts (theta functions, polygon mappings).

Section 1.10: origin

Since then, the program has grown enormously:

• cylindric geometries have been added;
• a magnetic field can be taken into account;
• interfaces with Magboltz and Heed have been added;
• finite element field maps can be read.

In 1984 the program had a length of 5000\&nbsp;lines. By 2001, Garfield had grown to 127000\&nbsp;lines (4.9\&nbsp;Mb), while Magboltz and Heed count respectively 21800 and 19800\&nbsp;lines (780\&nbsp;kb and 507\&nbsp;kb).

Section 1.11: units

When the input unit is shown as "user has the choice", then the quantity can, on input, be followed by a unit of the users choice. If no unit is indicated, then internal units are assumed.

To convert line charges into the more usual unit of C/cm, one should multiply the charge obtained from procedures such as GET_WIRE_DATA with 2\&pi;\&epsilon;\<SUB\>0\</SUB\>, approximately 5.56\&nbsp;10\<SUP\>-13\</SUP\>\&nbsp;C/V.cm. The wire charge shown in the table printed in response to the CELL-PRINT option and the PRINT-CELL command, includes this conversion factor.

Similarly, to convert point charges to C, one should multiply the charge expressed in V.cm with 4\&pi;\&epsilon;\<SUB\>0\</SUB\>.

Section 1.12: versions

http://cern.ch/garfield/files

/afs/cern.ch/user/r/rjd/Garfield/Files/garfield

Chapter 2: &MAIN

Main \→ Cell section  \→ algebra sub-section
                       graphics sub-section
                       ...
       Gas section   \→ algebra sub-section
                       graphics sub-section
        ...

&MAIN can also be used as final statement in jobs that run Magboltz to produce electron transport plots. &MAIN is in this context approximately equivalent to &STOP.

The cell and gas sections produce plots, write data sets and make their data available to the procedures when the section is left. Leaving the section can be done in 3\&nbsp;ways:

• by entering a new section;
• by issuing a &MAIN command to return to the top level;
• by issuing a &STOP command to stop program execution.

Example:

Global emin=100
Global emax=10000
&MAGNETIC
components 0 0 0.4 T

&GAS
options gas-plot
write "p10.gas" "b4000"
magboltz argon 90 methane 10 coll 2 n-e 4 n-angle 2 ...
   e-range {emin,emax}

&MAIN
Global n=100
Global e=emin*(emax/emin)^((row(n)-1)/(n-1))
Call transverse_diffusion(e, 0, 0, 0, 0, 0.4, dt)
Call longitudinal_diffusion(e, 0, 0, 0, 0, 0.4, dl)
Call plot_graph(e,(dt^2+dl^2),`E [V/cm]`, ...
   `sqrt(&sigma;<SUB>T</SUB><SUP>2</SUP>+&sigma;<SUB>L</SUB><SUP>2</SUP>)`, ...
   `Diffusion`)
Call plot_end

Chapter 3: &CELL

Everything you enter, is simply stored. A comprehensive check of the input is only performed when leaving the section. That is also the time the compact format cell dataset is written, if requested, the layout is plotted, the cell description is printed etc.

Format:

&CELL

Section 3.1: overview

• a full specification of the cell in the input
• retrieval of a cell from a dataset

Creating a new cell:

Retrieving a cell from a dataset:

Section 3.2: methods

3.2.1: potential_function

Each chamber type has its own potential function. For numerical purposes, nearly all potential functions are further subdivided into a set of domains according to the aspect ratio of the periodicities, the distance between wires and planes etc.

Versions of most potential functions exist which take advantage of vector hardware. The choice between scalar and vector versions is made a compilation time.

Use GET_CELL_DATA to find out which potential function is in use. The cell type is also displayed when the CELL-PRINT option is active and in response to the PRINT-CELL command.

Garfield has shape functions to deal with various element types such as straight triangles, curved triangles, straight tetrahedra, curved tetrahedra, hexahedra etc. Use CELL-PRINT as described above to find the shape functions used for the current chamber.

neBEM has a range of Green's functions too: line elements, right-angled triangles and rectangles. Most models contain several of these elements at the same time.

3.2.2: coordinate_system

One can use the GET_CELL_DATA to find out which system is in use.

3.2.2.1: Cartesian

Such a system is used for chambers constructed from wires and planes unless one of the following conditions is met:

• the chamber is declared to have a PERIODICITY in phi;
• the chamber contains a PLANE at constant r or phi;
• the chamber contains a TUBE.

3.2.2.2: Polar

• r: distance from the origin, in cm;
• \&phi;: angle with respect to the positive x-axis, in degrees;
• z: distance from the (x,y) plane, in cm.

Polar coordinates are internally dealt with by the conformal mapping:

(x,y) = exp(\ρ,\φ)
z     = \ζ

3.2.2.3: Tube

The tube coordinates are special in the sense that the wire locations are listed in Cartesian coordinates, while the tube is an object with a polar shape.

Garfield internally uses Cartesian coordinates for cells of this type. Potentials in round tubes are computed using the conformal mapping:

    z - z0
z = -----------
    1 - z0bar z

Potentials in polygonal tubes are computed by mapping the centre of the tube to a round tube, while the edges are mapped with a local Schwarz-Christoffel expansion.

3.2.3: shape_function

A. R. Mitchel and R. Wait, The finite element method in partial differential equations, Wiley (1977), in particular pp 108-110.

Section 3.3: CELL-IDENTIFIER

The string can be retrieved by means of the GET_CELL_DATA procedure.

The identification string is displayed in the plots using the COMMENT text representation.

Format:

CELL-IDENTIFIER string

Example:

CELL-ID "DC1 central cell"

Section 3.4: CUT-SOLIDS

After a cut operation, a solid will as a rule not be closed anymore. This does not pose a problem for neBEM field solutions provided that (mirror) periodicity conditions are applied.

This command is executed when preparing neBEM panels, i.e. on leaving the cell section. Any error will therefore only be reported at this stage and not when the command is issued. For the same reason, these commands can be placed anywhere in the cell section, even before the solids are defined.

When plotting the volumes, the outlines of solids do not reflect the cuts.

Example:

&CELL
Global r=0.2
solids
hole centre 0 0 -0.1 ...
     half-lengths 2 2 0.1 ...
     radius {r} ...
     conductor-1 ...
     label a ...
     voltage -1
hole centre 0 0  0.5 ...
     half-lengths 2 2 0.5 ...
     radius {r} ...
     epsilon 4 ...
     label a ...
     dielectric-1
hole centre 0 0  1.1 ...
     half-lengths 2 2 0.1 ...
     radius {r} ...
     conductor-1 ...
     label a ...
     voltage 1
hole centre 1 {sqrt(3)} -0.1 ...
     half-lengths 2 2 0.1 ...
     radius {r} ...
     conductor-1 ...
     label b ...
     voltage -1
hole centre 1 {sqrt(3)}  0.5 ...
     half-lengths 2 2 0.5 ...
     radius {r} ...
     epsilon 4 ...
     label b ...
     dielectric-1
hole centre 1 {sqrt(3)}  1.1 ...
     half-lengths 2 2 0.1 ...
     radius {r} ...
     conductor-1 ...
     label b ...
     voltage 1

nebem maximum-elements=3

cut plane x>0 solids all
cut plane y>0 solids all
cut plane x<1 solids all
cut plane y<{sqrt(3)} solids all
cut plane y<{sqrt(3)/2} solids a
cut plane y>{sqrt(3)/2} solids b

&FIELD
area -0.5 -0.5 -0.5  1.5 2 1.5 view 2*x+7*y-3*z=0 nebem
Call plot_field_area
Call plot_end

This example constructs the elementary cell of a GEM-like structure using 6 holes. The elementary cell contains 2 quarter-holes. The rest of the GEM is obtained by applying mirror symmetries in x and in y. Surface panels shown in red faced the inside (and were thus invisible) before the solids were cut.

Section 3.5: DEFINE

As usual, the current value of a variable is displayed if no new value is provided. All variables are displayed if arguments are absent altogether.

Do not confuse DEFINE with Global: DEFINE defines local variables for the cell section. Global defines variables that you can use anywhere. Expressions using local variables and the loop-variable are evaluated automatically. Expressions in terms of global variables have to be enclosed by curly brackets to obtain substitution.

Format:

DEFINE variable value

Example:

def vp_1=1000
def vp_2=2000
def r_1=5000
def r_2=5000
def vp_between=(vp_1*r_2+vp_2*r_1)/(r_1+r_2)
def vp_between

A simple resistor chain, the last line displays the value. You could in principle also enter the whole formula in the ROWS lines.

Global resistor=5000
define r_1 {resistor}
define r_2 {resistor}

The global variable RESISTOR is copied to the local variables R_1 and R_2. Note the use of curly brackets.

3.5.1: variable

The naming conventions for variable names should be observed.

The total number of variable names that can be stored is usually set to 100. If you need more, you'll have to recompile the program with a suitable value for MXVAR.

The variable name I is reserved as loop-variable.

3.5.2: value

Each variable may be defined in terms of previously defined variables and redefinition of variables is permitted at any time.

Section 3.6: DIELECTRICUM

Adds a slab of dielectric material to your cell. The slab extends from -infinity to +infinity in one direction and has a range you choose in the other.

x-Slabs and y-slabs of dielectric material are allowed to overlap provided they have the same dielectric constant. Slabs in one direction are not allowed to overlap, even if they have the same dielectric constant.

Wire may be located inside dielectric media, but the media must be inside the equipotential planes, if there are any in your cell.

Dielectrics slow the program down significantly.

Format:

DIELECTRICUM {X-RANGE|Y-RANGE} min max EPSILON \ε

Example:

DIELECTRICUM X -10 10 EPS 5

This slab of dielectric material covers the -10\&nbsp;<\&nbsp;x\&nbsp;<\&nbsp;10 part in x and the whole of y. The dielectric constant for the material is chosen to be 5.

3.6.1: min_max

3.6.2: \&epsilon;

Section 3.7: FIELD-MAP

Currently, field maps in the format generated by ANSYS, Maxwell Parameter Extractor 2D and 3D, Maxwell Field Simulator 2D and 3D as well as by Tosca can be read. Interfaces for files produced by other programs can be added on request (please contact the author).

When you read a field map in the cell section, any wire, plane, periodicity, dielectric medium and magnetic field that you entered sofar is deleted. Also field map components read with earlier FIELD-MAP commands are deleted.

The optimisation section has a FIELD-MAP command too. The field maps entered in the cell section serve as main field, i.e. this field map replaces the field generated by wires and planes. The field maps entered in the optimisation section are used e.g. when a finite element weighting field is needed in conjunction with a main field computed from wires and planes (see the weighting_field example), or when space charge computed with a finite element program is superimposed on a main field calculated for wires and planes. The two field maps share (for the moment) the same storage and can therefore not be used at the same time.

Reading large field maps is time consuming. To save time, you consider saving your field maps in binary format with SAVE-FIELD-MAP. Binary field maps are retrieved with READ-FIELD-MAP. Binary field maps are much smaller and much faster to read in, but they are not portable between computer systems.

The FIELD-MAP command can read magnetic fields computed by finite element programs. For the moment, there is no experience with such fields.

Format:

FIELD-MAP [FILES [contents_1] file_1 [LABEL label_1] ...
                 [contents_2] file_2 [LABEL label_2] ...
                 ...
                 [contents_n] file_n [LABEL label_n] ...
                 [format] ] ...
          [DRIFT-MEDIUM {SMALLEST-EPSILON | ...
                         SECOND-SMALLEST-EPSILON | ...
                         n | ...
                         SECOND-LARGEST-EPSILON | ...
                         LARGEST-EPSILON | ...
                         \ε}] ...
          [NOT-X-PERIODIC | X-PERIODIC | X-MIRROR-PERIODIC | X-AXIALLY-PERIODIC] ...
          [NOT-Y-PERIODIC | Y-PERIODIC | Y-MIRROR-PERIODIC | Y-AXIALLY-PERIODIC] ...
          [NOT-Z-PERIODIC | Z-PERIODIC | Z-MIRROR-PERIODIC | Z-AXIALLY-PERIODIC] ...
          [X-ROTATIONALLY-SYMMETRIC | Y-ROTATIONALLY-SYMMETRIC | Z-ROTATIONALLY-SYMMETRIC] ...
          [LINEAR | QUADRATIC | CUBIC] ...
          [INTERPOLATE-ELECTRIC-FIELD | COMPUTE-ELECTRIC-FIELD] ...
          [DELETE-BACKGROUND | KEEP-BACKGROUND] ...
          [UNIT {MICROMETRE | MILLIMETRE | CENTIMETRE | METRE}] ...
          [Z-RANGE zmin zmax] ...
          [OFFSET xoff yoff zoff] ...
          [PLOT-MAP | NOPLOT-MAP] ...
          [NOHISTOGRAM-MAP | HISTOGRAM-MAP] ...
          [RESET]

Example:

&CELL
field-map files "e_field.arg" "potential.arg" "epsilon.arg" ...
          drift-medium second-smallest ...
          x-periodic

(Maxwell Parameter Extractor 2D has been used to generate maps of the electric field, the potential and the dielectric constant. These maps are read in and the medium with the 2nd smallest dielectric constant is declared to be the drift medium. The map is also declared to be periodic in the x direction.)

3.7.1: FILES

• the potential,
• the electric E-field,
• the electric D-field,
• one or more weighting fields,
• the magnetic field,
• the dielectric constant.

Notes:

1. All maps, weighting fields included, must share the same grid.
2. The weighting field of an electrode is the electric field that results from setting the potential of that electrode to 1 and all others to 0. (Strictly speaking, the potential should be 1, and not 1\&nbsp;V.) This field is used to compute the signals induced on an electrode by moving charges.
3. The D field is only used to compute the dielectric constants by comparison with E.
4. Should you, under duress, have to use Windows to prepare the field maps, then take care to remove spurious end-of-line sequences, such as control-M, from the field maps.

3.7.1.1: contents

• field maps of which the format can not be identified automatically, such as ANSYS-plane-121; ANSYS-solid-123; Tosca, Tosca-118, Maxwell-2D-SV, COMSOL-2D-LINEAR, COMSOL-2D-QUADRATIC (formerly called FEMLAB-2D), COMSOL-3D-LINEAR, COMSOL-3D-QUADRATIC (formerly called FEMLAB-3D), QuickField
• files that contain a weighting field.

In case Maxwell Field Simulator has been used to generate the maps, identifying the mesh directory is recommended. The contents is optional for all other types of data written by Maxwell programs.

A warning is issued if the file contains other data than the declared contents.

Currently, the following contents types are recognised:

3.7.1.1.1: B-FIELD

3.7.1.1.2: ELECTRIC-FIELD

One reason is that the electric field is discontinuous across element boundaries. As a result, a node will typically have as many different electric field values associated with it, as there are elements of which the node is part. Potentials in contrast are unique.

Another reason is that the shape function method enables one to compute the electric field from the potential without need to take numerical derivatives. One does need the Jacobian of the coordinate transformation, but this is anyhow needed to compute the local isoparametric coordinates.

In other words, there is no significant gain in CPU time, and a major saving in memory, if one computes the electric field as needed, using the potentials.

The first finite element interfaces developed for Garfield were for programs that did output the electric field maps - and Garfield still allocates memory to store the electric field maps. All interfaces developed later arrange for the electric field to be computed from the potential map and it is expected that the stored electric field map will disappear in the foreseeable future.

See also the COMPUTE-ELECTRIC-FIELD and INTERPOLATE-ELECTRIC-FIELD options.

3.7.1.1.3: D-FIELD

3.7.1.1.4: MATERIAL

3.7.1.1.5: MESH

3.7.1.1.6: MODEL

3.7.1.1.7: BACKGROUND

3.7.1.1.8: POTENTIAL

3.7.1.1.9: WEIGHTING-FIELD

Since the current is a scalar and the velocity a vector, an intuitively plausible ansatz for the current reads:

I = factor Q Ew.v

Weighting fields resemble ordinary electric fields, and finite element programs do not distinguish them from electric fields. There are differences, though. For instance, as can be seen from the above formula, the unit of the weighting field is 1/cm, not V/cm.

Garfield stores only one mesh at the time and uses this mesh both for the ordinary field and for the weighting field. Care needs to be taken therefore that no mesh refinements occur between solving for the 2 types of field.

Finite element programs such as ANSYS output the weighting potential instead of the weighting field - Garfield computes the gradient internally.

3.7.1.2: file

These files are usually written by other programs than Garfield, and they therefore do not follow internally the Garfield format conventions. For notes on the way dataset names should be supplied to Garfield, see the guidelines for Garfield files.

For recipes for making these files, refer to the file format descriptions.

3.7.1.3: label

The label is a single upper case alphabetic character which serves two purposes:

1. The label links a weighting field with solids. For this association, the weighting field label should match one or more labels used in the SOLIDS listing. A solid label should not match more than one weighting field label, unless the signals for these weighting fields are summed.

   In the absence of a match, e.g. because no solids have been entered, all signals on the weighting field map are classified as cross induced. Such signals are only computed if the CROSS-INDUCED option is active.

2. The label identifies the weighting field to the SELECT statement, a prerequisite for the computation of signals in the electrodes for which the weighting field has been computed.

As for all finite element field maps, weighting field maps can be entered both in the cell section and in the optimisation section. When the main field is computed using a finite element program, then the weighting fields are entered, together with the main field, in the cell section. Entry of a weighting field in the optimisation section is used for weighting_field example when the main field can be calculated nearly exactly from wires and planes, while the shape of the read-out electrodes (typically pads) is such that the weighting field is more easily calculated using finite elements.

[By default, the label "S" is assigned to weighting field maps, which makes these maps are part of the initial, default, selection.]

3.7.1.4: format

• ANSYS-plane-121;
• ANSYS-solid-123;
• Tosca, from Vector Fields;
• Tosca-118,
• QuickField;
• COMSOL-2D-LINEAR;
• COMSOL-2D-QUADRATIC, formerly called FEMlab-2D;
• COMSOL-3D-LINEAR;
• COMSOL-3D-QUADRATIC, formerly called FEMlab-3D;
• Parameter-Extractor-2D, from Ansoft;
• Parameter-Extractor-3D, from Ansoft;
• Field-Simulator-3D, from Ansoft;
• Maxwell-2D-SV, from Ansoft;
• Maxwell-11, from Ansoft.

The layout of the field maps for the various Maxwell versions is so similar that Garfield can only rarely tell which version has been used. As of version\&nbsp;11, the situation is even worse in that the layout of version\&nbsp;9 and version\&nbsp;11 files is identical, but the node numbering sequence is different. It is therefore advisable to systematically specify the format explicitly.

3.7.1.4.1: PARAMETER-EXTRACTOR-2D

To generate your field maps with Maxwell Parameter Extractor 2D, you may wish to follow this recipe:

1. Go through the various steps until "Solve Parameters", taking care (before drawing anything) to adjust in "Draw Cross Section" the "Model Drawing Size" such that it fits exactly the area of your detector - do not leave any empty space around it. Then enter "View Fields" from where you perform the following steps:
2. Click on "calc", select "plane", if the upper area is not empty then click on "clear". Do also a "smooth" and a "push" to ensure the mesh is the same for all maps. Then click on "voltage" and do an ASCII "write" to a file ("write" is in the second set of commands to which you access via "next", to get back to the first set click on "prev"). Maxwell appends the string ".arg" to the file name you enter. This creates a map of the potential.
3. Repeat step 2 with "E_vector" instead of "voltage", choose a file name different from the one used in step\&nbsp;2. This creates a file that contains both Ex and Ey.
4. Depending on the Solver that you use:
   • In "Electrostatic" mode: click again on "calc", select again "plane", do a "clear" if needed. Click on "E_vector", then on "vec_cons", fill in 1\&nbsp;0\&nbsp;0 as vector, click on "execute", click on "Materials", click on "epsilon", ensure that multiplication is set to "yes" and "execute", then click on "scalar_x" and do an ASCII "write" of the result. Choose a file name different from those used in steps\&nbsp;2 and 3. This procedure leads to a file that contains the dielectric constant.
   • If you model you chamber in "DC conduction mode", then apply the same recipe with "epsilon" replaced by "sigma".
5. If you do not wish to compute signals, you are ready at this point. Otherwise, go back to the "Parameter Extractor" main menu, click on "Setup Boundaries/Sources", and select "Define", confirm that you wish to "Modify" and then adjust the voltages of all electrodes such that the electrode that you wish to read out is at 1\&nbsp;V and all other electrodes at 0\&nbsp;V. Then "Exit", confirming that you wish to save the modifications.
6. Go to the "Setup Solution Parameters" in the Parameter Extractor, click on "Capacitance", select "Current" as Starting Mesh, suppress "Adaptive Analysis". This ensures that the field is calculated on the same mesh as the field calculated in point\&nbsp;1.
7. Write out the electric field as described in step 2, choosing a file name different from the names chosen in steps\&nbsp;2, 3 and 4. This generates the weighting field. Repeat from step\&nbsp;5, if you intend to read out more than one electrode.

These steps should lead to a set files with names that end on .arg and that are located in the es.pjt sub-directory of your project.

Be sure to create the E, V, \&epsilon; or \&sigma; and weighting field maps with identical meshes and the E, V and \&epsilon;or \&sigma; maps with identical boundary conditions.

The names of these 4 files should be placed after the FILES keyword of the FIELD-MAP command, the name of the weighting field maps should be preceded by the keyword "WEIGHTING-FIELD" to distinguish it from the regular electric field map. The order is not important. There is no need to specify that the files come from Maxwell Parameter Extractor 2D.

Maxwell documentation at CERN can be found in http://wwwinfo.cern.ch/ce/ae/Maxwell/documentation.html

(Instructions from Pawel Majewski)

3.7.1.4.2: FIELD-SIMULATOR-2D

To generate your field maps with Maxwell\&nbsp;2D Field Simulator, you may like to follow the following recipe:

1. Go through the various steps until "Solve". Then enter "Post Process" for the "nominal problem" where you click on "calc", select "Plane" and, if the upper area is not empty click on "clear".
2. Click on "voltage" and do an ASCII "write" to a file ("write" is in the second set of commands to which you access via "next", to get back to the first set click on "prev"). Choose a file name like "V", Maxwell automatically appends the string ".arg" to the file name you enter. This creates a map of the potential.
3. Repeat step\&nbsp;2 with "E_Vector" instead of "voltage", choose a file name different from the one used in step 2. This creates a file that contains both Ex and Ey.
4. If you wish Garfield to know about the materials present in the chamber, then either:
   • Repeat step\&nbsp;2 with "D_Vector" instead of "voltage", choosing a file name different from those in steps 2 and 3. This creates a file with a field map of D. The dielectric constant is computed by Comparing D and E.
   • Do a "clear", then click on "E_Vector", then on "vec_cons", fill in 1\&nbsp;0\&nbsp;0 as vector, click on "Execute", click on "Materials", click on "epsilon", ensure that multiplication is set to "Yes" and "Execute", then click on "scalar_x" and do an ASCII "write" of the result. Choose a file name different from those used in steps\&nbsp;2 and 3. This procedure creates to a file that contains the dielectric constant.
   • If you model you chamber in "DC conduction" mode, then apply the above recipe with "epsilon" replaced by "sigma".
5. If you do not wish to perform signal calculations, you're ready at this point. Otherwise go back to the "2D Field Simulator" main menu, enter "Setup Boundaries/Sources", confirm that you wish to "Modify" and then adjust the voltages of all electrodes such that the electrode that you wish to read out is at 1\&nbsp;V and all other electrodes at 0\&nbsp;V. Then "Exit", confirming that you wish to save the modifications.
6. Go to the "Setup Solution" in the main menu, select "Options", select "Current" as Starting Mesh, suppress "Adaptive Analysis" and click "OK". Next go to "Solve" in the main menu and select "Nominal Problem". These steps compute the weighting field on the same mesh as the field calculated in point\&nbsp;1.
7. Write out the electric field as described in step\&nbsp;2, choosing a file name different from the names chosen in steps\&nbsp;2, 3 and 4. This generates the weighting field map. Repeat from step\&nbsp;5 if you intend to read more than one electrode.

These steps should lead to a set of files with names that end on .arg and that are located in your project directory.

Be sure to create the E, V, D, \&epsilon; or \&sigma; and weighting field maps with identical meshes and in addition the E, V and D maps with identical boundary conditions.

The names of these 4 files should be placed after the FILES keyword of the FIELD-MAP command, the name of the weighting field maps should be preceded by the keyword "WEIGHTING-FIELD" to distinguish it from the regular electric field map. The order is not important. There is no need to specify that the files come from Maxwell 2D Field Simulator.

Information about using Maxwell at CERN can be found in http://wwwinfo.cern.ch/ce/ae/Maxwell/Maxwell.html

3.7.1.4.3: PARAMETER-EXTRACTOR-3D

When generating your field maps with this program, you may wish to follow this recipe:

1. Go through the various steps until "Solve Parameters", taking care (before drawing anything) to adjust in "Draw Cross Section" the "Model Drawing Size" such that it fits exactly the area of your detector - do not leave any empty space around it. Then enter "View Fields" where you click on "calc", select "space" and, if the upper area is not empty click on "clear".
2. Click on "phi", do a "push" to ensure the mesh is the same for all maps and then "smooth" the potential map. Do an ASCII "write" to a file. Maxwell automatically appends the string ".arg" to the file name you enter, it is therefore sufficient to enter for instance just "V". This creates a map of the potential.
3. Repeat step 2. for "E_vector" and "D_vector", without doing a "push", and writing to files with different names. Creating the D field map is optional.
4. You may also wish to create weighting field maps as described for Maxwell Parameter Extractor 2D.

This procedure should create maps of the electrostatic potential, the E field, the D field and perhaps of a weighting field. The dielectric constants are computed by comparing E and D. These files will be located in the efs3d.pjt sub-directory of your project.

Be sure to create the E, V, D and weighting field maps with identical meshes and the E, V and D maps with identical boundary conditions.

Information about using Maxwell at CERN can be found in http://wwwinfo.cern.ch/ce/ae/Maxwell/Maxwell.html

3.7.1.4.4: FIELD-SIMULATOR-3D

Beware that files produced with Maxwell Version\&nbsp;11 can be read with the interface for earlier versions, and vice-versa, but the results will be incorrect. Be sure therefore to specify the correct Maxwell version on the FIELD-MAP command line.

When you use this program to create your field maps, you have to provide the following to Garfield:

1. The mesh: The mesh is contained in a .hyd and a .pnt file stored in the project directory (and not in an "efs3d.pjt" sub-directory of the project directory). When using the DELETE-BACKGROUND option, the project .shd file is needed in addition. The files have names like "fileset2", "fileset1", "current", "efs3d", "previous" and "initial".
   • If you do not specify a mesh file explicitly, then Garfield will look in the directory of the first field map for mesh files with the above names, starting from "fileset2".

   • To select a mesh manually, you provide the name of the .pnt, .hyd or .shd file (complete file name) and either place this name first in the list of files to be read, or identify it explicitly as containing a mesh by prefixing the MESH keyword.

2. The field maps of V, D and E written out in .reg format. With Maxwell\&nbsp;3D Field Simulator, there is no need to smooth the field maps, as opposed to Maxwell\&nbsp;3D Parameter Extractor.

   The field maps can be created as follows: After having gone through the various steps, in the "Post Process" menu, select "Nominal Problem". From the "Data" menu, select "Calculator". In the "Input" column select the "Qty" menu where you pick "phi". In the "Output" column select "Write\&nbsp;..." and write out the field to a file called, for instance, "V.reg". Repeat the same steps replacing "phi" by "E" and "D".

3. Optionally, you may also provide weighting fields. Weighting fields are electric fields that are obtained by setting the potential of all conductors to 0\&nbsp;V except the read-out conductor which is set to 1\&nbsp;V.

Be sure to create the E, V, D and weighting field maps with identical meshes and the E, V and D maps in addition with identical boundary conditions.

Information about using Maxwell at CERN can be found in http://wwwinfo.cern.ch/ce/ae/Maxwell/Maxwell.html

3.7.1.4.5: MAXWELL-2D-SV

After having worked your way through the various steps from model definition till problem solving, click on "Post\&nbsp;Process\&nbsp;..." and enter "Data/Calculator". Then:

1. Click on "Qty"
2. Select "phi" to create a map of the potential
3. Click on "Write ..."
4. Enter a name for the file (the extension *.reg will be appended automatically to the file name.)

Alternatively, the electric field can be derived from the potential by selecting the COMPUTE-ELECTRIC-FIELD option. Several users have reported problems with the electric field maps as exported by Maxwell and this approach can therefore be recommended.

When using Maxwell SV, you have to feed the following files to Garfield:

• The mesh files preceded by the contents indication MESH. Maxwell SV, contrary to earlier 2D versions of Maxwell, does not insert mesh information in the field maps. Garfield extracts the mesh structure from 2 files: a list of triangles (which has an extension of .tri) that contains pointers to a file with a list of mesh coordinates (extension .pts). Garfield will automatically read these files if they are located in the same directory as the field maps and have a file name of "fileset1" or of "fileset2". You may move these 2 files elsewhere and change their names, provided that they are given the same file name, that the extensions are unchanged and that the 2 files are placed in the same directory. You then also have to inform Garfield of the directory and file name by specifying one (and only one) of these files - the extension doesn't matter since Garfield fills it in itself.
• The model file preceded by the contents indication MODEL. The extension of this file is .sm2 and the file name is usually the same as the project name. Maxwell SV, like some other Ansoft programs, solves the problem in normalised mesh coordinates and the mesh files do not contain information regarding the problem domain. Garfield extracts the dimensions of the problem domain from the model file. The problem domain is set to the square region (-1,-1) to (1,1) in case the model file isn't read.
• The field maps, optionally preceded by a keyword to indicate the contents.
• You may in addition supply weighting fields. Weighting fields are computed as electric fields but the potential of all conductors should be set to 0 except the read-out conductor which is set to 1. Be sure to create the E, V, D and weighting field maps with identical meshes. This is achieved by first solving for E, V and D, then disabling mesh refinements when solving for the weighting fields. The E, V and D maps should in addition have identical boundary conditions.

An axis of rotational symmetry, if any, should be detected automatically and result in the Z-ROTATIONALLY-SYMMETRIC option being switched on.

(Procedure from Pawel Majewski.)

3.7.1.4.6: TOSCA

1. use OPERA version\&nbsp;7.0.
   • create the directory $VFDIR/opera/3d/util
   • copy in this directory the Makefile and the program util.f which can be found in http://consult.cern.ch/writeup/garfield/examples/tosca
   • run in the same directory the command "$VFDIR/install/makeprog $VFDIR"

2. Generate the geometrical mesh with the 3d Opera preprocessor.

3. Click on "MESH" and then choose the "quadrilaters" option.

4. Click again on "MESH" and choose the "Volume\&nbsp;mesh\&nbsp;...\&nbsp;Mesh\&nbsp;*" option.

5. Click on "FILE" and choose the "write node table" option in order to create the "username.table" file that contains the mesh node coordinates.

6. Generate, clicking again on "FILE", the usual username.OP3 file ready to be analysed by TOSCA.

7. Run the Fortran program "util" with the command: $VFDIR/opera/3d/util > "username1.table" and, after pushing the "return" button, typing "username.op3" on the keyboard and pushing "return" again. The file "username1.table" includes now a table that describes each element of the mesh, specifying the nodes that make it up.

8. Run TOSCA.

9. Run the 3d\&nbsp;Opera post-processor. Load the TOSCA result. Click on "FIELDS" and choose the "table of field points" sub-menu. In this sub-menu:
   1. Select "input from file" and give "username.table" (see item\&nbsp;6 above) as input.
   2. Choose an "username2.table" as output according to your taste
   3. Click on "output components options" and define:
      • Component 1 = X
      • Component 2 = Y
      • Component 3 = Z
      • Component 4 = Ex
      • Component 5 = Ey
      • Component 6 = Ez
      • Component 7 = Dx
      • Component 8 = Dy
      • Component 9 = Dz
      • Component 10 = V
   4. Click the "process table" option that will describe, for each mesh node, the value of the electric field and potential.

The files "username1.table" and "username2.table" (see item\&nbsp;6 and 10 above) are now ready for Garfield.

A Garfield input file that uses "username.table" and "username1.table" can be found in http://consult.cern.ch/writeup/garfield/examples/tosca/example

A single Tosca generated map can contain various kinds of data, such as the potential, the electric field and the D field. Since the file contains a description of the data, the contents field should only make clear that the file is not a mesh file. One can therefore set the contents field on the FIELD-MAP command to be any of the contained items.

It is advisable to use the INTERPOLATE-ELECTRIC-FIELD option when using Tosca field maps.

(Recipe from Guido Maria Urciuoli, INFN Gruppo Collegata Sanitá, Viale Regina Elena 299, 00161 Roma, Italia.)

3.7.1.4.7: TOSCA-118

The Tosca file, called a "simulation database" in Tosca-speak, should contain at least the following Tosca "datasets":

• 164: units
• 2412: mesh structure
• 2411: node location
• 2414: potential solution

After the model has been created in the Modeller, create the simulation database with

• 'element type' = quadratic and
• 'surface element type' = curved:

To achieve this, enter at the console:

SOLVERS PROGRAM=&VF_ANALYSISTYPE& -SOLVENOW OPTION=NEW
        ELEMENT=QUADRATIC SURFACE=CURVED FILE='YourFileName.op3';

Model \→ Create Analysis Database...

In the post-processor export the results to an I-DEAS Universal File, where it important is to set BASIS=ELEMENT, i.e. write values at every node of every element:

As a console command:

IDEAS FILE='YourFileName.unv' MODE=CREATE TYPE=REAL
      BASIS=ELEMENT FIELD=SCALAR COMP=V;

Tables \→ SDRC I-DEAS Unv File...

(Recipe provided by Konstantin Klementiev <kklementiev@cells.es>.)

3.7.1.4.8: COMSOL-2D-LINEAR

These elements have only 3 nodes, the potential is linear within each element and the local gradient is constant.

Although such field maps can be read, their use is not recommended. Use instead COMSOL-2D-QUADRATIC.

3.7.1.4.9: COMSOL-2D-QUADRATIC

For the recipe to write such field maps, please refer to COMSOL-3D-QUADRATIC.

Garfield doesn't recognise this format automatically, be sure therefore to specify that your field map is in COMSOL-2D-QUADRATIC format.

You may specify a distance unit for such field maps, centimetres are assumed if no unit is given.

Example:

&CELL
field-map files potential "COMSOLFIELD2D.txt" ...
                weighting-field "COMSOLFIELD2DElectrode1.txt" label s ...
        comsol-2d

&FIELD
plot-field contour v

&SIGNAL
select s
plot-field vector

3.7.1.4.10: COMSOL-3D-LINEAR

These elements have only 4 nodes, the potential is linear within each element and the local gradient is constant.

Although such field maps can be read, their use is not recommended. Use instead COMSOL-3D-QUADRATIC.

3.7.1.4.11: COMSOL-3D-QUADRATIC

Garfield doesn't recognise this format automatically, be sure therefore to specify that your field map is in COMSOL-3D format.

You may specify a distance unit for such field maps, centimetres are assumed if no unit is given.

First, solve your problem in COMSOL. Take care to select 2nd order Lagrange elements. Then export the field map as follows:

1. Go to menu File \&rarr; Export \&rarr; Post-Processing Data
2. Set path/filename to export, e.g. "exported.txt"
3. Choose file format "Nodes, elements, data"
4. Check that under the "Subdomain" tab "Electric Potential" is selected as Expression to export
5. Click "OK" to write the file

To import the file in Garfield:

1. Go to cell section (&CELL).
2. Import the exported file using the FIELD-MAP command, this may take quite some time depending on the size of the map.
3. Garfield does not recognise this format automatically, hence be sure to specify that your field map is in COMSOL-3D format.
4. If you get a warning stating that the number of tetrahedrons exceeds the compilation limit, then recompile Garfield with a larger value for MXMAP. Alternatively, check the quality of the mesh - large field maps frequently result from poorly refined field maps. These not only slow down all calculations performed with them, they also are of poor numeric quality. You may also wish to consider using virtual volumes surrounding tiny electrodes.
5. To save time next time you need the field map, you may wish to write a binary copy using SAVE-FIELD-MAP.

Example:

&CELL
field-map files "exported.txt" comsol-3d
save-field-map "exported.bin"

(Recipe written by Jeremy Janney <JJanneySG@hotmail.com> and Sven Lotze <lotze@physik.rwth-aachen.de>.)

3.7.1.4.12: ANSYS-PLANE-121

ANSYS will occasionally generate degenerate quadrilaterals, which are curved quadratic triangles.

The recipe assumes that the command format is used. Most of the commands cited can of course also be run from the GUI.

1. Clear earlier calculations and enter the pre-processor:

   FINISH
   /CLEAR,START
   /PREP7
   

2. If using the GUI, enter the preferences and ensure that the only discipline selected within the "Electromagnetic" group is "Electric". The equivalent commands are:

   KEYW,PR_ELMAG,1
   KEYW,MAGELC,1
   

   Disable the p-method solution options. This option leads to elements of higher polynomial order, which are a priori preferred, but Garfield does not yet have shape functions for these.

   /PMETH,OFF,1
   

3. Select the quadrilateral as element:

   ET,1,PLANE121
   

   In case your chamber has rotational symmetry around an axis, a non-default element behaviour needs to be selected:

   ET,1,PLANE121   ! Select plane quadrilaterals
   KEYOPT,1,3,1    ! Declare the element to be axisymmetric
   

   In ANSYS, the y-axis acts as axis of rotational symmetry and no part of the model should be located in x\&nbsp;\&lt;\&nbsp;0. When reading the field map with Garfield, you have to declare the symmetry again using X-ROTATIONALLY-SYMMETRIC, Y-ROTATIONALLY-SYMMETRIC or Z-ROTATIONALLY-SYMMETRIC.
4. When defining material properties, be sure that every material has its permittivity set. Choose material numbers starting from 1 and leave no holes in the numbering. Set the permittivity of conductors to a very high value. Set the resistivity of perfect conductors to 0 so as to make them eligible for removal as background (see the DELETE-BACKGROUND option). Try to avoid temperature-dependent properties as these can not be used by Garfield to identify materials. If you need to use them, then do not write out the MPLIST file (see below).

   For instance, to define a perfect conductor (material\&nbsp;1) and a dielectricum (material\&nbsp;2):

   MP, PERX, 1, 1e10 ! Metal
   MP, RSVX, 1, 0.0
   MP, PERX, 2, 4.5  ! Bulk dielectric constant
   

5. Create the model. See any of the numerous ANSYS tutorials for advice. Pay particular particular attention to gluing adjacent areas where necessary (AGLUE command). For instance, to create a conducting strip on the wall of a block of dielectric material:

   ! Define some dimensions, in microns
   halfpitch = 50
   thickbulk = 200
   halfstrip = 20
   thickstrip = 5
   
   BLC4, 0, 0, halfpitch, thickbulk   ! Area 1: dielectricum
   BLC4, 0, 0, halfstrip, thickstrip  ! Area 2: conductor
   ASBA, 1, 2, , , KEEP               ! Area 1 becomes area 3
   
   AGLUE, ALL                         ! Glue everything
   

6. Assign material properties with the AATT command:

   ASEL, S, , , 3             ! Select the dielectricum
   AATT, 2                    ! Properties of material 2
   ASEL, S, , , 2             ! Select the conductor
   AATT, 1                    ! Properties of material 1
   

7. Set boundary conditions:

   ASEL, S, , , 2             ! Select the metal
   LSLA, S                    ! Select all its border lines
   DL, ALL, 2, VOLT, 1000     ! Set the borders to 1000 V
   
   ASEL, S, , , 3             ! Select the dielectricum
   LSLA, S                    ! Select all its border lines
   LSEL, R, LOC, Y, thickbulk ! Sub-select lines at y=thickbulk
   DL, ALL, 3, VOLT, 0        ! Set this line to 0 V
   
   ASEL, S, , , 3
   LSLA, S
   LSEL, R, LOC, X, 0         ! Select the lines at x=0
   DL, ALL, 3, SYMM           ! Impose a symmetry condition
   ASEL, S, , , 3
   LSLA, S
   LSEL, R, LOC, X, halfpitch ! Idem for y=halfpitch
   DL, ALL, 3, SYMM
   

8. Mesh the problem. This can for instance be done using free meshing:

   LSEL,ALL
   ASEL, ALL
   MSHKEY,0
   SMRT, 3
   AMESH, 2,3
   

   It is not always necessary to mesh the metal parts of the device. Then solve the problem:

   /SOLU
   SOLVE
   FINISH
   

   Optionally visualise the solution:

   /POST1
   /EFACET,1
   PLNSOL, VOLT,, 0
   

9. Write the solution to files. The potentials at the nodes are written to a file with the PRNSOL command. In the example below, the file name is chosen to be "PRNSOL.lis" but feel free to use another name. It is the name of this file which must follow the FILES keyword.

   /OUTPUT, PRNSOL, lis
   PRNSOL
   /OUTPUT
   

   There is no need to write the electric field to a file since the COMPUTE-ELECTRIC-FIELD option is implied when using ANSYS.

   The PRNSOL file contains the potentials at the nodes. When interpolating between nodes, Garfield needs to know where each of these nodes is located in space. This information is contained in the output of the NLIST command, which should be written to a file called "NLIST.lis". Note the COORD option - without this option, the file would contain additional information which is not used in Garfield, at the price of reduced precision in the node coordinates. Garfield can read files in either format - but the COORD option is recommended.

   /OUTPUT, NLIST, lis
   NLIST,,,,COORD
   /OUTPUT
   

   Garfield also needs to know how the nodes are tied into elements. This structure is shown by the ELIST command, of which the output has to be written to a file called "ELIST.lis":

   /OUTPUT, ELIST, lis
   ELIST
   /OUTPUT
   

   Optionally, you may transmit the dielectric constants (permittivities) and the electric resistivities to Garfield. Only write this file if your material properties do not have a temperature dependence. The commands for writing the "MPLIST.lis" file are as follows:

   /OUTPUT, MPLIST, lis
   MPLIST
   /OUTPUT
   

   If you produce the field maps on operating systems like Windows, control-M will be appended to each line. These need to be removed before the field maps can be read with Garfield.
10. Make Garfield read the field maps. You only need to specify the potential map. The remaining files, ELIST.lis, NLIST.lis and MPLIST.lis are searched for in the same directory. An example follows.

    Since ANSYS allows the user to use any consistent system of units, the real size of the device can not be found in the field map files. The user therefore has to specify the distance UNIT.

    &CELL
    field-map files "../scratch0/PRNSOL.lis" ansys-plane-121 ...
       x-mirror-periodic unit micron
    
    &FIELD
    area -0.0100 0 0.0100 0.0200
    plot-field cont v
    

In order to compute signals, Garfield needs weighting fields. Refer to the ANSYS-solid-123 recipe.

3.7.1.4.13: ANSYS-SOLID-123

The recipe assumes that the command format is used. Most of the commands cited can of course also be run from the GUI.

1. Clear earlier calculations and enter the pre-processor:

   FINISH
   /CLEAR,START
   /PREP7
   

2. If using the GUI, enter the preferences and ensure that the only discipline selected is "Electric" within "Electromagnetic":

   KEYW,PR_ELMAG,1
   KEYW,MAGELC,1
   

   Disable the p-method solution options. This option leads to elements of higher polynomial order, which are a priori preferred, but Garfield does not yet have shape functions for these.

   /PMETH,OFF,1
   

3. Select the 2nd\&nbsp;order tetrahedron as element:

   ET,1,SOLID123
   

4. When defining material properties, be sure that every material has its permittivity set. Choose material numbers starting from 1 and leave no holes in the numbering. Set the permittivity of conductors to a very high value. Set the resistivity of perfect conductors to 0 so as to make them eligible for removal as background (see the DELETE-BACKGROUND option). Try to avoid temperature-dependent properties as these can not be used by Garfield to identify materials. If you need to use them, then do not write out the MPLIST file (see below).

   For instance, to define a perfect conductor (material\&nbsp;1), a gas (material 2) and a dielectricum (material\&nbsp;3):

   MP,PERX,1,1e10  ! Metal
   MP,RSVX,1,0     !
   MP,PERX,2,1     ! Gas
   MP,PERX,3,4.5   ! Dielectricum
   

5. Create the model. See any of the numerous ANSYS tutorials for advice. Pay particular particular attention to gluing adjacent volumes where necessary (VGLUE command).
6. Assign material properties with the VATT command.
7. Set boundary conditions. To set for instance the voltage on all surface areas of volume\&nbsp;2 (assumed to be a conductor) to 100\&nbsp;V:

   VSEL, S, VOLU, , 2 ! Select volume 2
   ASLV, S            ! Select all areas belonging to the selected volumes
   DA, ALL, VOLT, 100 ! Set a voltage boundary on all selected areas
   

   Similarly, a symmetry boundary on all selected areas can be set with the command:

   DA, ALL, SYMM
   

8. Mesh the problem. This can be done in numerous manners. For instance, to have a fine mesh, using free meshing, in volumes 1, 2, 3 and 15:

   SMRT, 2
   MSHKEY,0
   VMESH, 1, 3
   VMESH, 15
   

   It is not always necessary to mesh the metal parts of the device. Then solve the problem:

   /SOLU
   SOLVE
   

   Optionally visualise the solution:

   /POST1
   /EFACET,1
   PLNSOL, VOLT,, 0
   

9. Write the solution to files. The potentials at the nodes are written to a file with the PRNSOL command. In the example below, the file name is chosen to be "PRNSOL.lis" but feel free to use another name. It is the name of this file which must follow the FILES keyword.

   /OUTPUT, PRNSOL, lis
   PRNSOL
   /OUTPUT
   

   There is no need to write the electric field to a file since the COMPUTE-ELECTRIC-FIELD option is implied when using ANSYS.

   The PRNSOL file contains the potentials at the nodes. When interpolating between nodes, Garfield needs to know where each of these nodes is located in space. This information is contained in the output of the NLIST command, which should be written to a file called "NLIST.lis". Note the COORD option - without this option, the file would contain additional information which is not used in Garfield, at the price of reduced precision in the node coordinates. Garfield can read files in either format - but the COORD option is recommended.

   /OUTPUT, NLIST, lis
   NLIST,,,,COORD
   /OUTPUT
   

   Garfield also needs to know how the nodes are tied into elements. This structure is shown by the ELIST command, of which the output has to be written to a file called "ELIST.lis":

   /OUTPUT, ELIST, lis
   ELIST
   /OUTPUT
   

   Optionally, you may transmit the dielectric constants (permittivities) and the electric resistivities to Garfield. Only write this file if your material properties do not have a temperature dependence. The commands for writing the "MPLIST.lis" file are as follows:

   /OUTPUT, MPLIST, lis
   MPLIST
   /OUTPUT
   

   If you produce the field maps on operating systems like Windows, control-M will be appended to each line. These need to be removed before the field maps can be read with Garfield.
10. Make Garfield read the field maps. You only need to specify the potential map. The remaining files, ELIST.lis, NLIST.lis and MPLIST.lis are searched for in the same directory. An example follows.

    Since ANSYS allows the user to use any consistent system of units, the real size of the device can not be found in the field map files. The user therefore has to specify the distance UNIT.

    field-map files "PRNSOL.lis" units=mm ansys-solid-123
    

In order to compute signals, Garfield needs weighting fields. These are obtained by setting the read-out electrodes to a potential of\&nbsp;1 and all other electrodes to a potential of\&nbsp;0.

Garfield requires the weighting fields and the main field map to share one and the same mesh. To achieve this, follow the above recipe until the end, then clear the existing loads (LSCLEAR), apply new loads and solve without meshing again. This is illustrated in the following example of 3\&nbsp;strips:

FINISH
/CLEAR,START
/PREP7
! No polynomial elements
/PMETH,OFF,1
 
! Set electric preferences
KEYW,PR_ELMAG,1
KEYW,MAGELC,1
 
! Select element
ET,1,SOLID123
 
! Material properties
MP,PERX,1,1e10  ! Metal
MP,RSVX,1,0.0   !
MP,PERX,2,1.0   ! Gas
MP,PERX,3,4.0   ! Permittivity of FR4
 
! Construct the structure
metal = 0.2
gas = 2
sub = -1
BLOCK, -10, -5, -10, 10,     0, metal ! 1: Wide side strip
BLOCK,  -2, -4, -10, 10,     0, metal ! 2: First signal
BLOCK,  -1,  1, -10, 10,     0, metal ! 3: 2nd signal
BLOCK,   2,  4, -10, 10,     0, metal ! 4: 3rd signal
BLOCK,   5, 10, -10, 10,     0, metal ! 5: Wide side strip
BLOCK, -10, 10, -10, 10,   sub,     0 ! 6: Substrate
BLOCK, -10, 10, -10, 10,     0,   gas ! 7: Gas
 
! Subtract the strips from the gas
VSBV,  7, 1, , , KEEP   ! 7 \→ 8
VSBV,  8, 2, , , KEEP   ! 8 \→ 7
VSBV,  7, 3, , , KEEP   ! 7 \→ 8
VSBV,  8, 4, , , KEEP   ! 8 \→ 7
VSBV,  7, 5, , , KEEP   ! 7 \→ 8
 
! Glue everything together 1 = left wide, 2, 3, 4, 5 = wide, 7 = sub, 8 = gas
VGLUE, ALL
 
! Assign material attributes
VSEL, S, VOLU, , 1, 5 ! Metal strips
VATT, 1, ,1
VSEL, S, VOLU, , 7    ! Gas volume
VATT, 3, ,1
VSEL, S, VOLU, , 8    ! Substrate
VATT, 2, ,1
 
! Voltage boundary conditions on the metal
VSEL, S, VOLU, , 1, 5 ! All strips at ground
ASLV, S
DA, ALL, VOLT, 0
ASEL, S, LOC, Z, gas  ! Drift electrode
DA, ALL, VOLT, -1000
ASEL, S, LOC, Z, sub  ! Back plane
DA, ALL, VOLT, 0
 
! Meshing options
VSEL, S, VOLU, , 8    ! Only mesh the gas
ASLV, S
 
MSHKEY,0
SMRT, 4
VMESH, 1,8
 
! Solve the field
/SOLU
SOLVE
 
! Write the solution
/POST1
/OUTPUT, field, lis
PRNSOL
/OUTPUT
 
! Change to weighting field boundary conditions for first narrow strip
/SOLU
LSCLEAR,ALL
 
VSEL, S, VOLU, , 1
VSEL, A, VOLU, , 3, 5
ASLV, S
DA, ALL, VOLT, 0
 
VSEL, S, VOLU, , 2
ASLV, S
DA, ALL, VOLT, 1
 
ASEL, S, LOC, Z, gas
DA, ALL, VOLT, 0
ASEL, S, LOC, Z, sub
DA, ALL, VOLT, 0
 
! Meshing options
VSEL, S, VOLU, , 1, 8
ASLV, S
 
! Solve the field
SOLVE
 
! Write the solution
/POST1
/OUTPUT, weight1, lis
PRNSOL
/OUTPUT
 
! Change to weighting field boundary conditions for 2nd narrow strip
/SOLU
LSCLEAR,ALL
 
VSEL, S, VOLU, , 1, 2
VSEL, A, VOLU, , 4, 5
ASLV, S
DA, ALL, VOLT, 0
 
VSEL, S, VOLU, , 3
ASLV, S
DA, ALL, VOLT, 1
 
ASEL, S, LOC, Z, gas
DA, ALL, VOLT, 0
ASEL, S, LOC, Z, sub
DA, ALL, VOLT, 0
 
! Meshing options
VSEL, S, VOLU, , 1, 8
ASLV, S
 
! Solve the field
SOLVE
 
! Write the solution
/POST1
/OUTPUT, weight2, lis
PRNSOL
/OUTPUT
 
! Change to weighting field boundary conditions for last narrow strip
/SOLU
LSCLEAR,ALL
 
VSEL, S, VOLU, , 1, 3
VSEL, A, VOLU, , 5
ASLV, S
DA, ALL, VOLT, 0
 
VSEL, S, VOLU, , 4
ASLV, S
DA, ALL, VOLT, 1
 
ASEL, S, LOC, Z, gas
DA, ALL, VOLT, 0
ASEL, S, LOC, Z, sub
DA, ALL, VOLT, 0
 
! Meshing options
VSEL, S, VOLU, , 1, 8
ASLV, S
 
! Solve the field
SOLVE
 
! Write the solution
/POST1
/OUTPUT, weight3, lis
PRNSOL
/OUTPUT
 
! Write the mesh to files
/OUTPUT, NLIST, lis
NLIST,,,,COORD
/OUTPUT
 
/OUTPUT, ELIST, lis
ELIST
/OUTPUT
 
/OUTPUT, MPLIST, lis
MPLIST
/OUTPUT
 
! Show the solution
/EFACET,1
PLNSOL, VOLT,, 0

After processing this, the following files should have been created:

• field.lis: the main field map with ordinary potentials,
• weight1.lis, weight2.lis, weight3.lis: weighting fields for each of the 3 read-out strips,
• NLIST.lis: the list of node coordinates,
• MPLIST.lis: the material properties,
• ELIST.lis: the mesh structure.

These files can be processed in Garfield with the following commands:

&CELL
Global bin `strips.bin`
If exist(bin) Then                // Read binary if it exists
   read-field-map {bin}
Else
   field-map files potential "~/scratch0/field.lis" ...
                   weighting-field "~/scratch0/weight1.lis" label a ...
                   weighting-field "~/scratch0/weight2.lis" label b ...
                   weighting-field "~/scratch0/weight3.lis" label c ...
             units=cm ...
             ansys-solid-123
   save-field-map {bin}           // Otherwise, create a binary
Endif
 
&GAS
arg-50-eth-50                     // For demonstration only ...
 
&SIGNAL
area -5 -10 -2  5 10 8 x-z
window 0 0.0005                   // Sample signals every 0.5 nsec
select a b c                      // Read out all electrodes
 
grid 50                           // Improve granularity
plot-field vect ewx, ewy, ewz     // Plot the weighting fields
 
Call plot_drift_area
Call drift_electron_3(-2, 0, 1.8) // Drift one electron
Call plot_drift_line
Call add_signals
Call plot_end
 
plot-signals                      // Show signals

3.7.1.4.14: QUICKFIELD

Please refer to http://www.quickfield.com/demo/manual.pdf

3.7.1.4.15: MAXWELL-11

The recipe for making such field maps is similar to that for earlier versions like Field-Simulator-3D, with the exception that the solids file (with extension .shd) will be called "fields.shd", independent of the mesh iteration and it will be located in a different directory.

Beware that files produced with Maxwell Version\&nbsp;11 can be read with the interface for earlier versions, and vice-versa, but the results will be incorrect. Be sure therefore to specify the correct Maxwell version on the FIELD-MAP command line.

Use of the DELETE-BACKGROUND option is mandatory with this format.

3.7.2: DRIFT-MEDIUM

There are 3 ways to select the drift medium:

• via an integer: this is interpreted as a sequence number in the sorted list (from small to large) of dielectric constants or the conductivities;
• via a real: this is interpreted as a dielectric constant divided by \&epsilon;\<SUB\>0\</SUB\> (i.e. a gas typically has a value close to 1), or a conductivity (a gas usually does not conduct and has a conductivity close to 0); the list of material constants present in the field map is searched for the nearest match;
• via a keyword such as SMALLEST.

Beware: DRIFT-MEDIUM\&nbsp;3 is not the same as DRIFT-MEDIUM\&nbsp;3.0\&nbsp;! In the first case, the medium with the 3rd dielectric constant or the 3rd conductivity will be selected. In the second case, the medium with the dielectric constant or the conductivity closest to 3 will be taken.

When using the DC conduction mode, it may be more natural to use the keywords SMALLEST-SIGMA, SECOND-SMALLEST-SIGMA, SECOND-LARGEST-SIGMA and LARGEST-SIGMA which are treated as synonyms of the keywords listed in the command description.

[By default, the medium with the lowest dielectric constant or the lowest conductivity is assumed to be the drift medium.]

3.7.3: RESET

3.7.4: NOT-X-PERIODIC

[This is the default.]

3.7.5: X-PERIODIC

The length of one period is taken to be the maximum extent in x of the field map.

A cell can not be both X-PERIODIC and X-MIRROR-PERIODIC, but can be X-AXIALLY-PERIODIC in addition to being translation periodic in the x-direction.

[By default, a field map is not assumed to be periodic.]

3.7.6: X-MIRROR-PERIODIC

A cell can not be both X-PERIODIC and X-MIRROR-PERIODIC, but can be X-AXIALLY-PERIODIC in addition to being translation periodic in the x-direction.

[By default, a field map is not assumed to be periodic.]

3.7.7: X-AXIALLY-PERIODIC

The length of one period is deduced from the field map, and is therefore not specified on the FIELD-MAP statement.

The symmetry axis must pass through y=z=0.

A cell can not be both X-PERIODIC and X-MIRROR-PERIODIC, but can be X-AXIALLY-PERIODIC in addition to being translation periodic in the x-direction.

[By default, a field map is not assumed to be periodic.]

3.7.8: X-ROTATIONALLY-SYMMETRIC

The field map has to be 2-dimensional. Elements must be used that are suitable for rotational symmetry. Currently, all interfaced finite element programs use the second field map coordinate axis, which we refer to as height, h, as axis of rotational symmetry. We call the first coordinate axis the radius, r. The field map must not contain any element or part of element at r\&nbsp;\&lt;\&nbsp;0.

The way the finite element program is informed about the rotational symmetry varies with the programs - consult the documentation.

The above is common for all 3 rotational symmetries. The difference is in the way the (r,h) field-map coordinates are computed from the chamber (x,y,z) coordinates. When using X-ROTATIONALLY-SYMMETRIC, the assignment is:

r = \√(y\² + z\²)
h = x

A chamber can have only one rotational symmetry at the time.

[By default, a field map is not assumed to be periodic.]

3.7.9: NOT-Y-PERIODIC

[This is the default.]

3.7.10: Y-PERIODIC

The length of one period is taken to be the maximum extent in y of the field map.

A cell can not be both Y-PERIODIC and Y-MIRROR-PERIODIC, but can be Y-AXIALLY-PERIODIC in addition to being translation periodic in the y-direction.

[By default, a field map is not assumed to be periodic.]

3.7.11: Y-MIRROR-PERIODIC

A cell can not be both Y-PERIODIC and Y-MIRROR-PERIODIC, but can be Y-AXIALLY-PERIODIC in addition to being translation periodic in the y-direction.

[By default, a field map is not assumed to be periodic.]

3.7.12: Y-AXIALLY-PERIODIC

The length of one period is deduced from the field map, and is therefore not specified on the FIELD-MAP statement.

The symmetry axis must pass through x=z=0.

A cell can not be both Y-PERIODIC and Y-MIRROR-PERIODIC, but can be Y-AXIALLY-PERIODIC in addition to being translation periodic in the y-direction.

[By default, a field map is not assumed to be periodic.]

3.7.13: Y-ROTATIONALLY-SYMMETRIC

The field map has to be 2-dimensional. Elements must be used that are suitable for rotational symmetry. Currently, all interfaced finite element programs use the second field map coordinate axis, which we refer to as height, h, as axis of rotational symmetry. We call the first coordinate axis the radius, r. The field map must not contain any element or part of element at r\&nbsp;\&lt;\&nbsp;0.

The way the finite element program is informed about the rotational symmetry varies with the programs - consult the documentation.

The above is common for all 3 rotational symmetries. The difference is in the way the (r,h) field-map coordinates are computed from the chamber (x,y,z) coordinates. When using Y-ROTATIONALLY-SYMMETRIC, the assignment is:

r = \√(x\² + z\²)
h = y

A chamber can have only one rotational symmetry at the time.

[By default, a field map is not assumed to be periodic.]

3.7.14: NOT-Z-PERIODIC

[This is the default.]

3.7.15: Z-PERIODIC

The length of one period is taken to be the maximum extent in z of the field map.

A cell can not be both Z-PERIODIC and Z-MIRROR-PERIODIC, but can be Z-AXIALLY-PERIODIC in addition to being translation periodic in the z-direction.

[By default, a field map is not assumed to be periodic.]

3.7.16: Z-MIRROR-PERIODIC

A cell can not be both Z-PERIODIC and Z-MIRROR-PERIODIC, but can be Z-AXIALLY-PERIODIC in addition to being translation periodic in the z-direction.

[By default, a field map is not assumed to be periodic.]

3.7.17: Z-AXIALLY-PERIODIC

The length of one period is deduced from the field map, and is therefore not specified on the FIELD-MAP statement.

The symmetry axis must pass through x=y=0.

A cell can not be both Z-PERIODIC and Z-MIRROR-PERIODIC, but can be Z-AXIALLY-PERIODIC in addition to being translation periodic in the z-direction.

[By default, a field map is not assumed to be periodic.]

3.7.18: Z-ROTATIONALLY-SYMMETRIC

The field map has to be 2-dimensional. Elements must be used that are suitable for rotational symmetry. Currently, all interfaced finite element programs use the second field map coordinate axis, which we refer to as height, h, as axis of rotational symmetry. We call the first coordinate axis the radius, r. The field map must not contain any element or part of element at r\&nbsp;\&lt;\&nbsp;0.

The way the finite element program is informed about the rotational symmetry varies with the programs - consult the documentation.

The above is common for all 3 rotational symmetries. The difference is in the way the (r,h) field-map coordinates are computed from the chamber (x,y,z) coordinates. When using Z-ROTATIONALLY-SYMMETRIC, the assignment is:

r = \√(x\² + y\²)
h = z

A chamber can have only one rotational symmetry at the time.

[By default, a field map is not assumed to be periodic.]

3.7.19: LINEAR

This method can be applied to all field maps.

[By default, the highest order method permitted by the field map will be used.]

3.7.20: QUADRATIC

This method can only be applied to field maps with additional nodes halfway the vertices. This information is present in for instance all Maxwell field maps.

[By default, the highest order method permitted by the field map will be used.]

3.7.21: CUBIC

This method can only be applied to field maps with additional nodes at 1 third and at 2 thirds between the vertices. There are currently no field map formats with which this interpolation order can be used.

[By default, the highest order method permitted by the field map will be used.]

3.7.22: INTERPOLATE-ELECTRIC-FIELD

This interpolation is meaningful only if the finite element program outputs, for a single node, as many electric field vectors as there are elements to which the node belongs. The reason for this is that, contrary to the potential, the electric field is as a rule discontinuous across element boundaries. This discontinuity exists even if \&epsilon; is the same on both sides. Many finite element programs output only one electric field vector per node. When using these, COMPUTE-ELECTRIC-FIELD should be selected.

This option is currently only active for hexahedral field maps. It is automatically set for several field map formats, such as those produced by Ansoft programs..

[This option is default.]

3.7.23: COMPUTE-ELECTRIC-FIELD

For elements with use isoparametric coordinates, which is nearly always the case, this calculation entails little or no overhead since the Jacobian is reused from the iterative calculation of the local coordinates.

These derivatives are reliable also in case the nodes happen to lie on an interface between materials of different \&epsilon;s.

This option is automatically switched on when using ANSYS-solid-123, ANSYS-plane-121 and several other finite element programs.

[This option is not default.]

3.7.24: DELETE-BACKGROUND

Option active with Maxwell Field Simulator 3D and ANSYS:

• Maxwell: This option relies on the .shd project file. This file is produced by Maxwell as part of its regular output. In newer versions, it is sometimes written to a different directory from the mesh files. Garfield only looks for this file in the directory of the mesh files and you may therefore have to copy the file.
• ANSYS: Elements are eliminated if the resistivity of the material is strictly equal to 0. The resistivity is obtained from an MPLIST file stored in the same directory as the field map. No elements are deleted if no such file is found. Temperature-dependent resistivities are not processed.

Note: this option is implicit with the MAXWELL-11 format.

[This option is on by default.]

3.7.25: Z-RANGE

This argument is ignored if the field map is 3-dimensional.

[By default, the cell is assumed to go from -50\&nbsp;cm to +50\&nbsp;cm in the z-direction.]

3.7.26: OFFSET

By default, Garfield uses the coordinate system from the finite element program. As a rule, this doesn't lead to limitations.

However, in case overlays an analytic field with a finite element field, it may happen that the fields need to be aligned. Such an alignment can be obtained with the OFFSET option.

If you specify an offset of (xoff,yoff,zoff), then Garfield will interpolate the field map at (x-xoff,y-yoff,z-zoff) when it needs a field at (x,y,z).

All 3\&nbsp;coordinates should be specified, even if the field map is 2-dimensional.

[By default, the 3 offsets are set to 0. The offsets are saved with the binary field maps.]

3.7.27: UNIT

• MICROMETRE or MICRON or MUM
• MILLIMETRE or MM
• CENTIMETRE or CM
• METRE or M

[By default, the centimetre is assumed as length unit.]

3.7.28: PLOT-MAP

Materials are distinguished by their dielectric constant or their conductivity. A map of either of these must therefore be available for this option to have effect. Maps of the dielectric constant an the conductivity can be supplied as such. A map of the dielectric constant will automatically be computed also if maps of both E and B are present.

The material with the smallest dielectric constant is shown with representation MATERIAL-1. The medium with the next highest dielectric constant with MATERIAL-2 etc. The drift medium is never shown.

Elements of a 2D field map are only shown in X-Y views and in CUT views at a constant z. The cross sections of the viewing plane with the elements of a 3D field map are shown in X-Y, X-Z, Y-Z and CUT views, but not in 3D views.

Field maps do not usually cover areas filled with conducting material since there is no field inside. To visualise these, one has to enter them manually with the SOLIDS command. SOLIDS doesn't interfere with PLOT-MAP.

This option can also be switched on and off with the PLOT-MAP option of the AREA command.

[By default, the map is shown.]

3.7.29: HISTOGRAM-MAP

Elements with large aspect ratios can be a sign that the mesh is of poor quality. One should then consider using the so-called virtual-volumes technique to constrain the mesh elements.

Elements with a very large volume or surface are likely to cause problems when transporting particles since the finite element method only guarantees continuity of the potential, not of the electric field. With large elements, the discontinuity across element boundaries is likely to be large.

Switching on this option further enables checks on the elements to be carried out, in particular a search for irregular element degeneracy.

[These histograms are not made by default.]

Section 3.8: GET

This command is executed immediately and you may - with caution - replace some of the elements of the description after issuing the command.

Format:

GET file [member]

Examples:

get "~rjd/Garfield/Test/cell.dat"
get 'disk$zp:[veenhof.garfield]cell'

The first example is typical for a Unix system, note the use of double quotes to preserve the case. The second example, for Vax, will read the first member of type CELL from the library with file name "CELL.DAT". The extension .DAT is the default setting of the DEFAULT command, the upper case is the result of using single quotes. Libraries may contain members of other types - but only members of type CELL will be considered by GET.

3.8.1: file

3.8.2: member

Section 3.9: GRAVITY

The 3 arguments form a vector that indicates the direction in which gravity pulls on the wire. Only the direction of the vector is used, not its normalisation.

The default setting is (0,0,1) i.e. gravity works along the wires.

Format:

GRAVITY  x y z

Example:

gravity  0 0 1

This makes the wires run vertical, the default. In this situation, gravity does not produce a wire sag.

Section 3.10: NEBEM

Format:

NEBEM [ANGULAR-TOLERANCE eps_angle] ...
      [DISTANCE-TOLERANCE eps_distance] ...
      [LU-INVERSION | SVD-INVERSION] ...
      [MAXIMUM-ELEMENTS max] ...
      [MINIMUM-ELEMENTS min] ...
      [NEW-MODEL | REUSE-MODEL ] ...
      [NOKEEP-INVERTED-MATRIX | KEEP-INVERTED-MATRIX] ...
      [PERIODIC-COPIES copies] ...
      [QUALITY-THRESHOLD qthr] ...
      [SIZE-THRESHOLD sthr] ...
      [TARGET-ELEMENT-SIZE target] ...
      [X-PERIODIC-COPIES copies] ...
      [Y-PERIODIC-COPIES copies] ...
      [Z-PERIODIC-COPIES copies]

Example:

nebem min-elem 2 max-elem 10 target 0.1

3.10.1: ANGULAR-TOLERANCE

[Default value: 10^-6 radian.]

3.10.2: DISTANCE-TOLERANCE

Numerous warnings and error messages from the PLAOVL procedure are an indication that this parameter has an inappropriate value.

[Default value: 10^-6 cm.]

3.10.3: LU-INVERSION

[The is default.]

3.10.4: SVD-INVERSION

This technique is superior where the charges on several panels have nearly identical effects. This seems to happen in cylindrical structures. The differences are marginal in box-like layouts.

SVD is substantially slower than LU. E.g. for a matrix size of 4000, SVD takes nearly ten times more time than LU. The difference is significant only for structures with several 1000 or more elements.

[The default is LU-INVERSION.]

3.10.5: MAXIMUM-ELEMENTS

Largest number of elements produced along either axis of a single primitive.

There is no upper limit but CPU time consumption and memory requirements rise faster than linear with the number of elements in the model. If the minimum exceeds the maximum, then the values will be interchanged.

[Default: 10]

3.10.6: MINIMUM-ELEMENTS

Smallest number of elements produced along either axis of a single primitive.

The smallest value allowed is 1. If the minimum exceeds the maximum, then the values will be interchanged.

[Default: 1]

3.10.7: NEW-MODEL

Instructs neBEM to obtain the geometric and potential data from Garfield, to calculate the influence matrix and to solve the capacitance equation.

[This is default]

3.10.8: REUSE-MODEL

Instructs neBEM to obtain the geometric and potential data from Garfield, but to recover the influence matrix and the element charges from files that have been written during an earlier run. The user must ensure that the geometry, influence matrix and charges are coherent. This means in practice that the calculations must be run in the same directory as an earlier run with the NEW-MODEL flag in effect, with identical boundary conditions.

There is no option or command to request storing the model: neBEM always stores the model.

If the inverted influence matrix (capacitance matrix) has been stored, in response to specifying the KEEP-INVERTED-MATRIX option.then it too will be retrieved when re-specifying this option.

[This is not default.]

3.10.9: KEEP-INVERTED-MATRIX

This matrix is currently needed only for the calculation of weighting fields.

This matrix is large.

The flag must be set both during the initial run that computes and writes the element charges, and during the runs in which these charges are retrieved by means of the REUSE-MODEL option.

[By default, the inverted matrix is neither stored nor retrieved.]

3.10.10: PERIODIC-COPIES

neBEM currently does not have explicit periodic Green's functions for periodic configurations. It approximates these with the sum of a series of periodic copies of the non-periodic Green's function. The series runs from \<CODE\>-copies\</CODE\> to \<CODE\>copies\</CODE\>.

Since the Green's function are expensive to calculate, it is advisable to choose a low number of copies. In 3 dimensions, the series converges rapidly.

neBEM allows this parameter to be set individually for each primitive, but the Garfield interface stores only one value, common to all primitives.

The number of periodic copies can be set indivually along each axis, or collectively for all 3 axes.

[Default: 5, which corresponds to having in all 11 copies.]

3.10.11: QUALITY-THRESHOLD

This parameter currently only leads to reduction of the overall size of sharp-angled triangles, it does not yet stop them from being created.

The minimum quality must be larger than 1.

[Default setting: 150.]

3.10.12: SIZE-THRESHOLD

This parameter has currently not effect. A similar effect can be obtained by setting discretisation sizes on the solids and also by using the TARGET-ELEMENT-SIZE, MINIMUM-ELEMENTS and MAXIMUM-ELEMENTS parameters.

[Default setting: 0.001]

3.10.13: TARGET-ELEMENT-SIZE

Target linear size of the elements, measured along their edges, produced by neBEM's discretisation process. The element sizes are if needed increased or decreased to respect the MINIMUM-ELEMENTS and MAXIMUM-ELEMENTS parameters.

If specified before the SOLIDS command is issued, then the value will be used as default for all solids that are entered. The value can be overridden on any individual solid.

If specified after the SOLIDS command, then the value applies only to those faces for which the discretisation length has been is specified as "automatic".

[Default: 50 micron.]

3.10.14: X-PERIODIC-COPIES

neBEM currently does not have explicit periodic Green's functions for periodic configurations. It approximates these with the sum of a series of periodic copies of the non-periodic Green's function. The series runs from \<CODE\>-copies\</CODE\> to \<CODE\>copies\</CODE\>.

Since the Green's function are expensive to calculate, it is advisable to choose a low number of copies. In 3 dimensions, the series converges rapidly.

neBEM allows this parameter to be set individually for each primitive, but the Garfield interface stores only one value, common to all primitives.

The number of periodic copies can be set indivually along each axis, or collectively for all 3 axes.

[Default: 5, which corresponds to having in all 11 copies.]

3.10.15: Y-PERIODIC-COPIES

neBEM currently does not have explicit periodic Green's functions for periodic configurations. It approximates these with the sum of a series of periodic copies of the non-periodic Green's function. The series runs from \<CODE\>-copies\</CODE\> to \<CODE\>copies\</CODE\>.

Since the Green's function are expensive to calculate, it is advisable to choose a low number of copies. In 3 dimensions, the series converges rapidly.

neBEM allows this parameter to be set individually for each primitive, but the Garfield interface stores only one value, common to all primitives.

The number of periodic copies can be set indivually along each axis, or collectively for all 3 axes.

[Default: 5, which corresponds to having in all 11 copies.]

3.10.16: Z-PERIODIC-COPIES

neBEM currently does not have explicit periodic Green's functions for periodic configurations. It approximates these with the sum of a series of periodic copies of the non-periodic Green's function. The series runs from \<CODE\>-copies\</CODE\> to \<CODE\>copies\</CODE\>.

Since the Green's function are expensive to calculate, it is advisable to choose a low number of copies. In 3 dimensions, the series converges rapidly.

neBEM allows this parameter to be set individually for each primitive, but the Garfield interface stores only one value, common to all primitives.

The number of periodic copies can be set indivually along each axis, or collectively for all 3 axes.

[Default: 5, which corresponds to having in all 11 copies.]

Section 3.11: OPTIONS

Format:

OPTIONS [NOLAYOUT | LAYOUT] ...
        [NOCELL-PRINT | CELL-PRINT] ...
        [NOTISOMETRIC | ISOMETRIC] ...
        [NOWIRE-MARKERS | WIRE-MARKERS] ...
        [NOCHARGE-CHECK | CHARGE-CHECK] ...
        [NODIPOLE-TERMS | DIPOLE-TERMS]

Example:

OPT C-PR

Requests a summary of the elements present in the cell.

3.11.1: CELL-PRINT

The same listing can be obtained in the optimisation section using the PRINT-CELL command.

[This option is initially off but its setting is remembered from one cell section to the next.]

3.11.2: DIPOLE-TERMS

Dipole terms are significant for thick wires that are nearly at the ambient potential, such as gate wires in TPCs. This can be investigated with the MULTIPOLE-MOMENTS command.

Currently, dipole terms are available only for potential types A, B1X, B1Y, B2X and B2Y. Contact the author if you need dipole terms for other potentials.

Example: A wire with no net charge is located half-way between 2 conduction planes. With the DIPOLE-TERMS option switched off (left), the wire has no influence on the field, whereas the field is distorted when the option is switched on (right).

&CELL
plane y = -1
plane y = +1 v = 2000
rows
s 1 1 0 0 1000

opt nodipole // Switch dipole terms off

&FIELD
area -1.1 -1.1 1.1 1.1
pl cont v

&CELL
plane y = -1
plane y = +1 v = 2000
rows
s 1 1 0 0 1000

opt dipole // Switch dipole terms on

&FIELD
area -1.1 -1.1 1.1 1.1
pl cont v

[Dipole terms are by default not included.]

3.11.3: LAYOUT

The wire labels are shown next to the wires unless the WIRE-MARKERS option is active. The cell is plotted using the X-Y or R-PHI projection, as appropriate. To visualise the layout in other projections, use either the PLOT_FIELD_AREA or the PLOT_DRIFT_AREA procedure in the field respectively drift section.

Mainly used to check typing mistakes visually.

[This option is initially off but its setting is remembered from one cell section to the next.]

3.11.4: ISOMETRIC

This option has only effect on the layout plot, not on plots made in for instance the field and drift sections - where the aspect ratio is determined by projection method specified in the AREA statements. In those sections, one can obtain an isometric view by using the 3D projection.

Using this option in conjunction with a non-square VIEWPORT is not meaningful.

[This option is initially off, but its setting is remembered from one cell section to the next.]

3.11.5: WIRE-MARKERS

This option is shared between with the field, optimisation, drift and signal sections.

The type of marker used for a wire depends on the label that you have assigned to the wire in the ROWS listing. Each marker can be adjusted individually via the representations mechanism. The correspondence between labels and REPRESENTATION is as follows:

All wires are shown with the representation WIRES when the option is off.

The LAYOUT plot does not contain alphabetic wire labels if this option is active.

[This option is initially off, but its setting is remembered from one cell section to the next.]

3.11.6: CHARGE-CHECK

Only meaningful if the capacitance matrix has indeed been inverted - in the vectorised executables, this is as a rule not done: the numerical quality of the charge calculation is higher if the capacitance equations are solved by other means than matrix inversion.

[This option is initially off but its setting is remembered from one cell section to the next.]

Section 3.12: PERIODICITY

Chambers which have a repetitive structure over a considerable distance, as for instance in multiwire proportional chambers, should be declared periodic if you wish to enhance the numerical precision of the calculations. You will also gain CPU time by doing so. There are however instances where you may wish to enter explicit copies of the cell, increasing the periodicity length accordingly:

• Isochrons are computed for only one copy of each wire. This is merely an aesthetic disadvantage since the isochrons are identical for all copies.
• Drift-lines reaching periodic copies of a wire or a plane are assigned a status code which does not tell which copy has been hit. One can compute this information from the end point, but it is simpler to enter explicitly the copies which are likely to be hit.
• All copies of a wire undergo the same electrostatic (and gravitational) sag, hence the so-called zig-zag motion is not visible unless at least 2 copies of each wire are explicitly entered.
• The difference between the signals on the various copies of a wire is taken into account, but the signal on only one copy is computed. To study signals on neighbouring wires, one therefore has to enter at least 2, usually 3-5, copies of the chamber.

This statement is only used with chambers constructed from wires, planes and solids. If the field in the chamber is taken from a field map, options such as X-PERIODIC of the FIELD-MAP command should be used instead.

In chambers modelled using neBEM, periodicity-related parameters can be set using the NEBEM command.

Format:

PERIODICITY direction = length [REGULAR | MIRROR]

Example:

PERIOD X=1

3.12.1: direction

Repetition in r is not permitted because of the method used to calculate the potentials in cylindrical geometry.

Cylindrical geometries are handled via a conformal mapping onto a Cartesian coordinate system in which an r-periodicity would be equivalent to an x-periodicity with non-constant intervals. This is technically difficult to deal with. Contact the author if there is a genuine need for such a periodicity.

Periodicity in z is only allowed with neBEM field calculations, not in wire and planes chambers.

3.12.2: length

3.12.3: REGULAR

This is the only type of periodicity permitted in cells constructed of wires and planes. This type of periodicity is recognised by neBEM.

[If periodicity is requested, then it will by default have this type of periodicity.]

3.12.4: MIRROR

This is the type of periodicity is not permitted in cells constructed of wires and planes. This type of periodicity is recognised by neBEM.

[If periodicity is requested, then it will by default be regular.]

Section 3.13: PLANE

Note that one is not allowed to put a wire at the centre of a circular plane. Wires inside a circular plane, whether at the centre or not, are handled by TUBE geometries.

Planes are not compatible with a TUBE geometry. To generate a pie wedge, use a plane at constant r and two planes at constant \&phi;.

Format:

PLANE direction coordinate ...
      [V potential] ...
      [LABEL label] ...
      [{X-STRIP | Y-STRIP | R-STRIP | PHI-STRIP | Z-STRIP} strip_min strip_max ...
         [GAP gap] [LABEL strip_label]]

Examples:

pl x=-1, V=1000
plane phi=30

3.13.1: direction

3.13.2: coordinate

The r coordinate must be strictly positive (non-zero).

[No default, the coordinate is mandatory.]

3.13.3: potential

[Default: an earthed plane, at 0\&nbsp;V.]

3.13.4: label

The label is a single alphabetic upper case character. You may type a longer string, but only the first character will be stored.

A label is not mandatory, but signals induced in a plane are only computed if the plane can be selected, and this can only be done if the plane has a label.

[By default, no label is assigned to a plane.]

3.13.5: STRIP

Signals in strips are computed with weighting fields that are exclusively valid for parallel plate chambers without wires. This can perhaps most easily be seen in an MWPC where the weighting field (orange in the figure) of the strip (in red, covering -0.1\&nbsp;<\&nbsp;x\&nbsp;<\&nbsp;0.1\&nbsp;cm) is not influenced by the wires (purple) - while in reality, the influence of the wires is of course highly significant.

The reason for this limitation is that no exact weighting fields for strips are known for general wire-plane layouts. Should expressions be known for the particular case that interests you, then these can of course be added on demand.

See the weighting_field example for the FIELD-MAP command of the optimisation section for a method to address this using the finite element technique.

Subdivisions are permitted as follows:

3.13.6: strip_min

The location should be given in degrees for \&phi;-sectors, in cm for all other strips.

[Mandatory parameter, no default provided.]

3.13.7: strip_max

The location should be given in degrees for \&phi;-sectors, in cm for all other strips.

[Mandatory parameter, no default provided.]

3.13.8: strip_label

The label is a single alphabetic upper case character. You may type a longer string, but only the first character will be stored.

A label is not mandatory, but signals induced in a strip are only computed if the strip can be selected, and this can only be done if the strip has a label.

[By default, no label is assigned to a strip.]

3.13.9: gap

The gap is specified in cm for strips in x-, r- and y-planes, and in degrees for strips in \&phi;-planes.

[By default, this is taken to be the distance to the parallel plane, if there is one, otherwise the distance from the plane to which the strip belongs to the nearest electrode.]

3.13.10: representations

Strips, if any, are shown with the STRIPS representation.

Section 3.14: READ-FIELD-MAP

This command is executed immediately. Once the command has completed, you can use the FIELD-MAP command to modify for instance the selection of drift medium,

READ-FIELD-MAP has the same side effects as FIELD-MAP, i.e. the command deletes any wires, planes, periodicities, dielectric medium and magnetic field that may have been entered before the command is issued.

Reading binary field maps is, for most field map formats, much faster than reading the original files - but binary field maps are not portable. Files to be read with READ-FIELD-MAP must have been written on the same computer system.

Format:

READ-FIELD-MAP file ...
               [DRIFT-MEDIUM {SMALLEST-EPSILON | ...
                              SECOND-SMALLEST-EPSILON | ...
                              n | ...
                              SECOND-LARGEST-EPSILON | ...
                              LARGEST-EPSILON | ...
                              \ε}] ...
               [NOT-X-PERIODIC | X-PERIODIC | ...
                    X-MIRROR-PERIODIC | X-AXIALLY-PERIODIC] ...
               [NOT-Y-PERIODIC | Y-PERIODIC | ...
                    Y-MIRROR-PERIODIC | Y-AXIALLY-PERIODIC] ...
               [NOT-Z-PERIODIC | Z-PERIODIC | ...
                    Z-MIRROR-PERIODIC | Z-AXIALLY-PERIODIC] ...
               [LINEAR | QUADRATIC | CUBIC] ...
               [INTERPOLATE-ELECTRIC-FIELD | COMPUTE-ELECTRIC-FIELD] ...
               [PLOT-MAP | NOPLOT-MAP] ...
               [NOHISTOGRAM-MAP | HISTOGRAM-MAP]

&CELL
cell-identifier "Micromegas"
Global path=`/afs/cern.ch/exp/compass/scratch/d02/megas/Maxwell/mic3.pjt/`
Call inquire_file(path/`1000_400_0.1.bin`,exist)
If exist Then
   read-field-map {path/`1000_400_0.1.bin`}
Else
   field-map files potential "{path}/V_1000_400_0.1.arg" ...
                   e-field   "{path}/E_1000_400_0.1.arg" ...
             x-periodic y-mirror-periodic
Endif

If a binary field map exists, the map is read. Otherwise the field maps are read in their original format. The periodicity options need not be repeated: they are stored in the binary field map.

3.14.1: DRIFT-MEDIUM

3.14.2: NOT-X-PERIODIC

3.14.3: X-PERIODIC

3.14.4: X-MIRROR-PERIODIC

3.14.5: X-AXIALLY-PERIODIC

3.14.6: NOT-Y-PERIODIC

3.14.7: Y-PERIODIC

3.14.8: Y-MIRROR-PERIODIC

3.14.9: Y-AXIALLY-PERIODIC

3.14.10: NOT-Z-PERIODIC

3.14.11: Z-PERIODIC

3.14.12: Z-MIRROR-PERIODIC

3.14.13: Z-AXIALLY-PERIODIC

3.14.14: LINEAR

The order of the field map can not be increased when reading back a binary map.

3.14.15: QUADRATIC

The order of the field map can not be increased when reading back a binary map.

3.14.16: CUBIC

The order of the field map can not be increased when reading back a binary map.

3.14.17: INTERPOLATE-ELECTRIC-FIELD

3.14.18: COMPUTE-ELECTRIC-FIELD

3.14.19: PLOT-MAP

3.14.20: HISTOGRAM-MAP

Section 3.15: RESET

Format:

RESET [COORDINATES] ...
      [DIELECTRICA] ...
      [DEFINITIONS] ...
      [FIELD-MAP] ...
      [PERIODICITIES] ...
      [PLANES] ...
      [ROWS or WIRES] ...
      [SOLIDS] ...
      [TUBE]

Example:

RESET

3.15.1: COORDINATES

3.15.2: DEFINITIONS

3.15.3: DIELECTRICA

3.15.4: FIELD-MAP

3.15.5: PERIODICITIES

3.15.6: PLANES

3.15.7: ROWS

3.15.8: SOLIDS

3.15.9: TUBE

3.15.10: WIRES

Section 3.16: ROWS

If the wires are thick, short or non-parallel, then neBEM should be used to compute the field. For thin wires, WIRE solids should be used while CYLINDER solids are appropriate for thick wires.

The following properties of the wires can be entered:

• a label that identifies the kind of wire (e.g. S for a sense wire);
• the position of the wire;
• the potential applied to the wire;
• the diameter of the wire;
• the length of the wire;
• the weight with which the wire was stretched;
• the density of the material of which the wire is made.

The coordinate system in which the wire position is specified can either be Cartesian or polar. The wires in a cell that has a tube, are listed in Cartesian coordinates. Polar coordinates will be assumed if you put the keyword POLAR after ROWS, if you have already entered a plane in polar coordinates and if you have already entered a \&phi; periodicity. Otherwise Cartesian coordinates are assumed. Once a coordinate system has been selected in the cell section, it has to be used throughout the section.

ROWS is a multi-line command because chambers sometimes contain many wires. You may enter one wire per line, but if your cell contains regularly spaced series of wires, you may prefer to enter these as a single "row" in which at least the position, but possibly also the other properties, depends on the so-called loop-variable I which automatically assumes a series of values.

One may use control structures (If_block, If_line, Do, Call) in the listing of wires. Please keep in mind that a blank line must be present to signal the end of the list, whether typed by hand or generated with a loop.

Format of the whole command:

ROWS [CARTESIAN | POLAR | TUBE]
row
...
row
(blank line)

Format of the rows:

label n diameter x y [V [weight [length [density]]]]

Examples:

ROWS
s * * 0 0 1000
p * * 0 1 -2000
p * * 0 -1 -2000

This is a very simple example in which 3 wires are entered at (0,0), (0,1) and (0,-1). Defaults are used for the number of wires and the diameter.

ROWS
S * * 0 0 1000
P 2 * -1+i*2 -1+i*2 -2000

This examples shows how the same cell can be entered using the loop variable.

rows
Global n=100
For i From 1 To n Do
   Global r=1+2*(i/n)
   Global phi=4*pi*i/n
   If i=2*entier(i/2) Then
       P * * {r*cos(phi), r*sin(phi), -i*10}
   Else
       S * * {r*cos(phi), r*sin(phi), +i*10}
   Endif
Enddo

This, artificial, example illustrates the use of Global variables, a Do loop and an If_block to generate a spiral. Do not forget the blank line to mark the end of the list of rows !

3.16.1: CARTESIAN

This keyword need not be specified if the cell is already established to be in Cartesian coordinates, for instance if a plane at constant x has already been entered. This keyword is not valid if the cell is already established to be in polar or in tube coordinates.

When Cartesian coordinates are used, you may enter planes at constant x and at constant y. Also both x and y periodicities are permitted.

[If no coordinate system has yet been established when ROWS is entered, then Cartesian coordinates are assumed by default.]

3.16.2: POLAR

When the wires are listed in polar coordinates, the planes have to be entered in polar coordinates too. That is, the planes can be at constant r or at constant \&phi;.

Periodicity in \&phi; is permitted, but radial periodicity isn't.

These coordinates are transformed to an internal coordinates system which is a conformal map of a Cartesian system - but all frequently used instructions transform these internal coordinates back to polar coordinates when displaying the results.

This keyword need not be specified if the cell is already established to be in polar coordinates, for instance if a \&phi; periodicity has already been entered. This keyword is not valid if the cell is already established to be in Cartesian coordinates or in tube coordinates.

[If no coordinate system has been established yet when the ROWS command is entered, then Cartesian coordinates will be assumed by default.]

3.16.3: TUBE

The tube itself and the \&phi; periodicity, if any, is specified in polar coordinates, but the wires are listed in Cartesian coordinates.

Like for polar coordinates, a coordinate transformation is applied to the wire location but the internal coordinates never appear on output.

This keyword need not be specified if the cell is already established to be in tube coordinates because a TUBE statement has already been entered. This keyword is not valid if the cell is already established to be in Cartesian or polar coordinates.

[If no coordinate system has been established yet when the ROWS command is entered, then Cartesian coordinates will be assumed by default.]

3.16.4: label

These labels are used by the SELECT statements to single out (groups of) wires from which particles should drift, for which arrival time distributions are to be computed, on which signals can be recorded, etc.

[Initially, all wires with a label of S are selected for such treatment.]

3.16.5: n

Each wire in such a row will have the same status as if it were entered on a separate line. Entering wires in the form of rows has no incidence on the choice of potential_function used for the chamber.

The number of wires may be a symbolic expression in terms of DEFINEd variables but you may, of course, not use the loop-variable I.

[Default: 1, i.e. a single wire].

3.16.6: diameter

Since the electric fields are currently computed in the thin wire approximation, i.e. neglecting dipole and other higher order terms, care has to be taken that the wire diameters are small compared to the inter-wire distances. One can use the MULTIPOLE-MOMENTS instruction to investigate the need for higher order terms to describe the field around the wire.

Consider using the DIPOLE-TERMS in case dipole terms are thought to be important.

This may be a symbolic expression in terms of DEFINEd variables and you may use the loop-variable I in the expression if you wish.

[Default: 0.01\&nbsp;cm, i.e. 100\&nbsp;\&mu;m].

3.16.7: x

If the cell is described in Cartesian or Tube coordinates, then (x,y) coordinates should be used for the wire location. The wire coordinates should be given in (r,\&phi;) format for Polar cells.

This may be a symbolic expression in terms of DEFINEd variables and you may use the loop-variable I to construct symbolic expressions for the locations of the wires in the row. For instance, for a series of wires with coordinates 1, 2, 3 and 4 you could enter the expression

1+I

[Default: 0\&nbsp;cm.]

3.16.8: y

If the cell is described in Cartesian or Tube coordinates, then (x,y) coordinates should be used for the wire location. The wire coordinates should be given in (r,\&phi;) format for Polar cells.

This may be a symbolic expression in terms of DEFINEd variables and you may use the loop-variable I to construct symbolic expressions for the locations of the wires in the row. For instance, for a series of wires with coordinates 1, 4, 9 and 16 you could enter the expression

(1+I)^2

[Default: 0\&nbsp;cm, \&phi; should be in degrees.]

3.16.9: V

This may be a symbolic expression in terms of DEFINEd variables and you may use the loop-variable I to construct symbolic expressions for the locations of the wires in the row. For instance, for a series of wires with potentials 1000, 1000, 2000 and 2000, you could enter the expression

1000+entier(i/2)*1000

[Default: 0\&nbsp;cm.]

3.16.10: weight

Used by the FORCES command to estimate the wire displacement under gravitational and electrostatic forces.

This may be a symbolic expression in terms of DEFINEd variables and you may use the loop-variable I to construct symbolic expressions.

[Default: 50\&nbsp;grams.]

3.16.11: length

Used by the FORCES command to estimate the wire displacement under gravitational and electrostatic forces.

This may be a symbolic expression in terms of DEFINEd variables and you may use the loop-variable I to construct symbolic expressions.

Note that the length of the wires has no impact on the fields in the chamber. Fields in chambers that are made up of wires and planes are truly 2-dimensional and are identical at all z, irrespective of the length of the wires. If you're interested in the end-effects of finite length wires, then you should use a finite element field map.

[Default: 100\&nbsp;cm.]

3.16.12: density

Used by the FORCES command to estimate the wire displacement under gravitational and electrostatic forces. Not relevant if the wires are vertical.

For copper-beryllium wires, one can also enter CU-BE and for gold plated tungsten one can type TUNGSTEN or W.

This may be a symbolic expression in terms of DEFINEd variables and you may use the loop-variable I to construct symbolic expressions.

[Default: 19.3\&nbsp;g/cm\&sup3;, i.e. 20\&nbsp;\&mu;m gold-plated tungsten wire]

3.16.13: increments

This feature is less powerful than the method using the loop-variable and the increments have therefore been suppressed as of version\&nbsp;5.

This modification is not backwards compatible - input files prepared for Garfield\&nbsp;4 and earlier need to be modified.

3.16.14: loop-variable

This variable may be used for the diameter, the position, the potential, the stretching weight and the length of the wire.

The loop-variables can be used to construct non-standard electrode shapes using wires. Some examples are shown in the description of the wire position and voltage.

Note that the loop variable is not a Global variable: while substitution of expressions in terms of global variables has to be requested explicitly by means of curly brackets, expressions in terms of DEFINEd variables and the loop variable are automatically evaluated. Curly brackets should not be used with such variables.

Section 3.17: SAVE-FIELD-MAP

This command is executed immediately, unlike the WRITE command which is only executed when the section is left. The field map must therefore be present (via a FIELD-MAP or a READ-FIELD-MAP) when you issue the SAVE-FIELD-MAP command.

Binary field maps tend to be much smaller than field maps in the original format. In addition, restoring field maps from binary files is usually much faster. However, binary files are not portable between computer systems.

Please the original field map files - the format of binary field maps changes whenever new elements are added to the field map.

Format:

SAVE-FIELD-MAP   file

Example:

See READ-FIELD-MAP

Section 3.18: SOLIDS

Solids generate the field through an interface with neBEM if potentials, dielectric constants or other boundary conditions have been set for all of them. Otherwise, solids do not affect the field in the chamber, but they can nevertheless be useful for the following reasons:

• Solids can serve as start and end point of drift-lines. This is needed to compute the arrival time distributions for electrodes and to determine the collection statistics.
• Solids are shown in the drawings, thus making the interpretation of drift-lines easier.
• When associated with elements in a field map, solids are used to classify signals as direct or cross induced.

Entering these volumes is not mandatory. The drift-line calculation routines for instance, can infer their presence in most cases from the dielectric constants in the field map.

If you do not enter any solids in a chambers composed of wires and planes, then all wires are automatically copied to cylindrical solids to ensure the wires are visible in 3D and CUT type plots. This copy is not performed if you enter at least 1 solid yourself.

SOLIDS is a multi-line command. Each line after SOLIDS describes one volume. The end of the list is signalled by a blank line.

Only a few shapes are currently provided, other shapes can be added on request - contact the author.

Format:

SOLIDS
{BOX | CYLINDER | EXTRUSION | HOLE | RIDGE | SPHERE | WIRE} parameters
...
(blank line)

Example 1, solids not affecting the field:

solids
For x From -0.02 Step 0.02 To 0.02 Do
   For y From -0.02 Step 0.02 To 0.02 Do
      hole centre {x,y} +0.0110 direction 0 0 1 ...
         half-lengths 0.0100 0.0100 0.0010 ...
         upper-radius 0.0080 lower-radius 0.0080 ...
         n = 5 ...
         conductor-3
      centre {x,y} +0.0050 direction 0 0 1 ...
         half-lengths 0.0100 0.0100 0.0050 ...
         upper-radius 0.0070 lower-radius 0.0040 ...
         n = 5 ...
         dielectric
      centre {x,y} -0.0050 direction 0 0 1 ...
         half-lengths 0.0100 0.0100 0.0050 ...
         upper-radius 0.0040 lower-radius 0.0070 ...
         n = 5 ...
         dielectric
      centre {x,y} -0.0110 direction 0 0 1 ...
         half-lengths 0.0100 0.0100 0.0010 ...
         upper-radius 0.0080 lower-radius 0.0080 ...
         n = 5 ...
         conductor-3
   Enddo
Enddo

Example 2, dielectric materials:

&CELL
solids
box   centre 0 0 -1.2 ...
      half-lengths 5 5 0.2 ...
      conductor-1 ...
      voltage 1
box   centre 0 0 0 ...
      half-lengths 5 5 1 ...
      dielectricum-1 ...
      epsilon 2
ridge centre 0 0 1 ...
      half-lengths 2 5 ...
      notch 1 2 ...
      dir 0 0 1 ...
      epsilon 10 ...
      dielectricum-2
box   centre 0 0 8 ...
      half-lengths 5 5 0.2 ...
      conductor-1 ...
      voltage -1

nebem max-elem 2

&FIELD
// View the structure
area -9 -9 -2 9 9 9 ...
    nooutline ...
    light -20 -40 ...
    view -3*x+5*y-1*z=0 3d
Call plot_field_area
Call plot_end
// Contour plot
area -3 -1 -1  3 5 5 ...
    view y=0 cut rot 180
grid 25
plot-field cont

Example 3, importance of discretisation:

&CELL
solids
box      centre 0 0 0  ...
         half-lengths 5 5 0.1 ...
         voltage 1000 ...
         discretisation 10
box      centre 0 0 1  ...
         half-lengths 5 5 0.1 ...
         voltage 0 ...
         discretisation 10

&FIELD
area -7 -7 -1 7 7 2 view z=0.89
pl cont v n=50 range 0 500

&CELL
solids
box      centre 0 0 0  ...
         half-lengths 5 5 0.1 ...
         voltage 1000 ...
         discretisation 10
box      centre 0 0 1  ...
         half-lengths 5 5 0.1 ...
         voltage 0 ...
         discretisation 10 bottom-discretisation 1

&FIELD
area -7 -7 -1 7 7 2 view z=0.89
pl cont v n=50 range 0 500

Note that the boundary conditions are not strictly respected: in the boundary element approach, the fields are solutions of the Maxwell equations but they only satisfy the boundary conditions at the collocation points. In the finite element approach, the potentials are not solutions of the Maxwell equations, but they strictly respect the boundary conditions.

Example 4, selective discretisation:

&CELL
nebem target-element-size 0.1
solids
box      centre  0 0 0 half-lengths 1 1 1 voltage 1 ...
         discretisation 0.5
box      centre  3 0 0 half-lengths 1 2 2 voltage 1 ...
         front-discretisation 0.2 back-discretisation automatic
cylinder centre 10 0 0 half-length 1 radius 1 voltage -1 ...
         discretisation 0.5 top-discretisation 0.2

nebem target-element-size 0.8
opt cell-print
&MAIN

3.18.1: BOX

Format:

BOX  CENTRE cx cy cz ...
     HALF-LENGTHS lx ly lz ...
     [DIRECTION dx dy dz] ...
     [VOLTAGE v] ...
     [FLOATING-CONDUCTOR] ...
     [CHARGE q] ...
     [EPSILON eps] ...
     [material] ...
     [LABEL label]
     [FRONT-DISCRETISATION discretisation] ...
     [BACK-DISCRETISATION discretisation] ...
     [RIGHT-DISCRETISATION discretisation] ...
     [LEFT-DISCRETISATION discretisation] ...
     [TOP-DISCRETISATION discretisation] ...
     [BOTTOM-DISCRETISATION discretisation]

A set of boxes that are intersecting each other. Shown using the default colour density table, with outlining.

3.18.1.1: CENTRE

[No default.]

3.18.1.2: HALF-LENGTHS

[No default.]

3.18.1.3: DIRECTION

The normalisation of the vector is not used. Zero-norm vectors are not acceptable.

[By default, the box is not rotated i.e. the half lengths are assumed to have been measured along x, y and z.]

3.18.1.4: CHARGE

The charge is added to the surface charges needed to satisfy the boundary conditions. The box can either be a dielectric or a conductor.

In the process of being implemented - initially, the charge is equally distributed over all surfaces, selection of surface panels is planned to be added later.

Specifying this option implies the use of neBEM to solve the field.

3.18.1.5: VOLTAGE

Specifying this option implies the use of neBEM to solve the field.

3.18.1.6: FLOATING-CONDUCTOR

In the process of being implemented.

Specifying this option implies the use of neBEM to solve the field.

3.18.1.7: EPSILON

Specifying this option implies the use of neBEM to solve the field.

3.18.1.8: material

[Default: CONDUCTOR]

3.18.1.9: label

This label serves the same purpose as the wire label for wires, namely the selection of the solid as a place where signals can be measured, around which isochrons are drawn etc.

[By default, no label is assigned.]

3.18.1.10: discretisation

Garfield generates, for each solid, a set of flat panels that together cover the faces. These panels, arbitrary convex polygons, are sub-divided when isolating contact areas between solids and also in order to comply with the neBEM requirement that it be given only rectangles and right-angled triangles. The triangles and rectangles handed to neBEM are called "primitives".

For reasons of accuracy neBEM as a rule sub-divides the primitives into "elements", in a process called "discretisation". The sub-divisions of the primitives are called "elements".

Discretisation will perhaps eventually be automated, but for the time being this remains the responsability of the user. In neBEM, the level of discretisation requested is described by 2 integers: the number of elements that is to be generated along each of 2 sides adjacent to a right angle. Since the shape, orientation and size of the primitives are non-trivial to predict, the level of discretisation is specified on the Garfield side as the desired length of the sides of the elements.

The designation of the surfaces is as follows:

• front: the +x face of the box;
• back: the -x face of the box;
• right: the +y face of the box;
• left: the -y face of the box;
• top: the +z face of the box;
• bottom: the -z face of the box;

The discretisation length can be set in several ways, see Example\&nbsp;4 for the SOLIDS command:

• by setting a default discretisation length to be used for all solids, by means of the TARGET-ELEMENT-SIZE keyword of a NEBEM command issued before the SOLIDS command;
• collectively for all faces of a single solid, e.g. DISCRETISATION=0.1, this overrides the default used for all solids;
• individually for one or more faces of the solid, e.g. TOP-DISCRETISATION=0.2, this overrides any previous collective setting;
• by setting the discretisation length of a face to AUTOMATIC; if this face is in partial contact, then the discretisation length of the other face will be used, if it has been set; if not, and also in the absence of contact, the TARGET-ELEMENT-SIZE will be used that is in effect when leaving the cell section.

Discretisation lengths have to be given in cm.

[Default: the TARGET-ELEMENT-SIZE that is in effect at the time the solids are read.]

3.18.2: CYLINDER

For many purposes, cylinders and wires are equivalent, but the differences are important when using neBEM to compute the field:

• as a true 3-dimensional cylinder: appropriate if the radius of the cylinder is large compared to either its length or the distance to other electrodes;
• as a wire: the preferred approach if the radius is small compared to the length of the cylinder and to the distance to other electrodes; neBEM applies a thin-wire approximation which is more efficient, under these conditions, and which leads for an equal number of elements, to a more accurate near-field.

Mandatory parameters are the location of the centre, the radius and the length. The direction defaults to the z-axis.

Format:

CYLINDER  CENTRE cx cy cz ...
          RADIUS radius ... ...
          [OUTER-RADIUS | MEAN-RADIUS]
          HALF-LENGTH lz ...
          [DIRECTION dx dy dz] ...
          [VOLTAGE v] ...
          [FLOATING-CONDUCTOR] ...
          [CHARGE q] ...
          [EPSILON eps] ...
          [material] ...
          [LABEL label] ...
          [ROTATE angle] ...
          [N n] ...
          [TOP-LID-DISCRETISATION discretisation] ...
          [BODY-DISCRETISATION discretisation] ...
          [BOTTOM-LID-DISCRETISATION discretisation] ...
          [TOP-LID | NOTOP-LID] ...
          [BOTTOM-LID | NOBOTTOM-LID] ...
          [LIDS | NOLIDS]

A set of cylinders, partially hiding each other. Each cylinder is drawn with 50 panels, and 20 colour shades are used.

3.18.2.1: CENTRE

[No default.]

3.18.2.2: radius

The decision whether a particle is inside or outside the cylinder, is made assuming a genuine cylinder. For plotting and neBEM field calculations however, a polygonal approximation is made and the precise interpretation of the radius is influenced by the MEAN-RADIUS and OUTER-RADIUS options.

[No default.]

3.18.2.3: OUTER-RADIUS

3.18.2.4: MEAN-RADIUS

2/(1 + arcsinh(tan(\α) cos(\α) / tan(\α)))

\α = 1/4 \π / (N-1)

If you place a precisely fitting hole around the cylinder, then you should use the same option for the hole.

[This is not default.]

3.18.2.5: HALF-LENGTH

[No default.]

3.18.2.6: DIRECTION

The normalisation of the vector is not used. Zero-norm vectors are not acceptable.

[By default, the central axis is aligned with the z-axis.]

3.18.2.7: CHARGE

The charge is added to the surface charges needed to satisfy the boundary conditions. The cylinder can either be a dielectric or a conductor.

In the process of being implemented - initially, the charge is equally distributed over all surfaces, selection of surface panels is planned to be added later.

Specifying this option implies the use of neBEM to solve the field.

3.18.2.8: VOLTAGE

Specifying this option implies the use of neBEM to solve the field.

3.18.2.9: FLOATING-CONDUCTOR

In the process of being implemented.

Specifying this option implies the use of neBEM to solve the field.

3.18.2.10: EPSILON

Specifying this option implies the use of neBEM to solve the field.

3.18.2.11: material

[Default: CONDUCTOR]

3.18.2.12: label

This label serves the same purpose as the wire label for wires, namely the selection of the solid as a place where signals can be measured, around which isochrons are drawn etc.

[By default, no label is assigned.]

3.18.2.13: N

The interpretation of n is the same for holes and cylinders. Cylinders with a given n will precisely fit in holes with the same n, provided the radii and axes match.

Drift line termination assumes a perfect cylinder, the choice of n therefore has no importance for this purpose. However, the number of surface panels passed on to neBEM field calculations rises with n and the visual quality of 3D views improves with n.

[By default, N is chosen in function of the size occupied by the cylinder in the drawing. N must be larger than 1.]

3.18.2.14: WIRE

This is equivalent to entering a WIRE.

[This is not default and mutually exclusive with specifying N.]

3.18.2.15: ROTATE

Such a rotation is meaningful only if N has been chosen small.

Rotations have only an optical effect. The algorithm which determines whether a point is inside or outside a cylinder, assumes a perfect cylinder and thus does not take rotations into account.

[Default: -\&pi;/4\&nbsp;radian]

3.18.2.16: discretisation

Garfield generates, for each solid, a set of panels that together cover the faces. These panels, arbitrary convex polygons, are sub-divided when isolating contact areas between solids and also in order to comply with the neBEM requirement that it be given only rectangles and right-angled triangles. The triangles and rectangles handed to neBEM are called "primitives".

For reasons of accuracy neBEM as a rule sub-divides the primitives into "elements", in a process called "discretisation". The sub-divisions of the primitives are called "elements".

Discretisation will perhaps eventually be automated, but for the time being this remains the responsability of the user. In neBEM, the level of discretisation requested is described by 2 integers: the number of elements that is to be generated along each of 2 sides adjacent to a right angle. Since the shape, orientation and size of the primitives are non-trivial to predict, the level of discretisation is specified on the Garfield side as the desired length of the sides of the elements.

The designation of the surfaces is as follows:

• top: the circular area at +z;
• body: the outside of the cylindrical part, the only discretisation length which is used for wires.
• bottom: the circular area at -z.

The discretisation lengths can be set in several ways, see Example\&nbsp;4 for the SOLIDS command:

• by setting a default discretisation length to be used for all solids, by means of the TARGET-ELEMENT-SIZE keyword of a NEBEM command issued before the SOLIDS command;
• collectively for all faces of a single solid, e.g. DISCRETISATION=0.1, this overrides the default used for all solids;
• individually for one or more faces of the solid, e.g. TOP-DISCRETISATION=0.2, this overrides any previous collective setting;
• by setting the discretisation length of a face to AUTOMATIC; if this face is in partial contact, then the discretisation length of the other face will be used, if it has been set; if not, and also in the absence of contact, the TARGET-ELEMENT-SIZE will be used that is in effect when leaving the cell section.

Discretisation lengths have to be given in cm.

[Default: the TARGET-ELEMENT-SIZE that is in effect at the time the solids are read.]

3.18.2.17: TOP-LID

Not closing the cylinder results in smaller, more efficient neBEM models since polygonal lids are subdivided in a potentially large number of triangular elements, which are computationally less efficient. Leaving the cylinders open is therefore recommendable practice for periodic chambers.

The cylinder will appear closed for all visualisation techniques, except NEBEM.

This option has no effect on wire-type cylinders.

[This is default.]

3.18.2.18: BOTTOM-LID

Not closing the cylinder results in smaller, more efficient neBEM models since polygonal lids are subdivided in a potentially large number of triangular elements, which are computationally less efficient. Leaving the cylinders open is therefore recommendable practice for periodic chambers.

The cylinder will appear closed for all visualisation techniques, except NEBEM.

This option has no effect on wire-type cylinders.

[This is default.]

3.18.2.19: LIDS

Not closing the cylinder results in smaller, more efficient neBEM models since polygonal lids are subdivided in a potentially large number of triangular elements, which are computationally less efficient. Leaving the cylinders open is therefore recommendable practice for periodic chambers.

The cylinder will appear closed for all visualisation techniques, except NEBEM.

This option has no effect on wire-type cylinders.

[This is default.]

3.18.3: EXTRUSION

Mandatory parameters are the extrusion profile and the half-length. The direction defaults to the z-axis and the central position to (0,0,0).

Format:

EXTRUSION  CENTRE cx cy cz ...
           HALF-LENGTH lz ...
           PROFILE x1 y1  x2 y2  x3 y3 ... xn yn ...
           [DIRECTION dx dy dz] ...
           [VOLTAGE v] ...
           [FLOATING-CONDUCTOR] ...
           [CHARGE q] ...
           [EPSILON eps] ...
           [material] ...
           [LABEL label] ...
           [TOP-LID-DISCRETISATION discretisation] ...
           [BODY-DISCRETISATION discretisation] ...
           [BOTTOM-LID-DISCRETISATION discretisation] ...
           [TOP-LID | NOTOP-LID] ...
           [BOTTOM-LID | NOBOTTOM-LID] ...
           [LIDS | NOLIDS]

An extrusion

&CELL
nebem target-element-size 1
solids
box centre        0   0  10 ...
    half-lengths 10  10   0 ...
    volt          0
box centre        0   0 -10 ...
    half-lengths 10  10   0 ...
    volt          0
extrusion centre  0  0  0 ...
    half-length   4 ...
    profile       -5 -1   -2 -5   -2 -2  -3 -2   0 0    2 -2    3 4 ...
    voltage       1

opt cell-print
&FIELD
area -6 -6 -6 6 6 6 view x+2*y-3*z=0 nebem
Call plot_field_area
Call plot_end

3.18.3.1: CENTRE

[By default, (0,0,0).]

3.18.3.2: HALF-LENGTH

[No default.]

3.18.3.3: DIRECTION

The normalisation of the vector is not used. Zero-norm vectors are not acceptable.

[By default, the central axis is aligned with the z-axis.]

3.18.3.4: CHARGE

The charge is added to the surface charges needed to satisfy the boundary conditions. The extrusion can either be a dielectric or a conductor.

In the process of being implemented - initially, the charge is equally distributed over all surfaces, selection of surface panels is planned to be added later.

Specifying this option implies the use of neBEM to solve the field.

3.18.3.5: VOLTAGE

Specifying this option implies the use of neBEM to solve the field.

3.18.3.6: FLOATING-CONDUCTOR

In the process of being implemented.

Specifying this option implies the use of neBEM to solve the field.

3.18.3.7: EPSILON

Specifying this option implies the use of neBEM to solve the field.

3.18.3.8: material

[Default: CONDUCTOR]

3.18.3.9: label

This label serves the same purpose as the wire label for wires, namely the selection of the solid as a place where signals can be measured, around which isochrons are drawn etc.

[By default, no label is assigned.]

3.18.3.10: PROFILE

[Ny default, mandatory parameter.]

3.18.3.11: discretisation

Garfield generates, for each solid, a set of panels that together cover the faces. These panels, arbitrary convex polygons, are sub-divided when isolating contact areas between solids and also in order to comply with the neBEM requirement that it be given only rectangles and right-angled triangles. The triangles and rectangles handed to neBEM are called "primitives".

For reasons of accuracy neBEM as a rule sub-divides the primitives into "elements", in a process called "discretisation". The sub-divisions of the primitives are called "elements".

Discretisation will perhaps eventually be automated, but for the time being this remains the responsability of the user. In neBEM, the level of discretisation requested is described by 2 integers: the number of elements that is to be generated along each of 2 sides adjacent to a right angle. Since the shape, orientation and size of the primitives are non-trivial to predict, the level of discretisation is specified on the Garfield side as the desired length of the sides of the elements.

The designation of the surfaces is as follows:

• top: the profile at +z;
• body: the outside of the extruded part;
• bottom: the profile at -z.

The discretisation lengths can be set in several ways, see Example\&nbsp;4 for the SOLIDS command:

• by setting a default discretisation length to be used for all solids, by means of the TARGET-ELEMENT-SIZE keyword of a NEBEM command issued before the SOLIDS command;
• collectively for all faces of a single solid, e.g. DISCRETISATION=0.1, this overrides the default used for all solids;
• individually for one or more faces of the solid, e.g. TOP-DISCRETISATION=0.2, this overrides any previous collective setting;
• by setting the discretisation length of a face to AUTOMATIC; if this face is in partial contact, then the discretisation length of the other face will be used, if it has been set; if not, and also in the absence of contact, the TARGET-ELEMENT-SIZE will be used that is in effect when leaving the cell section.

Discretisation lengths have to be given in cm.

[Default: the TARGET-ELEMENT-SIZE that is in effect at the time the solids are read.]

3.18.3.12: TOP-LID

Not closing the extrusion results in smaller, more efficient neBEM models since polygonal lids are subdivided in a potentially large number of triangular elements, which are computationally less efficient. Leaving the extrusions open is therefore recommendable practice for periodic chambers.

The extrusion will appear closed for all visualisation techniques, except NEBEM.

This option has no effect on wire-type extrusions.

[This is default.]

3.18.3.13: BOTTOM-LID

Not closing the extrusion results in smaller, more efficient neBEM models since polygonal lids are subdivided in a potentially large number of triangular elements, which are computationally less efficient. Leaving the extrusions open is therefore recommendable practice for periodic chambers.

The extrusion will appear closed for all visualisation techniques, except NEBEM.

This option has no effect on wire-type extrusions.

[This is default.]

3.18.3.14: LIDS

Not closing the extrusion results in smaller, more efficient neBEM models since polygonal lids are subdivided in a potentially large number of triangular elements, which are computationally less efficient. Leaving the extrusions open is therefore recommendable practice for periodic chambers.

The extrusion will appear closed for all visualisation techniques, except NEBEM.

This option has no effect on wire-type extrusions.

[This is default.]

3.18.4: HOLE

Format:

HOLE  CENTRE cx cy cz ...
      RADIUS radius | UPPER-RADIUS r_up LOWER-RADIUS r_low ...
      [OUTER-RADII | MEAN-RADII]
      HALF-LENGTHS lx ly lz ...
      [DIRECTION dx dy dz] ...
      [VOLTAGE v] ...
      [FLOATING-CONDUCTOR] ...
      [CHARGE q] ...
      [EPSILON eps] ...
      [material] ...
      [LABEL label] ...
      [N n]
      [FRONT-DISCRETISATION discretisation] ...
      [BACK-DISCRETISATION discretisation] ...
      [RIGHT-DISCRETISATION discretisation] ...
      [LEFT-DISCRETISATION discretisation] ...
      [TOP-DISCRETISATION discretisation] ...
      [BOTTOM-DISCRETISATION discretisation] ...
      [CYLINDER-DISCRETISATION discretisation]

Two holes, on the left with N=2, on the right with N=20. Both are drawn with outlining.

3.18.4.1: CENTRE

[No default.]

3.18.4.2: radius

The decision whether a particle is inside or outside the cylindric part of the hole is made assuming a genuine cylinder. For plotting and neBEM field calculations however, a polygonal approximation is made and the precise interpretation of the radius is influenced by the MEAN-RADII and OUTER-RADII options.

[No default.]

3.18.4.3: OUTER-RADII

3.18.4.4: MEAN-RADII

2/(1 + arcsinh(tan(\α) cos(\α) / tan(\α)))

\α = 1/4 \π / (N-1)

If you insert a precisely fitting cylinder in the hole, then you should use the same option for the cylinder.

[This is not default.]

3.18.4.5: HALF-LENGTHS

[No default.]

3.18.4.6: DIRECTION

The normalisation of the vector is not used. Zero-norm vectors are not acceptable.

[By default, the central axis is aligned with the z-axis.]

3.18.4.7: CHARGE

The charge is added to the surface charges needed to satisfy the boundary conditions. The hole can either be a dielectric or a conductor.

In the process of being implemented - initially, the charge is equally distributed over all surfaces, selection of surface panels is planned to be added later.

Specifying this option implies the use of neBEM to solve the field.

3.18.4.8: VOLTAGE

Specifying this option implies the use of neBEM to solve the field.

3.18.4.9: FLOATING-CONDUCTOR

In the process of being implemented.

Specifying this option implies the use of neBEM to solve the field.

3.18.4.10: EPSILON

Specifying this option implies the use of neBEM to solve the field.

3.18.4.11: material

[Default: CONDUCTOR]

3.18.4.12: N

The interpretation of n is the same for holes and cylinders. Cylinders with a given n will precisely fit in holes with the same n, provided the radii and axes match.

Drift line termination assumes a perfect cylinder, the choice of n therefore has no importance for this purpose. However, the number of surface panels passed on to neBEM field calculations rises with n and the visual quality of 3D views improves with n.

[By default, N is chosen in function of the size occupied by the cylinder in the drawing. N must be larger than 1.]

3.18.4.13: label

This label serves the same purpose as the wire label for wires, namely the selection of the solid as a place where signals can be measured, around which isochrons are drawn etc.

[By default, no label is assigned.]

3.18.4.14: discretisation

Garfield generates, for each solid, a set of panels that together cover the faces. These panels, arbitrary convex polygons, are sub-divided when isolating contact areas between solids and also in order to comply with the neBEM requirement that it be given only rectangles and right-angled triangles. The triangles and rectangles handed to neBEM are called "primitives".

For reasons of accuracy neBEM as a rule sub-divides the primitives into "elements", in a process called "discretisation". The sub-divisions of the primitives are called "elements".

Discretisation will perhaps eventually be automated, but for the time being this remains the responsability of the user. In neBEM, the level of discretisation requested is described by 2 integers: the number of elements that is to be generated along each of 2 sides adjacent to a right angle. Since the shape, orientation and size of the primitives are non-trivial to predict, the level of discretisation is specified on the Garfield side as the desired length of the sides of the elements.

The designation of the surfaces is as follows:

• front: the +x face of the box;
• back: the -x face of the box;
• right: the +y face of the box;
• left: the -y face of the box;
• top: the +z face of the box;
• bottom: the -z face of the box;
• hole or cylinder: the surface of the hole.

The discretisation lengths can be set in several ways, see Example\&nbsp;4 for the SOLIDS command:

• by setting a default discretisation length to be used for all solids, by means of the TARGET-ELEMENT-SIZE keyword of a NEBEM command issued before the SOLIDS command;
• collectively for all faces of a single solid, e.g. DISCRETISATION=0.1, this overrides the default used for all solids;
• individually for one or more faces of the solid, e.g. TOP-DISCRETISATION=0.2, this overrides any previous collective setting;
• by setting the discretisation length of a face to AUTOMATIC; if this face is in partial contact, then the discretisation length of the other face will be used, if it has been set; if not, and also in the absence of contact, the TARGET-ELEMENT-SIZE will be used that is in effect when leaving the cell section.

Discretisation lengths have to be given in cm. [Default: the TARGET-ELEMENT-SIZE that is in effect at the time the solids are read.]

3.18.5: RIDGE

The ridge proper is by default aligned with the y-axis, the (x,y) plane is taken to the floor of the construction.

Format:

RIDGE  CENTRE cx cy cz ...
       HALF-LENGTHS lx ly ...
       NOTCH rx rz ...
       [DIRECTION dx dy dz] ...
       [VOLTAGE v] ...
       [FLOATING-CONDUCTOR] ...
       [CHARGE q] ...
       [EPSILON eps] ...
       [material] ...
       [LABEL label]
       [FRONT-DISCRETISATION discretisation] ...
       [BACK-DISCRETISATION discretisation] ...
       [RIGHT-DISCRETISATION discretisation] ...
       [LEFT-DISCRETISATION discretisation] ...
       [FLOOR-DISCRETISATION discretisation]

A ridge (blue) used to model a surface irregularity of a dielectric medium (yellow) between conductors (green).

3.18.5.1: CENTRE

[No default.]

3.18.5.2: HALF-LENGTHS

[No default.]

3.18.5.3: NOTCH

If the offset is set to 0, then the ridge will be symmetric. This parameter is mandatory and is by default set to 0.

The height must be specified and must be positive (non-zero).

3.18.5.4: DIRECTION

The normalisation of the vector is not used. Zero-norm vectors are not acceptable.

[By default, the box is not rotated i.e. the half lengths are assumed to have been measured along x, y and z.]

3.18.5.5: CHARGE

The charge is added to the surface charges needed to satisfy the boundary conditions. The box can either be a dielectric or a conductor.

In the process of being implemented - initially, the charge is equally distributed over all surfaces, selection of surface panels is planned to be added later.

Specifying this option implies the use of neBEM to solve the field.

3.18.5.6: VOLTAGE

Specifying this option implies the use of neBEM to solve the field.

3.18.5.7: FLOATING-CONDUCTOR

In the process of being implemented.

Specifying this option implies the use of neBEM to solve the field.

3.18.5.8: EPSILON

Specifying this option implies the use of neBEM to solve the field.

3.18.5.9: material

[Default: CONDUCTOR]

3.18.5.10: label

This label serves the same purpose as the wire label for wires, namely the selection of the solid as a place where signals can be measured, around which isochrons are drawn etc.

[By default, no label is assigned.]

3.18.5.11: discretisation

Garfield generates, for each solid, a set of panels that together cover the faces. These panels, arbitrary convex polygons, are sub-divided when isolating contact areas between solids and also in order to comply with the neBEM requirement that it be given only rectangles and right-angled triangles. The triangles and rectangles handed to neBEM are called "primitives".

For reasons of accuracy neBEM as a rule sub-divides the primitives into "elements", in a process called "discretisation". The sub-divisions of the primitives are called "elements".

Discretisation will perhaps eventually be automated, but for the time being this remains the responsability of the user. In neBEM, the level of discretisation requested is described by 2 integers: the number of elements that is to be generated along each of 2 sides adjacent to a right angle. Since the shape, orientation and size of the primitives are non-trivial to predict, the level of discretisation is specified on the Garfield side as the desired length of the sides of the elements.

The designation of the surfaces is as follows:

• front: the inclined rectangular face that looks towards +x;
• back: the inclined rectangular face that looks towards -x;
• right: the +y triangular face of the ridge;
• left: the -y triangular face of the ridge;
• floor: the z=0 floor of the ridge.

The discretisation lengths can be set in several ways, see Example\&nbsp;4 for the SOLIDS command:

• by setting a default discretisation length to be used for all solids, by means of the TARGET-ELEMENT-SIZE keyword of a NEBEM command issued before the SOLIDS command;
• collectively for all faces of a single solid, e.g. DISCRETISATION=0.1, this overrides the default used for all solids;
• individually for one or more faces of the solid, e.g. TOP-DISCRETISATION=0.2, this overrides any previous collective setting;
• by setting the discretisation length of a face to AUTOMATIC; if this face is in partial contact, then the discretisation length of the other face will be used, if it has been set; if not, and also in the absence of contact, the TARGET-ELEMENT-SIZE will be used that is in effect when leaving the cell section.

Discretisation lengths have to be given in cm.

[Default: the TARGET-ELEMENT-SIZE that is in effect at the time the solids are read.]

3.18.6: SPHERE

Format:

SPHERE  CENTRE cx cy cz ...
        RADIUS r ...
        [VOLTAGE v] ...
        [FLOATING-CONDUCTOR] ...
        [CHARGE q] ...
        [EPSILON eps] ...
        [material] ...
        [LABEL label] ...
        [N n]
        [DISCRETISATION discretisation] ...

A sphere with 50 by 50 panels, shown with a colour table of 50 elements.

3.18.6.1: CENTRE

[No default.]

3.18.6.2: RADIUS

[No default.]

3.18.6.3: CHARGE

The charge is added to the surface charges needed to satisfy the boundary conditions. The sphere can either be a dielectric or a conductor.

In the process of being implemented - initially, the charge is equally distributed over all surfaces, selection of surface panels is planned to be added later.

Specifying this option implies the use of neBEM to solve the field.

3.18.6.4: VOLTAGE

Specifying this option implies the use of neBEM to solve the field.

3.18.6.5: FLOATING-CONDUCTOR

In the process of being implemented.

Specifying this option implies the use of neBEM to solve the field.

3.18.6.6: EPSILON

Specifying this option implies the use of neBEM to solve the field.

3.18.6.7: material

[Default: CONDUCTOR]

3.18.6.8: N

N must be equal to, or larger than, 3.

[By default, N is chosen in function of the size occupied by the sphere in the drawing. If you decide to specify N manually, then the that setting will be used no matter how large or small the sphere appears in the drawing.]

3.18.6.9: label

This label serves the same purpose as the wire label for wires, namely the selection of the solid as a place where signals can be measured, around which isochrons are drawn etc.

[By default, no label is assigned.]

3.18.6.10: discretisation

Garfield generates, for each solid, a set of panels that together cover the faces. These panels, arbitrary convex polygons, are sub-divided when isolating contact areas between solids and also in order to comply with the neBEM requirement that it be given only rectangles and right-angled triangles. The triangles and rectangles handed to neBEM are called "primitives".

For reasons of accuracy neBEM as a rule sub-divides the primitives into "elements", in a process called "discretisation". The sub-divisions of the primitives are called "elements".

Discretisation will perhaps eventually be automated, but for the time being this remains the responsability of the user. In neBEM, the level of discretisation requested is described by 2 integers: the number of elements that is to be generated along each of 2 sides adjacent to a right angle. Since the shape, orientation and size of the primitives are non-trivial to predict, the level of discretisation is specified on the Garfield side as the desired length of the sides of the elements.

All panels covering the sphere are subject to the same discretisation.

The discretisation lengths can be set in several ways, see Example\&nbsp;4 for the SOLIDS command:

• by setting a default discretisation length to be used for all solids, by means of the TARGET-ELEMENT-SIZE keyword of a NEBEM command issued before the SOLIDS command;
• collectively for all faces of a single solid, e.g. DISCRETISATION=0.1, this overrides the default used for all solids;
• individually for one or more faces of the solid, e.g. TOP-DISCRETISATION=0.2, this overrides any previous collective setting;
• by setting the discretisation length of a face to AUTOMATIC; if this face is in partial contact, then the discretisation length of the other face will be used, if it has been set; if not, and also in the absence of contact, the TARGET-ELEMENT-SIZE will be used that is in effect when leaving the cell section.

Discretisation lengths have to be given in cm. [Default: the TARGET-ELEMENT-SIZE that is in effect at the time the solids are read.]

3.18.7: WIRE

These are to be used if the cell contains wires that are non-parallel or short compared to their length. If the cell can be described in terms rows of long and parallel wires, planes, a tube and periodicity, then it is preferable to do so.

Wire solids are treated as cylinders for most purposes, but neBEM handles them as charges distributed along the axis in such a manner that the surface is at the specified potential. This is equivalent to the thin-wire approximation used for wire and plane cells. This approach makes more efficient use of the elements than a solid cylinder in case the radius of the cylinder is small compared to its length and to the distance to other electrodes. A CYLINDER should be used if these conditions are not fulfilled.

Wires are always conductors.

Mandatory parameters are the location of the centre, the radius and the length. The direction defaults to the z-axis.

Format:

WIRE  CENTRE cx cy cz ...
      RADIUS r ...
      HALF-LENGTH lz ...
      [DIRECTION dx dy dz] ...
      [VOLTAGE v] ...
      [FLOATING-CONDUCTOR] ...
      [material] ...
      [LABEL label] ...
      [DISCRETISATION discretisation]

Example: Two perpendicular wires cross each other at a distance of 1\&nbsp;mm.

&CELL
nebem target-element-size 0.01 maximum-elements 100
solids
wire centre      0      0   -0.05 ...
     half-length 1 ...
     radius      0.0100 ...
     direction   1      0    0 ...
     voltage    -1
wire centre      0      0   +0.05 ...
     half-length 1 ...
     radius      0.0100 ...
     direction   0      1    0 ...
     voltage    +1

&FIELD
area -0.25 -0.25 -0.25 0.25 0.25 0.25 view z=0
grid 50
plot-field surface e

area -1.2 -1.2 -1.2 1.2 1.2 1.2 view z=0
plot-field surface e

track -1 0.010001 -0.05   1 0.010001 -0.05
plot-field graph v range -1.01 -0.99

3.18.7.1: CENTRE

[No default.]

3.18.7.2: RADIUS

[No default.]

3.18.7.3: HALF-LENGTH

[No default.]

3.18.7.4: DIRECTION

The normalisation of the vector is not used. Zero-norm vectors are not acceptable.

[By default, the central axis is aligned with the z-axis.]

3.18.7.5: VOLTAGE

Specifying this option implies the use of neBEM to solve the field.

3.18.7.6: FLOATING-CONDUCTOR

In the process of being implemented.

Specifying this option implies the use of neBEM to solve the field.

3.18.7.7: material

[Default: CONDUCTOR]

3.18.7.8: label

This label serves the same purpose as the wire label for wires, namely the selection of the solid as a place where signals can be measured, around which isochrons are drawn etc.

[By default, no label is assigned.]

3.18.7.9: discretisation

Garfield generates for each wire a single primitive: the centre line of the wire. neBEM sub-divides this primitive into "elements", in a process called "discretisation". The sub-divisions of the primitives are called "elements".

Discretisation will perhaps eventually be automated, but for the time being this remains the responsability of the user who has to indicate the length of the desired elements.

The discretisation length has to be given in cm. Also the value AUTOMATIC is allowed, in which case the TARGET-ELEMENT-SIZE will be used that is in effect when the cell section is being left.

[Default: the TARGET-ELEMENT-SIZE that is in effect at the time the solids are read.]

Section 3.19: TUBE

The main difference between a cell described in polar coordinates with a plane at constant r and a tube with radius r, is that one can put a wire at the centre of a tube, but not at the centre of a cell with a circular plane.

With Tube coordinates, you enter the wire location in Cartesian coordinates which you can combine with a \&phi; periodicity in degrees. Periodicities in x or y are not permitted, nor are planes in any direction.

The potential function for a square tube is expensive to compute compared to the equivalent potential which is used for a cell that has 2 planes at constant x and 2 planes at constant y.

Format:

TUBE  [RADIUS r] ...
      [VOLTAGE v] ...
      [EDGES n] ...
      [LABEL label] ...
      [{PHI-STRIP | Z-STRIP} strip_min strip_max ...
         [GAP gap] [LABEL strip_label]]

Examples:

tube r=2, v=2000
tube hexagonal r=5

In the first example, a circular tube (EDGES is not specified, one could also have added CIRCLE or EDGES=0) is defined with a radius of 2\&nbsp;cm and at a potential of 2000\&nbsp;V. In the second example, the tube is hexagonal and with radius 5\&nbsp;cm. This tube is grounded.

3.19.1: RADIUS

[No default is provided.]

3.19.2: VOLTAGE

[By default 0\&nbsp;V.]

3.19.3: EDGES

Polygons with a larger number of edges can be made available on request.

3.19.4: label

A label is not mandatory, but signals induced in the tube are only computed if the tube can be selected, and this can only be done if the tube has a label.

[By default, no label is assigned.]

3.19.5: STRIP

Two kinds of sub-divisions are permitted: radial sectors and slices along the z-axis.

3.19.6: strip_min

The location should be indicated in degrees for radial sectors and in cm for slices in z.

[Mandatory parameter, no default provided.]

3.19.7: strip_max

The location should be indicated in degrees for radial sectors and in cm for slices in z.

[Mandatory parameter, no default provided.]

3.19.8: strip_label

The label is a single alphabetic upper case character. You may type a longer string, but only the first character will be stored.

A label is not mandatory, but signals induced in a strip are only computed if the strip can be selected, and this can only be done if the strip has a label.

[By default, no label is assigned to a strip.]

3.19.9: gap

The gap is specified in cm for z-slices and in degrees for \&phi;-sectors.

[By default, this is taken to be the distance to the central wire, if there is one.]

3.19.10: representations

Strips, if any, are shown with the STRIPS representation.

Section 3.20: WINDOW

This command has effect only if issued after a FIELD-MAP or READ-FIELD-MAP command.

Formats for 2D and 3D field maps respectively:

WINDOW xmin ymin xmax ymax
WINDOW xmin ymin zmin xmax ymax zmax

Example:

&CELL
Global bin `gabriele.bin`
If exist(bin) Then
   read-field-map {bin}
Else
   field-map files "e.reg" "v.reg" keep-background maxwell-11 ...
      x-mirror-periodic y-mirror-periodic
   save-field-map {bin}
Endif
window -0.0070 -0.0035 -10 0.0070 0.0035 10
opt cell-print

Section 3.21: WRITE

Although written in plain text, this kind of dataset is not meant to be human-readable. Use the LAYOUT option to visualise a cell and CELL-PRINT to obtain a table of the wire locations, charges etc. Compact format cells should not be edited.

The format is chosen to enable a fast restore of wire data. This is useful for chambers which contain large numbers of wires (several 1000s). Otherwise, the overhead is not worth the loss in flexibility. The capacitance matrix is not stored in compact format cell datasets.

Field maps are, because of their large size, not saved by the WRITE statement. If reading them with the FIELD-MAP command takes too much time, and if the size of the full field maps is a point of concern, then consider using SAVE-FIELD-MAP and READ-FIELD-MAP, which perform a binary (i.e. non-portable) save and retrieve.

The writing operation takes place when the section is left, not when the WRITE command is issued. The statement can appear at any place in the cell section.

Compact format cell datasets are written in a machine independent format - files written on one type of computer can be read on other computers.

Format:

WRITE DATASET file [member] [REMARK remark]

Examples:

WR DATA cell.dat cell1 REM "Some cell"
WR cell.dat cell1 "Some cell"

(These two examples are equivalent, they show that the keywords DATA and REMARK are not needed if the parameters are in the right order.)

3.21.1: file

3.21.2: member

3.21.3: remark

The field is left blank by default.

Chapter 4: &MAGNETIC

• by using the COMPONENTS command in this section, you can set a parametrised magnetic field as well as a constant field with arbitrary orientation, optionally distorted by the difference in permeability between the wire material and the gas;
• by means of the FIELD-MAP command in the &CELL section, you can enter a magnetic field map computed by a finite element program.

The cell and gas descriptions are not touched when you enter a magnetic field, but commands like MAGBOLTZ will try and calculate a sensible default B-field range and range of E-B angles if a magnetic field is entered beforehand.

[Initially, the magnetic field is off.]

Section 4.1: COMPONENTS

The radial and angular components of the magnetic field must be zero if your cell has been entered in polar coordinates. Only the z component may be non-zero in this case.

Format:

COMPONENTS  {value_Bx | vector_Bx VS {X|Y|Z} = vector_x | formula_Bx} ...
            {value_By | vector_By VS {X|Y|Z} = vector_y | formula_By} ...
            {value_Bz | vector_Bz VS {X|Y|Z} = vector_z | formula_Bz} ...
            [GAUSS | OERSTED | TESLA | V.MICROSEC/CM2]

Examples:

comp 0 0 5000 G

A constant magnetic field of 5000\&nbsp;G, or 0.5\&nbsp;T, along the z-axis.

comp -y x 0

A toroidal field specified with 2\&nbsp;formulae and 1\&nbsp;constant value.

4.1.1: value

If this format is used for all 3\&nbsp;components of the magnetic field, then the PERMEABILITY is taken into account.

The magnetic field component should have the form of a Number.

4.1.2: vector

If this format is used for 1 or more components of the magnetic field, then the PERMEABILITY is not taken into account.

Both the field vector and the coordinate vector have to be in the form of a 1-dimensional Matrix. These 2\&nbsp;vectors must have the same length.

When you issue the COMPONENTS command, a copy of the vectors is made. You may therefore change the vectors afterwards - changes to the vectors do not, however, affect the magnetic field.

4.1.3: formula

If this format is used for 1 or more components of the magnetic field, then the PERMEABILITY is not taken into account.

Components of the magnetic field that use this format should have the form of a String which uses the variables X, Y and Z when Cartesian coordinates are used, and R, PHI and Z when the cell is described in polar coordinates.

4.1.4: units

You have to express all components in the same unit, even if you use different formats.

You have to use this unit in calls to the various procedures which take magnetic fields as arguments, such as MAGNETIC_FIELD or DRIFT_VELOCITY.

The default unit for the COMPONENTS statement is the Tesla, if you wish to use other units, then you have to specify this.

Section 4.2: OPTIONS

Section 4.3: PERMEABILITY

The permeability is taken into account only in case all 3 COMPONENTS of the magnetic field have been entered as a constant value.

Format:

PERMEABILITY perm_wire perm_gas

Example:

PERM 1 0

Chapter 5: &GAS

Some of these properties can be computed: the Magboltz program will calculate the electron drift velocity, diffusion, Townsend and attachment coefficient for nearly arbitrary gas mixtures. The Heed program takes care of clustering, also for nearly arbitrary gas mixtures.

If you have measured gas properties, or have access to measurements you trust, you can enter this data in the form of tables. One can also replace parts of the Magboltz tables with measurements.

For rapid studies which do not require great accuracy, descriptions of a few common gas mixtures are built in to the program.

All existing gas information is cleared by entering the gas section.

Format:

&GAS

Section 5.1: overview

• gas mixture prepared during the run
• fully user specified gas mixture
• built-in gas mixtures with fixed proportions
• retrieval of a gas description previously stored

A couple of instructions can be used regardless of the origin.

Gas mixture prepared during the run:

User specified gas mixture:

Historically, Garfield contains a number of experiment-based gas tables. They remain available for backwards compatibility, but their use is not recommended for new applications:

Retrieval of a gas description previously stored:

General purpose instructions:

Section 5.2: methods

5.2.1: coordinate_system

• E, the electric field
• Btrans: component of B transverse to E, provided B is neither 0 nor parallel with E, otherwise any axis perpendicular to E
• E\&times;B provided B is neither 0 nor parallel with E, otherwise the axis perpendicular to the axes mentioned before

Section 5.3: built_in

For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Example:

ARG-50-ETH-50

(Until further notice, the program will use 50\&nbsp;% argon, 50\&nbsp;% ethane.)

5.3.1: ARGON-20-ETHANE-80

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Drift velocities taken from Jean-Marie et. al. (1979), diffusion from Ramanantsizehena (1979). Mobility and most probable energy loss are questionable. Supplied by Matthias Grosse Perdekamp (Freiburg, Germany).

5.3.2: ARGON-50-ETHANE-50

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Supplied by Manfred Guckes (transport properties) and Giorgio Sartori and Michela Giavedoni (Padova, parameters part).

5.3.3: ARGON-80-ETHANE-20

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Drift velocities taken from Jean-Marie et al. (1979), diffusion from Ramanantsizehena (1979). Mobility and most probable energy loss are questionable. Supplied by Matthias Grosse Perdekamp (Freiburg, Germany)

5.3.4: ARGON-73-METHANE-20-PROPANOL-7

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Drift velocities and diffusion from F. Piuz Cern-EF 82-11 and Fehlmann et. al. (1983). Clustering parameters with large, unknown errors. Supplied by Matthias Grosse Perdekamp (Freiburg).

5.3.5: CO2

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Karl Dederichs and Fran\&ccedil;ois Piuz (drift velocity and diffusion) and Fran\&ccedil;ois Rohrbach (multiplication).

5.3.6: CO2-80-ETHANE-20

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Data supplied by Diego Bettoni.

5.3.7: CO2-90-ETHANE-10

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Data supplied by Diego Bettoni and Reyad Sawafti.

5.3.8: CO2-90-ISOBUTANE-10

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Data supplied Manfred Guckes (transport properties) and Helmut Boettcher (clustering properties).

5.3.9: ETHANE

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Supplied by Ingo Herbst.

5.3.10: ISOBUTANE

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Supplied by Emile Schmoetter. Clustering properties from Helmut Boettcher.

5.3.11: METHANE

This command is provided mainly for reasons of backwards compatibility. For new applications, consider using HEED for ionisation of gas mixtures due to charged particles, MAGBOLTZ for the electron transport properties, and ADD to add ion mobility data, e.g. from the H.W. Ellis et al. papers.

Source: Ingo Herbst, for the drift velocity and the diffusion and from "Basic data of plasma physics, 1966", Sanborn C. Brown.

Section 5.4: ADD

The ADD command has 2 formats:

• parametrised data in the form of a function
• tabulated data of a gas property VS E/p

Beware that the WRITE command executes only when the section is left. Therefore, if you modify Magboltz computed gas tables with the ADD command, the modified tables will be written - not the original Magboltz data, no matter where you place the WRITE and ADD statements,

REPLACE is a synonym for ADD. The MERGE command should be used if you wish to combine the existing gas data with data from a gas file.

Format:

ADD  item_1 { function_1 | value_1 VS ep_1 [ORDER order_1] } ...
     item_2 { function_2 | value_2 VS ep_2 [ORDER order_2] } ...
     ...

Example:

Global pbar = 3
magboltz argon 91 nitrogen 4 methane 5 ...
   e/p-range 0.05 135
Vector E_Ar_Ar K_Ar_Ar
   0  1.53
   8  1.53
  10  1.53
  12  1.53
  15  1.52
  20  1.51
  25  1.49
  30  1.47
  40  1.44
  50  1.41
  60  1.38
  80  1.32
 100  1.27
 120  1.22
 150  1.16
 200  1.06
 250  0.99
 300  0.95
 400  0.85
 500  0.78
 600  0.72
 800  0.63
1000  0.56
1200  0.51
1500  0.46
2000  0.40

Global E_Ar_Ar = E_Ar_Ar/(0.010354*300)
Global K_Ar_Ar = K_Ar_Ar*1e-6/pbar
add ion-mobility K_Ar_Ar vs E_Ar_Ar
extrapolations low-ion-mobility constant high-ion-mobility linear

Magboltz is used to generate an electron transport table. This also sets the E/p scale.

Next, a file is read in that contains mobilities as function of E/N for Ar\<SUP\>+\</SUP\> ions in Ar at a pressure of 1 atm. The data is taken from the literature, in this case Hornbeck '51 and Beaty '68 (for an extensive compilation consult the H. W. Ellis et al. papers). The E/N values are stored in the matrix E_Ar_Ar, while the mobilities are kept in K_Ar_Ar.

The E/N vector is transformed to E/p. The mobility is divided by the pressure, and its units are changed from cm\&sup2;/sec.V to cm\&sup2;/\&mu;sec.V.

Finally, the mobility is added to the gas tables using the ADD statement.

References:

[1]

H.W. Ellis, R.Y. Pai, E.W. McDaniel, E.A. Mason and L.A. Viehland, Transport properties of gaseous ions over a wide energy range, At. Data and Nucl. Data Tables 17 (1976) 177-210.

[2]

H.W. Ellis, E.W. McDaniel, D.L. Albritton, L.A. Viehland, S.L. Lin and E.A. Mason, Transport properties of gaseous ions over a wide energy range, part II, At. Data and Nucl. Data Tables 22 (1978) 179-217.

[3]

H.W. Ellis, M.G. Thackston, E.W. McDaniel and E.A. Mason, Transport properties of gaseous ions over a wide energy range, part III, At. Data and Nucl. Data Tables 31 (1984) 113-151.

[4]

L.A. Viehland and E.A. Mason, Transport properties of gaseous ions over a wide energy range, part IV, At. Data and Nucl. Data Tables 60 (1995) 37-95.

[5]

J. A. Hornbeck, The drift velocities of molecular and atomic ions in Helium, Neon and Argon, Phys. Rev. 84 (1951) 615-620.

[6]

E. C. Beaty, Proc 5th International conference on ionisation phenomena in gasses, München (1961), Vol 1, p 183, North Holland. Phys. Rev. 170 (1968) 116.

5.4.1: item

Note that the same scalings have to be applied as for the TABLE.

5.4.2: function

The variable EP can always be used, ANGLE_EB and B can only be used in tables prepared for magnetic fields. The transport properties can be used only insofar as they have been entered already.

5.4.3: VS

• a 1-dimensional Matrix that contains the E/p values at which the measurements were done;
• a 1-dimensional Matrix that contains the corresponding measured values of the selected item.

The E/p vector should in principle cover the entire range of the table. Values outside the range of the E/p vector are left untouched - no attempt is made to extrapolate. Since most items are initialised to values outside their permissible range, an error will in general be reported from the checks that are carried out while leaving the gas section. To avoid this, one can first set the item with an approximate function and then override in part with more precise values. This is illustrated here for He\<SUP\>+\</SUP\> in He:

// Experimental data
Vector E_He_He K_He_He
   0  10.5
   6  10.3
   8  10.2
  10  10.2
  12  10.1
  15  10.0
  20   9.90
  25   9.74
  30   9.60
  40   9.28
  50   8.97
  60   8.67
  80   8.12
 100   7.67
 120   7.25
 150   6.78
 200   6.12
 250   5.60
 300   5.19
 400   4.58
 500   4.17
 600   3.81
 700   3.57

// Scaling from Td to V/cm.Torr and from V/cm\².sec to V/cm\².\μsec
Global E_He_He = E_He_He/(0.010354*300)
Global K_He_He = K_He_He*1e-6
// Fit an exponential to the shape
Call fit_exponential(E_He_He,K_He_He,1e-8,p0,p1,p2,p3,ep0,ep1,ep2,ep3)
// Provisionally set the mobility to the exponential function
add ion-mobility exp({p0}+{p1}*ep+{p2}*ep^2+{p3}*ep^3)
// Override the values that are in the range
add ion-mobility K_He_He vs E_He_He

The E/p values in your vector do not have to coincide with the E/p values present in the table - your vectors will be interpolated at the values of the table and these interpolations are stored instead of the values from the vector.

5.4.4: order

When the data is smooth, a value of 2 (quadratic interpolation) is a good choice. This may however lead to intermediate points with a negative value in for instance Townsend coefficient tables that usually start at 0. For such tables, linear interpolation is advised.

Instead of ORDER 1, you may also type LINEAR. QUADRATIC is a synonym for ORDER 2, CUBIC for ORDER 3.

Section 5.5: CLUSTER

• entering a parametrisation,
• listing of all probabilities and
• a mixed form.

The cluster size distribution is not by itself enough to generate clusters along a track. The EXPONENTIAL-SPACING clustering model which uses the distribution entered here, also needs to know the mean number of clusters per cm.

If you use the HEED interface, then you neither need to enter a cluster size distribution nor the cluster spacing. Entering a cluster size distribution and initialising Heed is however allowed. It is only at the TRACK level that you decide which clustering model you are going to use.

5.5.1: Parametrisation

In the areas between absorption shells, the distribution usually follows simple power laws, but the shell structure is in general not something which can be neglected.

Format:

CLUSTER FUNCTION cluster_function [N nmax]

Example:

cluster function 1/n^3 n 15

Doing this will produce a warning since, to compute probability to have a cluster size of 0, one would divide by zero.

5.5.1.1: cluster_function

This function will be evaluated between N=0 to N=nmax-1 at integer and half-integer values.

The cluster size distribution starts at a size of 0, not 1. The reason for this is that most interactions between charged particles and gas molecules result in excitation, rather than ionisation. In the absence of Penning transfers, these interactions will not lead to ionisation electrons. In case you enter a cluster spacing which only takes ionisations, and not excitations, into account, then you have to set the probability at N=0 to 0. This can most easily be done using the Mixed format.

Samples are taken at N, N+0.5 and N+1 and the probability that is assigned for a cluster size of N is the Simpson integral over these 3 points. The rationale for this approach is that it is anticipated that an energy transfer probability divided by work will be entered, so that the derived cluster size is the ratio truncated to the next lower integer, rather than the ratio rounded to the nearest integer.

You don't have to worry about the normalisation.

[There is no default function.]

5.5.1.2: nmax

Values between 1 and MXPAIR are permitted.

If set to 1, then only clusters of size 0 will ge generated. I.e. not a single ionisation electron will be produced.

[Default is MXPAIR, set to 2000 at the time of writing.]

5.5.2: Listing

Please note that the first number is the probability to have a cluster size of 0, i.e. a cluster without ionisation electrons. When a charged particle traverses a gas, most interactions result only in excitation, not in ionisation. If you set a mean number of clusters per cm which only takes clusters into account that contain at least 1 electron, then you have to set the first probability to 0.

Format:

CLUSTER
prob_size0 prob_size1
...
(blank line)

Example:

CLUSTER
0 0 0.1 0.2 0.5
0.2 0.1 0

// Note that the preceding line is left blank

5.5.3: Mixed

Format:

CLUSTER FUNCTION cluster_function [N nmax] OVERLAP-TABLE-AND-FUNCTION
prob_size0 prob_size1
...
(blank line)

Example:

CLUSTER FUNCTION 21.6/N^2 N=200 OVERLAP
0 86 20 10

There has to be a blank line after the cluster sizes. One can also simulate this format by using a Do loop:

cluster
0 86 20 10
For i From 4 To 200 Do
   {21.6/i^2}
Enddo

// Note that the previous line is left blank !

But this would be less efficient since the formula inside the loop (21.6/i^2) is translated each iteration of the loop. Note that there has to be a blank line after Enddo.

A more efficient version of the latter would be:

cluster
0 86 20 10 {21.6/row(200)^2}

// Note that the previous line is blank !

Section 5.6: COMPOSITION

The composition is set by the MAGBOLTZ command and is preserved in gas files (written by WRITE and read with GET). There is therefore no need to use the COMPOSITION command when running Magboltz nor when retrieving Magboltz generated electron transport tables.

The information supplied by this command is only used by the microscopic electron tracking procedures such as DRIFT_MICROSCOPIC_ELECTRON and MICROSCOPIC_AVALANCHE.

This command does not provide the electron transport tables needed by the other electron tracking methods. You will therefore, in general, have to provide electron transport tables (e.g. using TABLE) when using the COMPOSITION statement.

All fractions must be strictly positive. The fractions may add up to any non-zero value - they will be normalised by Magboltz.

Format: see MAGBOLTZ

Example:

composition argon 80 co2 20

Section 5.7: EXTRAPOLATIONS

The EXTRAPOLATIONS command has no effect on extrapolation in 2-dimensional tables, such as those produced by Magboltz when the B field is non-zero. For such tables, polynomial extrapolation is performed with the order set with the INTERPOLATIONS command.

EXTRAPOLATE can be used as synonym for this command.

Format:

EXTRAPOLATIONS item1 method1 item2 method2 ...

Examples:

extrapolate drift: linear, diff: const, town: const
extrapolate drift exp

5.7.1: item

The prefix HIGH- is optional for backwards compatibility. DIFFUSION can be used instead of LONGITUDINAL-DIFFUSION.

5.7.2: method

Constant extrapolation means values for any E/p outside the range of the table are set to the value for the first or last E/p in the table, as appropriate.

In the case of linear and exponential extrapolation the first or last two table points are used as basis for the extrapolation.

Section 5.8: GAS-IDENTIFIER

The MAGBOLTZ and MIX commands set an identification string that contains a description of the gas mixture. It is advisable not to override this string. Instead, one can use the GET_GAS_DATA procedure to obtain the identifier set by these commands, and then add further information to it.

The identification string is displayed in the plots using the COMMENT text representation.

Format:

GAS-IDENTIFIER string

Examples:

GAS-ID "Some gas"

Sets a simple identification string.

temperature 300 K
magboltz argon 50 dme 50
*** Ar++ in Ar, T=300 K, error 1 % (Mason McDaniel I, Beaty 68)
Vector E_Ar_Ar_2 K_Ar_Ar_2
 40   2.49
 50   2.47
 60   2.45
 70   2.42
 80   2.39
 90   2.37
100   2.34
120   2.28
140   2.23
160   2.19
180   2.15
200   2.11

Call get_gas_data(p,t,gasid)
Global E_Ar_Ar_2 = p*E_Ar_Ar_2/(0.010354*t)
Global K_Ar_Ar_2 = K_Ar_Ar_2*1e-6
add ion-mobility K_Ar_Ar_2 vs E_Ar_Ar_2
extrapolations low-ion-mobility constant high-ion-mobility linear
gas-id "{gasid} with Ar<SUP>++</SUP>"

Magboltz is used to compute electron transport properties, and these are complemented with experimental Ar mobility at the same temperature and pressure. The addition is registered in the gas identifier.

Section 5.9: GET

The compact gas description contains electron transport property tables, the ion mobility, cluster size and cluster spacing data, Heed initialisation information, SRIM energy loss, range and straggling tables, the pressure and the temperature. GET overwrites all of these.

Since format version\&nbsp;8, an attempt has been made to maintain backwards compatibility of file formats. Beware however that older formats will as a rule not contain as much information as the newer versions, which may result in the failure of certain newer commands.

Format:

GET file [member]

Example:

GET gas_data.dat gas2

5.9.1: file

5.9.2: member

Section 5.10: HEED

The TEMPERATURE and the PRESSURE should be specified before issuing the HEED command. Defaults are assumed if they follow the HEED command.

Neither temperature nor pressure scaling is applied to the cluster information provided by HEED.

The author of Heed, Igor Smirnov, should be contacted for further information about this program.

Format:

HEED  [ HYDROGEN  fraction ]   [ HELIUM-4  fraction ] ...
      [ NEON  fraction ]       [ ARGON  fraction ] ...
      [ KRYPTON  fraction ]    [ XENON  fraction ] ...

      [ NITROGEN  fraction ]   [ OXYGEN  fraction ] ...

      [ METHANE   fraction ]   [ ETHANE  fraction ] ...
      [ ETHENE  fraction ]     [ ACETYLENE  fraction ]  ...
      [ PROPANE  fraction ]    [ ISOBUTANE  fraction ] ...
      [ NEOPENTANE  fraction ] ...

      [ WATER  fraction ]      [ CO2  fraction ] ...
      [ DME  fraction ]        [ NITROUS-OXIDE  fraction ] ...
      [ AMMONIA  fraction ]    [ SF6 fraction ] ...
      [ CS2 fraction ] ...

      [ CF4  fraction ]        [ C2F4H2  fraction ] ...
      [ C2F5H  fraction ]      [ C3F8 fraction ]

Example:

pressure {3*760}
Heed argon 50 ethane 50

(If you have a 3\&nbsp;atm 50/50 argon-ethane mixture in your chamber.)

Section 5.11: INTERPOLATIONS

By default, the gas tables are interpolated using quadratic Newton polynomials. Use this statement if you wish to select splines, lower order polynomials or higher order polynomials.

The interpolation method is ignored if the gas table contains only a single electric field strength.

INTERPOLATE can be used as a synonym for this command.

Format:

INTERPOLATIONS item1 method1 item2 method2 ...

Examples:

interpolate drift-velocity newton 2, long-diffusion newton 1
int townsend spline

5.11.1: item

5.11.2: method

Spline interpolation leads to smooth looking graphs, but tends to oscillate making the method less suited for numerical calculations. Spline interpolation can not be used on the 2-dimensional gas tables that are produced by programs like Magboltz when a magnetic field is present.

The order of polynomial interpolation must be between 1 and the smallest of the two numbers: 10 and number of table entries - 1. Orders larger than 2 are not recommended.

Formats:

INTERPOLATIONS item SPLINES
INTERPOLATIONS item NEWTON order

Section 5.12: MAGBOLTZ

Contrary to the related MIX instruction, Magboltz takes cross sections for non-elastic processes into account. Furthermore, Magboltz is not limited to the 0th and 1st order terms of the spherical harmonics expansion used by MIX. Magboltz does need considerably more calculation time.

In Garfield up to version\&nbsp;8, this command gave access to both version\&nbsp;1 and version\&nbsp;2 of Magboltz. These programs differed by the integration technique use: ANALYTIC-INTEGRATION for version\&nbsp;1 and MONTE-CARLO-INTEGRATION for version\&nbsp;2. Version\&nbsp;1 was to be preferred for pure noble gases and mixtures of exclusively noble gases, without addition of quenchers or other additives. Version\&nbsp;2, which became default, was recommended for all other pure gases and for all gas mixtures. Even though these older versions of Magboltz did compute the Townsend and attachment coefficients, one used the Imonte program (from the same author) to compute these with better precision.

From Garfield version\&nbsp;9 on, Magboltz version\&nbsp;7 and higher is called. This Magboltz version only does Monte Carlo integration. It can be used for gas mixtures both with and without quenchers, even if the program will be slow for the latter. Magboltz version\&nbsp;7 includes the Imonte functionality - which is therefore no longer needed.

Since Magboltz takes the magnetic field into account to compute the transport properties, the &MAGNETIC section should precede the gas section. If there is a magnetic field, the program computes a drift velocity vector, otherwise a scalar.

Likewise, TEMPERATURE and PRESSURE statements should be issued before invoking Magboltz. If the temperature has not been specified when Magboltz runs, then a default temperature of 300\&nbsp;K will be assumed. No scaling will be applied if the temperature is changed later on. The default pressure is 760\&nbsp;Torr. The transport properties will be scaled according to simple scaling laws if the pressure is modified after the transport properties have been computed. It is not recommended, however, to rely on these scaling laws since these are very approximate.

The author of Magboltz, Steve Biagi, should be contacted for further information about this program.

Format:

MAGBOLTZ [ HYDROGEN frac ] ...
         [ DEUTERIUM frac ] ...
         [ HELIUM-3-ANISOTROPIC frac ] ...
         [ HELIUM-3-ISOTROPIC frac ] ...
         [ HELIUM-4-ANISOTROPIC frac ] ...
         [ HELIUM-4-ISOTROPIC frac ] ...
         [ NEON-ANISOTROPIC frac ] ...
         [ NEON-ISOTROPIC frac ] ...
         [ ARGON-ANISOTROPIC frac ] ...
         [ ARGON-ISOTROPIC frac ] ...
         [ KRYPTON-ANISOTROPIC frac ] ...
         [ KRYPTON-ISOTROPIC frac ] ...
         [ XENON-ANISOTROPIC frac ] ...
         [ XENON-ISOTROPIC frac ] ...
         [ NITROGEN-ANISOTROPIC frac ] ...
         [ NITROGEN-ISOTROPIC frac ] ...
         [ OXYGEN frac ] ...
         [ OZONE frac ] ...
         [ FLUORINE frac ] ...
         [ CAESIUM frac ] ...
         [ MERCURY frac ] ...
         [ METHANE frac ] ...
         [ DEUTERATED-METHANE frac ] ...
         [ ETHANE frac ] ...
         [ ETHENE frac ] ...
         [ ACETYLENE frac ] ...
         [ PROPANE frac ] ...
         [ CYCLOPROPANE frac ] ...
         [ PROPENE frac ] ...
         [ ISOBUTANE frac ] ...
         [ N-BUTANE frac ] ...
         [ NEOPENTANE frac ] ...
         [ N-PENTANE frac ] ...
         [ METHANOL frac ] ...
         [ ETHANOL frac ] ...
         [ PROPANOL frac ] ...
         [ CARBON-MONOXIDE frac ] ...
         [ CARBON-DIOXIDE frac ] ...
         [ WATER frac ] ...
         [ NITRIC-OXIDE frac ] ...
         [ NITROUS-OXIDE frac ] ...
         [ METHYLAL frac ] ...
         [ DME frac ] ...
         [ TRIFLUOROMETHANE frac ] ...
         [ TRIFLUOROBROMOMETHANE frac ] ...
         [ TETRAFLUOROMETHANE frac ] ...
         [ TETRAFLUOROETHANE frac ] ...
         [ HEXAFLUOROETHANE frac ] ...
         [ OCTAFLUOROPROPANE frac ] ...
         [ BORON-TRIFLUORIDE frac ] ...
         [ SULPHUR-HEXAFLUORIDE frac ] ...
         [ AMMONIA frac ] ...
         [ CARBON-DISULPHIDE frac ] ...
         [ CARBONYL-SULPHIDE frac ] ...
         [ HYDROGEN-SULPHIDE frac ] ...
         [ GERMANE frac ] ...
         [ SILANE frac ] ...
         [ REID-STEP frac ] ...
         [ MAXWELL-MODEL frac ] ...
         [ REID-RAMP frac ] ...


         [ [ ELECTRIC-FIELD-RANGE emin emax ] ...
              [ N-E ne ] ...
              [ LINEAR-E-SCALE | LOGARITHMIC-E-SCALE ] | ...
           [ ELECTRIC-FIELD {efield1 efield2 ... | vector} ] ] ...
         [ [ ANGLE-RANGE amin amax ] [ N-ANGLE nangle ] | ...
           [ ANGLE {angle1 angle2 ... | vector} ] ] ...
         [ [ B-FIELD-RANGE bmin bmax ] [ N-B nb ] | ...
           [ B-FIELD {bfield1 bfield2 ... | vector} ] ] ...

         [ NOPLOT-DISTRIBUTION-FUNCTIONS | PLOT-DISTRIBUTION-FUNCTIONS ] ...
         [ NOPLOT-CROSS-SECTIONS | PLOT-CROSS-SECTIONS ] ...
         [ NOKEEP | KEEP ] ...
         [ NOPRINT | PRINT ]

         [ ANALYTIC-INTEGRATION ...
            [ SECOND-ORDER-TERMS | FIRST-ORDER-TERMS | ORDERS n ] ...
            [ NOITERATE-ALPHA | ITERATE-ALPHA ] ...
            [ SWITCH [alpha/pressure] | NOSWITCH ] ...
            [ F0-TRANSVERSE-DIFFUSION | ...
              H1-TRANSVERSE-DIFFUSION | ...
              MEAN-ENERGY-TRANSVERSE-DIFFUSION ] ...
            [ F0-LONGITUDINAL-DIFFUSION | ...
              H1-LONGITUDINAL-DIFFUSION | ...
              G0-LONGITUDINAL-DIFFUSION ] | ...
         [ MONTE-CARLO-INTEGRATION ...
            [ COLLISIONS ncoll ] ] ] ...

         [ MOBILITY mob ]

Example:

magboltz argon 50 ethane 50

(You've a mixture of 50\&nbsp;% argon and 50\&nbsp;% ethane in your chamber, and you trust the default settings for the electric field range, for the magnetic field and for the angles between E and B field as well as the default precision.)

5.12.1: ingredient

5.12.1.1: HYDROGEN

Identifiers

\<UL\>\<LI\>HYDROGEN\<LI\>H2\</UL\>

Structure

H\<SUB\>2\</SUB\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/h2_2001.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Triplet excitation	HYDROGEN-TRIPLET	8.85 eV
Singlet excitation	HYDROGEN-SINGLET	12.0 eV
Ionisation	HYDROGEN-IONISATION	15.427 eV

Last update

2001

Quality

Excellent (5*)

5.12.1.2: DEUTERIUM

Identifiers

\<UL\>\<LI\>DEUTERIUM\<LI\>D2\</UL\>

Structure

D\<SUB\>2\</SUB\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/D2_98.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Triplet excitation	DEUTERIUM-TRIPLET	8.85 eV
Singlet excitation	DEUTERIUM-SINGLET	12.0 eV
Ionisation	DEUTERIUM-IONISATION	15.427 eV

Last update

1998

Quality

Excellent (5*)

5.12.1.3: HELIUM-3-ANISOTROPIC

Identifiers

\<UL\>\<LI\>HELIUM-3\<LI\>HELIUM-3-ANISOTROPIC\</UL\>

Structure

\<SUP\>3\</SUP\>He

Cross section

No plot available (similar to \<SUP\>4\</SUP\>He)

Energy levels

\

Level description	Identifier	Energy [eV]
Triplet excitation	HELIUM-3-TRIPLET	19.82 eV
Singlet excitation	HELIUM-3-SINGLET	20.61 eV
Ionisation	HELIUM-3-IONISATION	24.587 eV

Last update

2002

Quality

Excellent (5*)

5.12.1.4: HELIUM-3-ISOTROPIC

Identifiers

\<UL\>\<LI\>HELIUM-3-ISOTROPIC\</UL\>

Structure

\<SUP\>3\</SUP\>He

Cross section

No plot available (similar to \<SUP\>4\</SUP\>He)

Energy levels

\

Level description	Identifier	Energy [eV]
Triplet excitation	HELIUM-3-ISOTROPIC-TRIPLET	19.82 eV
Singlet excitation	HELIUM-3-ISOTROPIC-SINGLET	20.6 eV
Ionisation	HELIUM-3-ISOTROPIC-IONISATION	24.59 eV

Last update

1992

Quality

Excellent (5*)

5.12.1.5: HELIUM-4-ANISOTROPIC

Identifiers

\<UL\>\<LI\>HELIUM-4\<LI\>HELIUM-4-ANISOTROPIC\</UL\>

Structure

\<SUP\>4\</SUP\>He

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/he2002.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Triplet excitation	HELIUM-4-TRIPLET	19.82 eV
Singlet excitation	HELIUM-4-SINGLET	20.61 eV
Ionisation	HELIUM-4-IONISATION	24.587 eV

Last update

2002

Quality

Best known gas (5*)

5.12.1.6: HELIUM-4-ISOTROPIC

Identifiers

\<UL\>\<LI\>HELIUM-4-ISOTROPIC\</UL\>

Structure

\<SUP\>4\</SUP\>He

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/He_97log.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Triplet excitation	HELIUM-4-ISOTROPIC-TRIPLET	19.82 eV
Singlet excitation	HELIUM-4-ISOTROPIC-SINGLET	20.61 eV
Ionisation	HELIUM-4-ISOTROPIC-IONISATION	24.587 eV

Last update

1997

Quality

Best known gas (5*)

5.12.1.7: NEON-ANISOTROPIC

Identifiers

\<UL\>\<LI\>NEON\<LI\>NEON-ANISOTROPIC\</UL\>

Structure

Ne

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/ne2003.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
1s\<SUB\>5\</SUB\> excitation	NEON-1S5	16.618 eV
1s\<SUB\>4\</SUB\> excitation	NEON-1S4	16.670 eV
1s\<SUB\>3\</SUB\> excitation	NEON-1S3	16.715 eV
1s\<SUB\>2\</SUB\> excitation	NEON-1S2	16.857 eV
2p\<SUB\>2\</SUB\>-2p\<SUB\>10\</SUB\> excitations	NEON-2P2-2P10	18.381 eV
2p\<SUB\>1\</SUB\> excitation	NEON-2P1	18.965 eV
2s excitations	NEON-2S	19.663 eV
3d+3s excitations	NEON-3D-3S	20.033 eV
3p excitations	NEON-3P	20.200 eV
Ionisation	NEON-IONISATION	21.56 eV

Last update

2003

Quality

Excellent (5*)

5.12.1.8: NEON-ISOTROPIC

Identifiers

\<UL\>\<LI\>NEON-ISOTROPIC\</UL\>

Structure

Ne

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/Ne_97.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
1s\<SUB\>5\</SUB\> excitation	NEON-ISOTROPIC-1S5	16.618 eV
1s\<SUB\>4\</SUB\> excitation	NEON-ISOTROPIC-1S4	16.670 eV
1s\<SUB\>3\</SUB\> excitation	NEON-ISOTROPIC-1S3	16.715 eV
1s\<SUB\>2\</SUB\> excitation	NEON-ISOTROPIC-1S2	16.857 eV
2p\<SUB\>2\</SUB\>-2p\<SUB\>10\</SUB\> excitations	NEON-ISOTROPIC-2P2-2P10	18.381 eV
2p\<SUB\>1\</SUB\> excitation	NEON-ISOTROPIC-2P1	18.965 eV
2s excitations	NEON-ISOTROPIC-2S	19.663 eV
3d+3s excitations	NEON-ISOTROPIC-3D-3S	20.033 eV
3p excitations	NEON-ISOTROPIC-3P	20.200 eV
Ionisation	NEON-ISOTROPIC-IONISATION	21.56 eV

Last update

2003

Quality

Excellent (5*)

5.12.1.9: ARGON-ANISOTROPIC

Identifiers

\<UL\>\<LI\>ARGON\<LI\>ARGON-ANISOTROPIC\</UL\>

Structure

Ar

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/ar2002.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
s-level excitations	ARGON-S	11.55 eV
p-level excitations	ARGON-P	13.0 eV
d-level excitations	ARGON-D	14.0 eV
Ionisation	ARGON-IONISATION	15.70 eV

Last update

2002

Quality

Excellent (5*)

5.12.1.10: ARGON-ISOTROPIC

Identifiers

\<UL\>\<LI\>ARGON-ISOTROPIC\</UL\>

Structure

Ar

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/Ar_97lg.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
s-level excitation	ARGON-ISOTROPIC-S	11.55 eV
p-level excitation	ARGON-ISOTROPIC-P	13.0 eV
d-level excitation	ARGON-ISOTROPIC-D	14.0 eV
Ionisation	ARGON-ISOTROPIC-IONISATION	15.70 eV

Last update

2002

Quality

Excellent (5*)

5.12.1.11: KRYPTON-ANISOTROPIC

Identifiers

\<UL\>\<LI\>KRYPTON\<LI\>KRYPTON-ANISOTROPIC\</UL\>

Structure

Kr

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/kr2002.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
s-level excitations	KRYPTON-S	9.915 eV
p-level excitations	KRYPTON-P	11.304 eV
d+p-level excitations	KRYPTON-D-P	11.998 eV
Other excitations	KRYPTON-REST	12.75 eV
Ionisation	KRYPTON-IONISATION	13.996 eV

Last update

2002

Quality

Very good (4*)

5.12.1.12: KRYPTON-ISOTROPIC

Identifiers

\<UL\>\<LI\>KRYPTON-ISOTROPIC\</UL\>

Structure

Kr

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/Kr_log.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
s-level excitations	KRYPTON-ISOTROPIC-S	9.915 eV
p-level excitations	KRYPTON-ISOTROPIC-P	11.304 eV
d+p-level excitations	KRYPTON-ISOTROPIC-D-P	11.998 eV
Other excitations	KRYPTON-ISOTROPIC-REST	12.75 eV
Ionisation	KRYPTON-ISOTROPIC-IONISATION	13.996 eV

Last update

2001

Quality

Very good (4*)

5.12.1.13: XENON-ANISOTROPIC

Identifiers

\<UL\>\<LI\>XENON\<LI\>XENON-ANISOTROPIC\</UL\>

Structure

Xe

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/xe2002.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
8.315 eV excitation	XENON-1	8.315 eV
9.447 eV excitation	XENON-2	9.447 eV
9.917 eV excitation	XENON-3	9.917 eV
11.70 eV excitation	XENON-4	11.70 eV
Ionisation	XENON-IONISATION	12.13 eV

Last update

2003

Quality

Very good (4*)

5.12.1.14: XENON-ISOTROPIC

Identifiers

\<UL\>\<LI\>XENON-ISOTROPIC\</UL\>

Structure

Xe

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/Xe_log.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
8.315 eV excitation	XENON-ISOTROPIC-1	8.315 eV
9.447 eV excitation	XENON-ISOTROPIC-2	9.447 eV
9.917 eV excitation	XENON-ISOTROPIC-3	9.917 eV
11.70 eV excitation	XENON-ISOTROPIC-4	11.70 eV
Ionisation	XENON-ISOTROPIC-IONISATION	12.13 eV

Last update

2003

Quality

Very good (4*)

5.12.1.15: NITROGEN-ANISOTROPIC

Identifiers

\<UL\>\<LI\>NITROGEN\<LI\>NITROGEN-ANISOTROPIC\<LI\>N2\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_n2.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/n22003.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Triplet 1 excitation	NITROGEN-TRIPLET-1	6.17 eV
Triplet 3 excitation	NITROGEN-TRIPLET-3	7.35 eV
Triplet 5 excitation	NITROGEN-TRIPLET-5	7.80 eV
Triplet 7 excitation	NITROGEN-TRIPLET-7	11.03 eV
Triplet 8 excitation	NITROGEN-TRIPLET-8	11.87 eV
Singlet 2 excitation	NITROGEN-SINGLET-2	8.55 eV
Singlet 5 excitation	NITROGEN-SINGLET-5	13.0 eV
Ionisation	NITROGEN-IONISATION	15.60 eV

Note

The lowest triplet A\<SUP\>3\</SUP\>\&Sigma; level at 6.2\&nbsp;eV is metastable with a long life. The level can not be quenched by Penning transfer in most of the typical quenchers. So it floats around the chamber as an excited neutral and, on collision with a metal or insulating surface, will remove an electron into the gas and de-excite. The resultant electron current is not time-correlated with the production mechanism since the motion of the neutral excited nitrogen is very slow and can occur many milliseconds or seconds later. (Steve Biagi, January 2009.)

Last update

2004

Quality

Very good (4*)

5.12.1.16: NITROGEN-ISOTROPIC

Identifiers

\<UL\>\<LI\>NITROGEN-ISOTROPIC\<LI\>N2-ISOTROPIC\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_n2.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/N2_pp.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Triplet 1 excitation	NITROGEN-ISOTROPIC-TRIPLET-1	6.17 eV
Triplet 3 excitation	NITROGEN-ISOTROPIC-TRIPLET-3	7.35 eV
Triplet 5 excitation	NITROGEN-ISOTROPIC-TRIPLET-5	7.80 eV
Triplet 7 excitation	NITROGEN-ISOTROPIC-TRIPLET-7	11.03 eV
Triplet 8 excitation	NITROGEN-ISOTROPIC-TRIPLET-8	11.87 eV
Singlet 2 excitation	NITROGEN-ISOTROPIC-SINGLET-2	8.55 eV
Singlet 5 excitation	NITROGEN-ISOTROPIC-SINGLET-5	13.0 eV
Ionisation	NITROGEN-ISOTROPIC-IONISATION	15.60 eV

Note

The lowest triplet A\<SUP\>3\</SUP\>\&Sigma; level at 6.2\&nbsp;eV is metastable with a long life. The level can not be quenched by Penning transfer in most of the typical quenchers. So it floats around the chamber as an excited neutral and, on collision with a metal or insulating surface, will remove an electron into the gas and de-excite. The resultant electron current is not time-correlated with the production mechanism since the motion of the neutral excited nitrogen is very slow and can occur many milliseconds or seconds later. (Steve Biagi, January 2009.)

Last update

2004

Quality

Very good (4*)

5.12.1.17: OXYGEN

Identifiers

\<UL\>\<LI\>OXYGEN\<LI\>O2\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_o2.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/ox2004.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Excitation A1	OXYGEN-A1	0.977 eV
Excitation B1	OXYGEN-B1	1.627 eV
Excitation C1+C3	OXYGEN-C1-C3	4.50 eV
Dissociation A3	OXYGEN-DISSOCIATION-A3	6.10 eV
Dissociation B3	OXYGEN-DISSOCIATION-B3	8.40 eV
Other excitations	OXYGEN-REST	9.30 eV
Ionisation	OXYGEN-IONISATION	12.072 eV

Last update

2004

Quality

Very good (4*)

5.12.1.18: OZONE

Identifiers

\<UL\>\<LI\>OZONE\<LI\>O3\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_ozone.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/oz2002.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Excitation Chappuis	OZONE-CHAPPUIS	1.50 eV
Excitation Hartley	OZONE-HARTLEY	4.85 eV
Other excitations	OZONE-REST	9.00 eV
Ionisation	OZONE-IONISATION	12.75 eV

Last update

2002

Quality

Good (3*)

5.12.1.19: FLUORINE

Identifiers

\<UL\>\<LI\>FLUORINE\<LI\>F2\</UL\>

Structure

F\<SUB\>2\</SUB\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/f2.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
3.16 eV excitation	FLUORINE-1	3.16 eV
4.34 eV excitation	FLUORINE-2	4.34 eV
11.57 eV excitation	FLUORINE-3	11.57 eV
13.08 eV excitation	FLUORINE-4	13.08 eV
Ionisation	FLUORINE-IONISATION	15.69 eV

Last update

Not known

Quality

Low (2*)

5.12.1.20: CAESIUM

Identifiers

\<UL\>\<LI\>CAESIUM\<LI\>CESIUM\<LI\>CS\</UL\>

Structure

Cs

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/cesium.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
P 1/2 excitation	CAESIUM-P12	1.3859 eV
P 3/2 excitation	CAESIUM-P32	1.4546 eV
D 3/2 + D 5/2 excitation	CAESIUM-D32-D52	1.7977 eV
S 1/2 excitation	CAESIUM-S12	2.2981 eV
Other excitations	CAESIUM-REST	2.6986 eV
Ionisation	CAESIUM-IONISATION	3.8926 eV

Last update

2001

Quality

Low (2*)

5.12.1.21: MERCURY

Identifiers

\<UL\>\<LI\>MERCURY\<LI\>HG\<LI\>HG2\</UL\>

Structure

Hg, Hg\<SUB\>2\</SUB\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/hg2003.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Dimer super excitation	MERCURY-DIMER-SUPER	-0.040 eV
Dimer excitation	MERCURY-DIMER	0.040 eV
3P0 excitation	MERCURY-3P0	4.667 eV
3P1 excitation	MERCURY-3P1	4.887 eV
3P2 excitation	MERCURY-3P2	5.461 eV
1P1 excitation	MERCURY-1P1	6.704 eV
1S0 excitation	MERCURY-1S0	7.926 eV
Other excitations	MERCURY-REST	8.60 eV
Ionisation	MERCURY-IONISATION	10.4375 eV

Last update

2003

Quality

Low (2*)

5.12.1.22: METHANE

Identifiers

\<UL\>\<LI\>METHANE\<LI\>CH4\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_methane.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/ch42004.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
9 eV dissociation	METHANE-DISSOCIATION-1	9.0 eV
10 eV dissociation	METHANE-DISSOCIATION-2	10.0 eV
11 eV dissociation	METHANE-DISSOCIATION-3	11.0 eV
11.8 eV dissociation	METHANE-DISSOCIATION-4	11.8 eV
Ionisation	METHANE-IONISATION	12.99 eV

Last update

2004

Quality

Excellent (5*)

5.12.1.23: DEUTERATED-METHANE

Structure:

Cross section:

Alternative names:

• DEUTERATED-METHANE
• DH4

Excited states:

5.12.1.24: ETHANE

Identifiers

\<UL\>\<LI\>ETHANE\<LI\>C2H6\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_ethane.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/c2h6.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
8.2 eV excitation	ETHANE-1	8.2 eV
10.3 eV excitation	ETHANE-2	10.3 eV
17.0 eV excitation	ETHANE-3	17.0 eV
Ionisation	ETHANE-IONISATION	11.52 eV

Last update

1999

Quality

Excellent (5*)

5.12.1.25: ETHENE

Structure:

Cross section:

Alternative names:

• ETHENE
• ETHYLENE
• C2H4

Excited states:

5.12.1.26: ACETYLENE

Structure:

Cross section:

Alternative names:

• ACETYLENE
• ETHYNE
• C2H2

Excited states:

5.12.1.27: PROPANE

Identifiers

\<UL\>\<LI\>PROPANE\<LI\>C3H8\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_propane.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/C3H8_95.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
7.7 eV excitation	PROPANE-1	7.7 eV
10.0 eV excitation	PROPANE-2	10.0 eV
17.0 eV excitation	PROPANE-3	17.0 eV
Ionisation	PROPANE-IONISATION	10.95 eV

Last update

1999

Quality

Very good (4*)

5.12.1.28: CYCLOPROPANE

Structure:

Cross section:

Alternative names:

• CYCLOPROPANE
• CYCLO-PROPANE
• CYCLO-C3H6

Excited states:

5.12.1.29: PROPENE

Structure:

Cross section:

Alternative names:

• PROPENE
• PROPYLENE
• C3H6

Excited states:

5.12.1.30: ISOBUTANE

Identifiers

\<UL\>\<LI\>ISOBUTANE\<LI\>IC4H10\<LI\>ISO-C4H10\<LI\>C4H10\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_isobutane.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/C4H10_95.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
7.4 eV excitation	ISOBUTANE-1	7.40 eV
9.7 eV excitation	ISOBUTANE-2	9.70 eV
17 eV excitation	ISOBUTANE-3	17.0 eV
Ionisation	ISOBUTANE-IONISATION	10.67 eV

Last update

1999

Quality

Very good (4*)

5.12.1.31: N-BUTANE

Structure:

Cross section:

Alternative names:

• N-BUTANE
• N-C4H10

Excited states:

5.12.1.32: NEOPENTANE

Structure:

Cross section:

Alternative names:

• NEOPENTANE
• NEO-PENTANE
• NEO-C5H12
• C5H12

Excited states:

5.12.1.33: N-PENTANE

Structure:

Cross section:

Alternative names:

• N-PENTANE
• N-C5H12

Excited states:

5.12.1.34: METHANOL

Structure:

Cross section:

Alternative names:

• METHANOL
• METHYL-ALCOHOL
• WOOD-ALCOHOL
• CH3OH

Excited states:

5.12.1.35: ETHANOL

Structure:

Cross section:

Alternative names:

• ETHANOL
• ETHYL-ALCOHOL
• GRAIN-ALCOHOL
• C2H5OH

Excited states:

5.12.1.36: PROPANOL

Structure:

Cross section:

Alternative names:

• PROPANOL
• 2-PROPANOL
• ISO-PROPANOL
• ISOPROPANOL
• ISOPROPYL-ALCOHOL
• C3H7OH

Excited states:

5.12.1.37: CARBON-MONOXIDE

Structure:

Cross section:

Alternative names:

• CARBON-MONOXIDE
• CO

Excited states:

5.12.1.38: CARBON-DIOXIDE

Identifiers

\<UL\>\<LI\>CARBON-DIOXIDE\<LI\>CO2\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_co2.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/co22004.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
7.9 eV excitation	CO2-1	7.9 eV
8.9 eV excitation	CO2-2	8.9 eV
10.5 eV excitation	CO2-3	10.5 eV
12.2 eV excitation	CO2-4	12.2 eV
13.2 eV excitation	CO2-5	13.2 eV
15.0 eV excitation	CO2-6	15.0 eV
Ionisation	CO2-IONISATION	13.773 eV

Last update

2004

Quality

Excellent (5*)

5.12.1.39: WATER

Identifiers

\<UL\>\<LI\>WATER\<LI\>WATER-VAPOUR\<LI\>H2O\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_water.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/h2o2004.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
4.20 eV excitation	H2O-1	4.20 eV
7.40 eV excitation	H2O-2	7.40 eV
13.1 eV excitation	H2O-3	13.1 eV
Ionisation	H2O-IONISATION	12.61 eV

Last update

2004

Quality

Very good (4*)

5.12.1.40: NITRIC-OXIDE

Identifiers

\<UL\>\<LI\>NITRIC-OXIDE\<LI\>NITROGEN-MONOXIDE\<LI\>NO\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_nitric_oxide.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/NO_95.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
6.10 eV excitation	NITRIC-OXIDE-1	6.10 eV
Ionisation	NITRIC-OXIDE-IONISATION	9.2644 eV

Last update

1995

Quality

Low (2*)

5.12.1.41: NITROUS-OXIDE

Identifiers

\<UL\>\<LI\>NITROUS-OXIDE\<LI\>DINITROGEN-MONOXIDE\<LI\>LAUGHING-GAS\<LI\>N2O\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_nitrous_oxide.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/n2o2004.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
4.06 eV excitation	NITROUS-OXIDE-1	4.06 eV
8.50 eV excitation	NITROUS-OXIDE-2	8.50 eV
9.60 eV excitation	NITROUS-OXIDE-3	9.60 eV
Ionisation	NITROUS-OXIDE-IONISATION	12.886 eV

Last update

2004

Quality

Very good (4*)

5.12.1.42: METHYLAL

Identifiers

\<UL\>\<LI\>METHYLAL\<LI\>METHYLAL-HOT\<LI\>DIMETHOXYMETHANE\<LI\>DMM\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_dmm.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/methylal.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
6.3 eV excitation	METHYLAL-1	6.3 eV
8.3 eV excitation	METHYLAL-2	8.3 eV
Ionisation	METHYLAL-IONISATION	10.0 eV

Last update

1988

Quality

Low (2*)

5.12.1.43: DME

Identifiers

\<UL\>\<LI\>DME\<LI\>DIMETHYL-ETHER\<LI\>METHOXYMETHANE\<LI\>METHYL-ETHER\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_dme.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/DME_97.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
7.7 eV excitation	DME-1	7.70 eV
8.5 eV excitation	DME-2	8.50 eV
Ionisation	DME-IONISATION	10.04 eV

Last update

1998

Quality

Very good (4*)

5.12.1.44: TRIFLUOROMETHANE

Structure:

Cross section:

Alternative names:

• TRIFLUOROMETHANE
• FREON-23
• CHF3

Excited states:

5.12.1.45: TRIFLUOROBROMOMETHANE

Structure:

Cross section:

Alternative names:

• TRIFLUOROBROMOMETHANE
• HALON-1301
• FREON-13B1
• CF3BR

Excited states:

5.12.1.46: TETRAFLUOROMETHANE

Identifiers

\<UL\>\<LI\>CF4\<LI\>FREON-14\<LI\>FREON\<LI\>TETRAFLUOROMETHANE\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_freon.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/cf4_2001.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Dissociation	CF4-DISSOCIATION	12.5 eV
Ionisation	CF4-IONISATION	15.90 eV

Last update

2001

Quality

Excellent (5*)

5.12.1.47: TETRAFLUOROETHANE

Structure:

Cross section:

Alternative names:

• TETRAFLUOROETHANE
• C2H2F4
• C2F4H2
• FREON-134
• FREON-134-A
• PENTAFLUOROETHANE
• C2HF5
• C2F5H
• FREON-125
• ZYRON-125

Excited states:

5.12.1.48: PENTAFLUOROETHANE

5.12.1.49: HEXAFLUOROETHANE

Structure:

Cross section:

Alternative names:

• HEXAFLUOROETHANE
• C2F6
• FREON-116
• ZYRON-116
• ZYRON-116-N5

Excited states:

5.12.1.50: OCTAFLUOROPROPANE

Structure:

Cross section:

Alternative names:

• OCTAFLUOROPROPANE
• R218
• FREON-218
• PERFLUOROPROPANE
• RC-218
• PFC-218

Excited states:

5.12.1.51: BORON-TRIFLUORIDE

Identifiers

\<UL\>\<LI\>BF3\<LI\>BORON-TRIFLUORIDE\</UL\>

Structure

\<IMG SRC='\http://cern.ch/magboltz/cross/formula_borontrifluoride.png'\>

Cross section

\<IMG SRC='\http://cern.ch/magboltz/cross/bf3.png'\>

Energy levels

\

Level description	Identifier	Energy [eV]
Excitation	BF3-EXCITATION	10.0 eV
Ionisation	BF3-IONISATION	15.56 eV

Last update

2001

Quality

Very good (4*)

5.12.1.52: SULPHUR-HEXAFLUORIDE

Structure:

Cross section:

Alternative names:

• SULPHUR-HEXAFLUORIDE
• SULFUR-HEXAFLUORIDE
• SF6

Excited states:

5.12.1.53: AMMONIA

Structure:

Cross section:

Alternative names:

• AMMONIA
• NH3

Excited states:

5.12.1.54: CARBON-DISULPHIDE

Structure:

Cross section:

Alternative names:

• CARBON-DISULPHIDE
• CARBON-DISULFIDE
• CS2

Excited states:

5.12.1.55: CARBONYL-SULPHIDE

Structure:

Cross section:

Alternative names:

• CARBONYL-SULPHIDE
• CARBONYL-SULFIDE
• COS

Excited states:

5.12.1.56: HYDROGEN-SULPHIDE

Structure:

Cross section:

Alternative names:

• HYDROGEN-SULPHIDE
• HYDROGEN-SULFIDE
• HEPATIC-ACID
• SEWER-GAS
• SULFUR-HYDRIDE
• DIHYDROGEN-MONOSULFIDE
• DIHYDROGEN-MONOSULPHIDE
• SULPHUR-HYDRIDE
• STINK-DAMP
• SULFURATED-HYDROGEN
• H2S

Excited states:

5.12.1.57: GERMANE

Structure:

Cross section:

Alternative names:

• GERMANE
• GERMANIUM-HYDRIDE
• GERMANIUM-TETRAHYDRIDE
• GERMANOMETHANE
• MONOGERMANE
• GEH4

Excited states:

5.12.1.58: SILANE

Structure:

Cross section:

Alternative names:

• SILANE
• SILICON-HYDRIDE
• SILICON-TETRAHYDRIDE
• SILICANE
• MONOSILANE
• SIH4

Excited states:

5.12.1.59: REID-STEP

5.12.1.60: REID-RAMP

5.12.1.61: MAXWELL-MODEL

5.12.2: frac

The sum of the fractions is normalised - in the examples, fractions usually add up to 1 or to 100, but this is not mandatory.

[Each fraction is 0 by default.]

5.12.3: ELECTRIC-FIELD

• To request calculations for a range, use the keyword ELECTRIC-FIELD-RANGE followed by a minimum and a maximum electric field specified in V/cm, or use the keyword E/P-RANGE followed by a minimum and a maximum E/p in V/cm.Torr.

  In either case, you can set the number of points with N-E or N-E/P (which are synonyms) and you have the choice between linear and logarithmic spacing of the points.

• To request transport properties for a set of fields, use the ELECTRIC-FIELD or E/P keyword followed either by a list of fields or by the name of a Matrix that contains the field values.

  In either case, ensure that all fields are strictly positive and that they are in strictly increasing order.

Make sure that the all fields present in your chamber are covered by the table and do not rely on the EXTRAPOLATIONS. Pay particular attention to the region in the immediate vicinity of wires. Use e.g. the field section CHECK WIRES commands to determine the field there.

Try to be reasonable when selecting the number of electric fields at which you run Magboltz. On the one hand the number of points must be large enough so as to represent any fine structure that may be present in the transport properties. On the other hand, an excessively large number of points may lead to oscillations in the interpolation.

It is permissible to request transport properties for only a single field, for instance to study the dependence of the transverse diffusion on the magnetic field. The interpolation methods need not be specified in this case and only constant extrapolations can be used.

If you ask for a small number of points, e.g. 2, then you can only request low order INTERPOLATIONS.

[By default E ranges from 100\&nbsp;V/cm to 100000\&nbsp;V/cm in 20 logarithmically spaced steps.]

5.12.4: B-FIELD

You can either ask Magboltz to compute the transport properties at evenly spaced magnetic fields within a range or for a set of magnetic fields that you specify.

• To ask for a range, you use the MAGNETIC-FIELD-RANGE keyword followed by a minimum and a maximum magnetic field specified in Tesla, irrespective of the units used when entering the magnetic field.

  You can set the number of points with N-B.

• To request transport properties for a set of fields, use the MAGNETIC-FIELD keyword followed either by a list of fields or by the name of a Matrix that contains the field values.

  In either case, ensure that the fields are expressed in Tesla, also be sure that they are strictly positive.

If you ask for only 1 magnetic field strength and only 1 angle between E and B, then Magboltz will generate a 1-dimensional table for which you have greater control over the INTERPOLATIONS and EXTRAPOLATIONS methods.

These parameters can not be used if there is no magnetic field.

[If the magnetic field can be determined to be constant or zero, then Magboltz by default only computes a table for the magnetic field that is present in the chamber. If the B field is not constant, but of known range, then Magboltz will by default be run for 6 magnetic fields ranging from the minimum field to the maximum field present in the chamber. In all other cases, it will compute tables for 0, 1, 2, 3, 4 and 5 T.]

5.12.5: ANGLE

You can either ask Magboltz to compute the transport properties for angles between E and B that are evenly spaced over a range, or for a user-specified set of angles between the 2 fields:

• To ask for a range, you use the ANGLE-RANGE keyword followed by a minimum and a maximum angle in degrees.

  Ensure that the range is entirely contained in [0\&deg;,\&nbsp;90\&deg;].

  You can set the number of angles with N-ANGLES.

• To request transport properties for a set of angles, use the ANGLES keyword followed either by a list of angles or by the name of a Matrix that contains the angles.

  In either case, ensure that the angles are expressed in degrees, also be sure that they are in the range [0\&deg;,\&nbsp;90\&deg;].

  It is advisable to use this format, with ANGLE=90, if your chamber is such that E is always perpendicular to B.

  It is bad practice to set ANGLE=0 in TPCs where E is parallel with B in the drift volume. Other orientations occur in the read-out chambers, and these orientations have impact on the resolution of the TPC.

If you ask for only 1 magnetic field strength and only 1 angle between E and B, then Magboltz will generate a 1-dimensional table for which you have greater control over the INTERPOLATIONS and EXTRAPOLATIONS methods.

These parameters can not be used if there is no magnetic field.

[Magboltz will, if B is non-zero, by default be asked to compute tables for angles of 0\&deg;, 30\&deg;, 60\&deg; and 90\&deg; between the E and B field.]

5.12.6: PLOT-DISTRIBUTION-FUNCTIONS

• When using analytic integration, which is only available with Garfield versions\&nbsp;7 and earlier, F0, F1, F2 and F3 will be plotted. Such plots are useful to understand the behaviour of the drift velocity, which is dominated by the first anisotropic term F1 and the diffusion, which depends mostly on the isotropic term F0.

  Keep in mind that Magboltz only computes F2 and F3 on request: to get F2 and F3 you need to request SECOND-ORDER-TERMS (or ORDERS 2) and for a reasonably accurate F3 you should specify ORDERS 3. Both are incompatible with the option ITERATE-ALPHA which enables a more precise computation of the Townsend coefficient.

  F0 is plotted with representation FUNCTION-1, F1 as FUNCTION-2, F2 as FUNCTION-3 and F3 as FUNCTION-4.

• When using Monte Carlo integration, the energy distribution function is not expanded in a series, and only a single graph is displayed.

  This function is plotted with representation FUNCTION-1,

[This option is off by default, but it is switched on automatically in case there are concerns about the validity of the energy range.]

5.12.7: PLOT-CROSS-SECTIONS

Plotted is the quantity used inside Magboltz: the stp cross section scaled by pressure and temperature, multiplied with the Loschmidt number - a quantity that can be interpreted as the reciprocal of the mean free path.

This option is provided to enable a rapid inspection of the cross sections. The KEEP option is recommended to make better quality graphs.

The total cross section is plotted with representation FUNCTION-1, the elastic cross section with FUNCTION-2, the attachment cross section with FUNCTION-3 and the ionisation cross sections for the various components with FUNCTION-4.

[This option is off by default.]

5.12.8: KEEP

The energy range over which these quantities are stored is set by the Magboltz program so as to obtain optimal accuracy for the calculation of the transport parameters. This range can not be set directly from the command line. However, the maximum energy is strongly influenced by the electric field, which can therefore be used to select the range.

The names of the global variables are shown in the table below. In order not to overwrite parameters from earlier calculations, a sequential number "n" is appended to the name. The names are displayed while the command executes.

Cross sections are given for the temperature and pressure that was specified in the gas section (or that was default).

For the conversion from cross section, given in cm\&sup2;, to mean free path, one uses the relation (the constant is known as Loschmidt number):

\λ = 1 / (L \× \σ)
L = 2.6867775 \&times; 10\<SUP\>19\</SUP\> molecules / cm\&sup3;

Example 1:

&GAS
magboltz argon 80 co2 1 coll 20 e-field 20000 keep
!options log-x log-y
Call plot_frame(0.01,1e-18,100,2e-15, ...
   `Electron energy [eV]`, ...
   `Cross section [cm2]`, ...
   `Cross section in argon 90 % CO2 20 %`)
Call plot_line(e_1,cst_1,`function-1`)       // Total
Call plot_line(e_1,cse_1,`function-2`)       // Elastic
Call plot_line(e_1,csa_1,`function-3`)       // Attachment
Call plot_line(e_1,csi_1,`function-4`)       // Ionisation
Call plot_end

Example 2:

&GAS
magboltz argon 100   co2   0   coll 20 e-field 200 keep
magboltz argon  99.5 co2   0.5 coll 20 e-field 200 keep
magboltz argon  99   co2   1   coll 20 e-field 200 keep
magboltz argon  98   co2   2   coll 20 e-field 200 keep
magboltz argon  95   co2   5   coll 20 e-field 200 keep
magboltz argon  90   co2  10   coll 20 e-field 200 keep
magboltz argon  50   co2  50   coll 20 e-field 200 keep
magboltz argon   0   co2 100   coll 20 e-field 200 keep
!options lin-x lin-y
Call plot_frame(0,0,6,1, ...
   `Electron energy [eV]`, ...
   `Energy distribution [normalised]`, ...
   `Electron energy in argon CO2 mixtures`)
Call plot_line(e_1,f_1,`function-1`)
Call plot_line(e_2,f_2,`function-2`)
Call plot_line(e_3,f_3,`function-3`)
Call plot_line(e_4,f_4,`function-4`)
Call plot_line(e_5,f_5,`function-5`)
Call plot_line(e_6,f_6,`function-6`)
Call plot_line(e_7,f_7,`function-7`)
Call plot_line(e_8,f_8,`function-1`)
Call plot_end

[This option is not on by default.]

5.12.9: ANALYTIC-INTEGRATION

This option, which is not default, is provided mainly for backwards compatibility, and only in Garfield up to version\&nbsp;8. Monte Carlo integration is currently believed to be superior for all gas mixtures. Analytic integration may still be the method of choice for a pure noble gas.

Several anisotropic gases can not be used when analytic integration is requested.

This option does not exist anymore in Garfield versions\&nbsp;9 and higher, which call Magboltz version\&nbsp;7 and higher. Magboltz version\&nbsp;7 can deal with pure noble gases - but it will be very slow.

5.12.9.1: ORDERS

Values larger than 1 are not compatible with ITERATE-ALPHA, this setting is overruled by the SWITCH option.

This option can only be used with ANALYTIC-INTEGRATION integration.

[Default: n=2, equivalent to SECOND-ORDER-TERMS.]

5.12.9.2: SECOND-ORDER-TERMS

SWITCH overrules this selection.

HIGH-PRECISION is synonymous to SECOND-ORDER-TERMS.

This option can only be used with ANALYTIC-INTEGRATION integration, available only in Garfield version \&nbsp; and earlier.

[This is the default order, but is overruled by SWITCH.]

5.12.9.3: FIRST-ORDER-TERMS

LOW-PRECISION is synonymous to FIRST-ORDER-TERMS.

This option can only be used with ANALYTIC-INTEGRATION integration, available only in Garfield version\&nbsp;7 and earlier.

[The default is SECOND-ORDER-TERMS.]

5.12.9.4: ITERATE-ALPHA

This option can only be used with ANALYTIC-INTEGRATION integration, available only in Garfield version\&nbsp;7 and earlier.

[This is not default.]

5.12.9.5: SWITCH

If \&alpha;/pressure is smaller than the threshold, the quantities are computed with SECOND-ORDER-TERMS, NOITERATE-ALPHA

Otherwise, they are computed with FIRST-ORDER-TERMS, ITERATE-ALPHA.

This guarantees that the drift velocity, diffusion and Lorentz angle are accurate at low field values, which is where they matter most, whereas the Townsend coefficient is accurate at higher field values, at the price of a somewhat reduced accuracy for the other quantities.

This option can only be used with ANALYTIC-INTEGRATION integration, available only in Garfield version\&nbsp;7 and earlier.

[This option is default, \&alpha;/pressure is set to 50/pressure.]

5.12.9.6: diffusion

• The method from the textbook of Huxley and Crompton, for both the transverse and the longitudinal diffusion, either with the F0 or the H1 distribution functions.

  These formulae are only valid when the approximation that the longitudinal and transverse diffusion are equal is true. This is of course never true, but one can get a correction to the longitudinal diffusion from the ratio of the longitudinal to transverse diffusion without the magnetic field in the given gas at the E-field of interest. [from Steve Biagi]

  These diffusion coefficients are obtained when you specify F0-TRANSVERSE-DIFFUSION, H1-TRANSVERSE-DIFFUSION, F0-LONGITUDINAL-DIFFUSION and H1-LONGITUDINAL-DIFFUSION. The correction to the longitudinal diffusion is applied, using the G0 estimate of the longitudinal diffusion.

  F0-TRANSVERSE-DIFFUSION is default.

• For the transverse diffusion, an alternative estimate based on the mean energy, computed with F0, is offered.

• For the longitudinal diffusion, Magboltz computes on request a more accurate value using the so-called G0 functions. This is the default.

These options can only be used with ANALYTIC-INTEGRATION integration, available only in Garfield version\&nbsp;7 and earlier.

5.12.10: MONTE-CARLO-INTEGRATION

This technique, which is believed to be more accurate than analytic integration for nearly all gas mixtures, is default. Pure noble gases seem to be the only exception to this rule.

Garfield up to version\&nbsp;8 maintained an interface to both the analytic integration method from Magboltz version\&nbsp;1 and the Monte Carlo method from Magboltz version\&nbsp;2. Garfield version\&nbsp;9 is interfaced only with Magboltz version\&nbsp;7, which uses Monte Carlo techniques, since the format of the gas descriptions used by this Magboltz version is no longer compatible with Magboltz version\&nbsp;1.

[Monte Carlo integration is default.]

5.12.10.1: COLLISIONS

Low values (e.g. 2-5) are suitable for mixtures than contain substantial amounts of quenchers. Nearly pure noble gases call for larger values (e.g. 10-20) while very large values (100 and more) are needed for pure noble gases. But in the latter case, it is preferable to use Magboltz\&nbsp;1 (see ANALYTIC-INTEGRATION).

The statistical accuracy of the drift velocity calculation improves with the square root of this parameter, while the CPU time consumption increases linearly. Since the accuracy depends on the gas mixture and on the field, it may be worthwhile in critical applications to estimate the statistical error of the Magboltz calculations for a given gas and a given field by repeatedly calculating the transport parameters:

Call book_histogram(vhist,50)
Call book_histogram(dlhist,50)
Call book_histogram(dthist,50)
Global nrndm=200
For irndm From 1 To nrndm Do
   Say "Iteration {irndm}/{nrndm}"
   &GAS
   magboltz argon 90 methane 10 coll 5 e-field 125

   &MAIN
   Call drift_velocity(125,0,0,v)
   Call fill_histogram(vhist,v)
   Call transverse_diffusion(125,0,0,dt)
   Call fill_histogram(dthist,10000*dt)
   Call longitudinal_diffusion(125,0,0,dl)
   Call fill_histogram(dlhist,10000*dl)
Enddo

Call plot_histogram(vhist,`v<SUB>D</SUB> [cm/microsec]`,`Drift velocity`)
Call plot_end
Call plot_histogram(dthist,`&sigma;<SUB>T</SUB> [micron for 1 cm]`, ...
   `Transverse diffusion`)
Call plot_end
Call plot_histogram(dlhist,`&sigma;<SUB>L</SUB> [micron for 1 cm]`, ...
   `Longitudinal diffusion`)
Call plot_end

From the histograms, one concludes that, for argon 90\&nbsp;% methane 10\&nbsp;% and E=125\&nbsp;V/cm, COLLISION=5 leads to a statistical error of 0.4\&nbsp;% on the drift velocity, 4.5\&nbsp;% on the transverse diffusion and 7\&nbsp;% on the longitudinal diffusion.

[By default: 10\&nbsp;\&times;\&nbsp;960.000 collisions.]

5.12.11: MOBILITY

This format only allows for mobilities that are constant or depend in a simple way on E/p. In the latter case, the argument of MOBILITY should be a function with EP as variable.

ADD provides a similar functionality, and can in addition be used if the mobility is available in tabular form.

The unit of mobility in Garfield is cm\&sup2;/\&mu;sec.V.

[By default: no mobility.]

5.12.12: PRINT

This output contains amongst others the ionisation, attachment and excitation rates which are needed if one wishes to correct the Townsend coefficients for Penning transfers. One also finds there the energy distribution.

This output tends to be long and it may therefore be advisable to write it to a file:

&GAS
pressure 3 bar
temperature 25 C
> magboltz.rates
magboltz argon 90 co2 10 ...
   e-field 100 200 500 1000 2000 5000 10000 20000 50000 100000 ...
   coll 3 ...
   print
>

[By default, this option is switched off.]

Section 5.13: MATERIAL

The MATERIAL command takes a chemical composition as argument,

Format:

MATERIAL  [ALUMINIUM n]    [ARGON n]     [CARBON n] ...
          [FLUORINE n]     [HELIUM n]    [HYDROGEN n] ...
          [KRYPTON n]      [LITHIUM n]   [NEON n] ...
          [NITROGEN n]     [OXYGEN n]    [SILICON n] ...
          [SULPHUR n]      [XENON n] ...
          DENSITY density ...
          WORK work ...
          [FANO fano]

Example:

material C 12 H 22 O 11 density 1.59 work 3

Which would fill your device with sucrose, ordinary sugar.

5.13.1: n

This number is mandatory, if you fill your chamber with pure silicon, for instance, you have to specify:

material Si 1 density 2.3 work 3.6

[No default]

5.13.2: density

[Mandatory parameter, no default.]

5.13.3: work

[Mandatory parameter, no default.]

5.13.4: fano

[By default set to 0.19.]

Section 5.14: MERGE

This only works if the current data and the data in the file have at least 2 of the following 3 axes in common: the set of electric field values, the set of angles between E and B and the set of magnetic field values. This condition is trivially met if the current gas data and the data in the file both concern a zero magnetic field situation.

If precisely 2 of the 3 axes coincide, then the merged data will contain only the transport properties which are found in both the current data and in the file.

If all 3 axes coincide, then the merged data will contain all the transport properties that are found in either the current data or the file.

Also the ADD command adds transport properties to the gas tables, under somewhat different conditions.

Contrary to the GET command, MERGE can not read files written in earlier formats. The way out consists in reading old-format files with GET, writing them out using WRITE and then using the file thus obtained for the merge.

Format:

MERGE file [member]  [KEEP-OLD | REPLACE-OLD]

Example:

get "low.gas"
merge "high.gas"

5.14.1: file

5.14.2: member

5.14.3: KEEP-OLD

[This is default.]

5.14.4: REPLACE-OLD

[Default is to keep the existing data.]

Section 5.15: MIX

The main limitation of this method is that it neglects ionisation effects and that it treats excitation inaccurately. This implies that the results are not valid for large E/p values, i.e. close to the electrodes.

Another limitation is that these calculations neglect the magnetic field - this is not an inherent limitation of the method, but there is no intention to invest further effort in this instruction. Garfield nowadays has an interface to the MAGBOLTZ program of Steve Biagi which is far superior in accuracy to this instruction.

Format:

MIX [ ARGON  frac ]          [ HELIUM  frac ] ...
    [ METHANE  frac ]        [ ETHANE  frac ] ...
    [ NEON  frac ]           [ NITROGEN  frac ] ...
    [ ISOBUTANE  frac ]      [ XENON  frac ] ...
    [ CO2  frac ]            [ METHYLAL  frac ] ...
    [ KRYPTON  frac ]        [ AMMONIA  frac ] ...

    [ MINIMUM-ENERGY emin ] ...
    [ MAXIMUM-ENERGY emax ] ...
    [ STEPSIZE-ENERGY estep ] ...

    [ CRITICAL-F0-FRACTION frcrit ] ...

    [ E/P-RANGE epmin epmax ] ...
    [ N-E/P n ] ...
    [ LINEAR-E/P-SCALE | LOGARITHMIC-E/P-SCALE ] ...

    [ PLOT-F0 | NOPLOT-F0 ] ...
    [ PLOT-ENERGY-LOSS | NOPLOT-ENERGY-LOSS ] ...
    [ PLOT-CROSS-SECTION | NOPLOT-CROSS-SECTION ] ...
    [ PLOT-PATH | NOPLOT-PATH ] ...

    [ PRINT-TABLES | NOPRINT-TABLES ] ...

    [ MOBILITY mob ] ...
    [ TOWNSEND-COEFFICIENT \α/p ] ...
    [ ATTACHMENT-COEFFICIENT \η/p ]

Example:

mix argon 50 ethane 50

The gas in your chamber will be 50\&nbsp;% argon and 50\&nbsp;% ethane.

5.15.1: frac

The fractions do not necessarily have to add up to 1.

[Each fraction is 0 by default.]

5.15.2: emin

[By default 0.01\&nbsp;eV.]

5.15.3: emax

This parameter should be chosen sufficiently large, otherwise the program might not be able to detect ionisation. The adverse effect of choosing this parameter too large is an increased CPU time consumption.

[By default 25\&nbsp;eV.]

5.15.4: estep

[By default 0.5\&nbsp;eV.]

5.15.5: frcrit

Also the energy distribution plot (see PLOT-F0) shows whether ionisation and excitation phenomena are likely to play a role.

[By default 0.01.]

5.15.6: E/P-RANGE

[By default 0.5 to 50.]

5.15.7: N-E/P

[By default 20.]

5.15.8: scale

[Logarithmic by default.]

5.15.9: PLOT-F0

The curve is plotted using polyline representation FUNCTION-1 if ionisation and excitation are not expected to be a problem, and using representation FUNCTION-2 if a fraction frcrit or more of the energy distribution exceeds the first ionisation or excitation threshold.

[This plot is made by default.]

5.15.10: PLOT-ENERGY-LOSS

The curve is plotted using polyline representation FUNCTION-1.

[This plot is by default not made.]

5.15.11: PLOT-CROSS-SECTION

The curve is plotted using polyline representation FUNCTION-1.

[This plot is made by default.]

5.15.12: PLOT-PATH

The curve is plotted using polyline representation FUNCTION-1.

[This plot is by default not made.]

5.15.13: PRINT-TABLES

[This table is by default not printed.]

5.15.14: MOBILITY

This format only allows for mobilities that are constant or depend in a simple way on E/p. In the latter case, the argument of MOBILITY should be a function with EP as variable.

ADD provides similar functionality, and caters in addition for mobilities that are available in tabular form.

The Garfield unit for mobility is cm\&sup2;/V.\&mu;sec.

[By default: no mobility.]

5.15.15: TOWNSEND-COEFFICIENT

This format only allows for Townsend coefficients that depend in a simple way on E/p. The argument of TOWNSEND-COEFFICIENT should be a function with EP as variable. ADD is more flexible in that it provides similar functionality, but it caters in addition for Townsend coefficients that are available in tabular form.

Note that MAGBOLTZ can be used to compute Townsend coefficients.

The Townsend coefficient should be entered as \&alpha;/pressure, with \&alpha; in units 1/cm and the pressure in Torr.

[By default: no Townsend coefficient.]

5.15.16: ATTACHMENT-COEFFICIENT

This format only allows for attachment coefficients that depend in a simple way on E/p. The argument of ATTACHMENT-COEFFICIENT should be a function with EP as variable. ADD is more flexible in that it provides similar functionality, but it caters in addition for attachment coefficients that are available in tabular form.

Note that MAGBOLTZ can be used to compute attachment coefficients.

The attachment coefficient should be entered as \&eta;/pressure, with eta in units 1/cm and the pressure in Torr.

[By default: no attachment coefficient.]

Section 5.16: OPTIONS

Format:

OPTIONS [NOGAS-PLOT | GAS-PLOT] ...
        [NOGAS-PRINT | GAS-PRINT]

Examples:

plot-options drift-velocity nodiffusion notownsend
opt gas-plot nogas-print

Requests a plot of the drift velocity. If cluster data has been entered, then also a cluster plot will be made (this is default) but diffusion and multiplication graphs are not shown. Using further PLOT-OPTIONS options, one could have fixed for instance the scale of the drift velocity plot.

&GAS
magboltz argon 70 dme 30
opt gas-print nogas-plot
>ArDME.print
&MAIN
>

MAGBOLTZ is called to compute transport properties for a 70/30 mixture of argon and DME. The transport tables are printed when leaving the section - note the use of the &MAIN command to close the gas section. They do not appear on the screen, but are output to the file ArDME.print.

5.16.1: GAS-PLOT

If SRIM data has been entered, then in addition the energy loss, range and straggling parameters are plotted.

These plots are made when the gas section is left, not when the option is switched on. Use e.g. &MAIN to close the section. Once outside the gas section, the plots can be obtained by entering the &OPTIMISE section and issued a PLOT-GAS command.

The representations used in the graphs are the following:

• Drift velocity: In the absence of a magnetic field, only the drift velocity is shown, using polyline representation FUNCTION-1. If the magnetic field is not zero, then the component parallel with E uses FUNCTION-1, the component parallel with the orthogonal part of B uses FUNCTION-2 while the component parallel with E\&times;B is shown using FUNCTION-3.
• Ion mobility: The ion mobility curve is drawn with FUNCTION-1.
• Diffusion: The longitudinal diffusion uses FUNCTION-1 while the transverse diffusion uses FUNCTION-2.
• Multiplication: The Townsend coefficient is drawn with FUNCTION-1, the attachment coefficient is shown using FUNCTION-2 and the ion dissociation coefficient is shown using FUNCTION-3.
• Cluster size: the cluster size distribution is drawn with FUNCTION-1.
• SRIM: the SRIM total energy loss is shown with FUNCTION-1, the electromagnetic energy loss with FUNCTION-2, and the nuclear energy loss with FUNCTION-3.
• SRIM: the SRIM projected range uses FUNCTION-1, the longitudinal straggling FUNCTION-2 and the transverse straggling FUNCTION-3.
• Excitation and ionisation: the excitation rates use FUNCTION-1 and the ionisation rates use FUNCTION-2.

[These graphs are not made by default.]

With the PLOT-OPTIONS command, you have further control over the axes (linear or logarithmic) and the vertical scale of these plots. This command also enables you to suppress one or more of the plots.

Use the ATTACHMENT, DRIFT_VELOCITY, GET_E/P_TABLE, ION_MOBILITY, LONGITUDINAL_DIFFUSION, LORENTZ_ANGLE, TOWNSEND, TRANSVERSE_DIFFUSION, VELOCITY_E, VELOCITY_BTRANSVERSE, VELOCITY_ExB, EXCITATION_RATE and IONISATION_RATE procedures for fully customised plots.

[This option is off initially, its setting is remembered from one gas section to the next.]

5.16.2: GAS-PRINT

The tables are printed when the gas section is being left, not when the option is switched on. Use e.g. &MAIN to close the section. As a consequence, if you wish to output the tables to a file, then you have to start the re-routing just before leaving the section and revert to normal output once you are in the next section:

Once outside the gas section, this table can be obtained by entering the &OPTIMISE section and issued a PRINT-GAS command.

&GAS
magboltz argon 80 co2 20
opt gas-print
> Ar_80_CO2_20.print
&MAIN
>

The output can not be used directly as input to the program, use the WRITE instruction for that purpose.

[This option is off initially, its setting is remembered from one gas section to the next.]

Section 5.17: PARAMETERS

Originally, most of this data was only used for a simple Landau-based backup estimate of the cluster size distribution if the CLUSTER size distribution is not known from data and if the HEED model can not be used.

Some of the parameters are however used for other purposes too:

• The mean number of clusters is used if the clustering model you plan to choose with the TRACK command, is based on the cluster size distribution entered with CLUSTER.
• The number of nucleons in an atom and the nuclear charge (A and Z) is used also by the SRIM clustering model.
• The ion diffusion coefficients are used when performing MC drift of ions.

Format:

PARAMETERS [ A a ] ...
           [ Z z ] ...
           [ RHO density ] ...
           [ E-PAIR epair ] ...
           [ E-MOST-PROBABLE emprob ] ...
           [ MEAN mean_number_of_clusters ] ...
           [ TRANSVERSE-ION-DIFFUSION {THERMAL | sigma_T} ] ...
           [ LONGITUDINAL-ION-DIFFUSION {THERMAL | sigma_L} ]

As shown in the format description, several lines may be used although a single line is perfectly acceptable as well.

Example:

PARA MEAN 20

This format could be used if you wish to compute arrival time spectra and enter the cluster size distribution with CLUSTER.

5.17.1: A

This parameter is used by (and mandatory for):

• the SRIM clustering model;
• the Landau model which is used to compute the cluster size distribution if you didn't enter such a distribution yourself with CLUSTER nor asked HEED to simulate the ionisation process.

5.17.2: E-MOST-PROBABLE

This parameter is used only to compute the cluster size distribution if you didn't enter such a distribution yourself with CLUSTER nor asked HEED to simulate the ionisation process.

You may also type MOST-PROBABLE-ENERGY-LOSS.

5.17.3: E-PAIR

This parameter is used only to compute the cluster size distribution if you didn't enter such a distribution yourself with CLUSTER nor asked HEED to simulate the ionisation process.

You may also type PAIR-CREATION-ENERGY.

5.17.4: MEAN

This parameter is not used when clustering is performed according to the HEED model, but it is required for the EXPONENTIAL-SPACING and EQUAL-SPACING clustering models. In the latter 2 cases, the parameter is required even if a cluster size distribution has been entered with a CLUSTER statement.

You may also type N-MEAN.

[No default setting.]

5.17.5: RHO

This parameter is used by:

• the SRIM clustering model;
• the simple Landau model which is used to compute the cluster size distribution if you didn't enter such a distribution yourself with CLUSTER nor asked HEED to simulate the ionisation process.

SRIM files contain a density estimate and, when reading such a file with the SRIM command in the gas section, the gas density will be overwritten. It is therefore advisable to issue the PARAMETERS command after the SRIM command if you know the gas density.

5.17.6: Z

This parameter is used by (and mandatory for):

• the SRIM clustering model;
• the Landau model which is used to compute the cluster size distribution if you didn't enter such a distribution yourself with CLUSTER nor asked HEED to simulate the ionisation process.

5.17.7: THERMAL

         .------
        / 2 k\<SUB\>B\</SUB\> T
\&sigma; = \\  /  ------
     \\/    q\<SUB\>e\</SUB\> E

Where

• k\<SUB\>B\</SUB\> = Boltzmann constant, 1.38... 10\<SUP\>-23\</SUP\> J/K,
• T = temperature of the gas [K],
• q\<SUB\>e\</SUB\> = charge of the electron, 1.6... 10\<SUP\>-19\</SUP\> C,
• E = local electric field [V/cm]

[By default, the diffusion is set to 0.]

5.17.8: sigma

These coefficients are used for Monte_Carlo drift-line integration of ion trajectories.

The diffusion coefficients should be expressed in cm of diffusion over 1\&nbsp;cm of drift.

[Both diffusion coefficients default to 0.]

Section 5.18: PLOT-OPTIONS

Several plots may be modified in a single statement.

Use DRIFT_VELOCITY and related procedures to have full control over the presentation of the plot.

Format:

PLOT-OPTIONS [plot [options]] ...

Example:

plot-options drift lin-x log-y nodiff nocluster

(Requests a linear E/p axis and a logarithmic drift velocity axis, the opposite of the default. The diffusion coefficients and the cluster size distribution are not plotted.)

5.18.1: plot

The following are known, all of which can be negated to suppress the plot:

Notes:

1. The transverse and the longitudinal diffusion are shown together in a single graph. To suppress one of them but not the other requires a RESET of the item that is not desired. The same applies to the Townsend and attachment coefficients, and to the ionisation and excitation rates.
2. One may use ATTACHMENT-COEFFICIENT-PLOT as synonym for TOWNSEND-COEFFICIENT-PLOT.
3. For SRIM plots, the options are not honoured.

5.18.2: options

Notes:

1. The transverse and longitudinal diffusion coefficients, the Townsend and attachment coefficients, as well as the ionisation and excitation rates, are plotted in one graph and have therefore a common set of axes.
2. RANGE does not apply to the cluster size distribution.
3. These options do not apply for the SRIM plots.

Section 5.19: PRESSURE

The pressure is used by the gas mixing instructions MIX and MAGBOLTZ as well as by HEED. Please be sure to specify the pressure before issuing these commands.

If you specify the pressure after a mixing command, then the tables will be prepared for standard atmospheric pressure and the conversion to the pressure you specify will be done by relying on the simple scaling laws.

Format:

PRESSURE pressure [unit]

Example:

pressure 2 bar

5.19.1: pressure

[Initially set to 760\&nbsp;Torr.]

5.19.2: unit

Garfield internally stores the pressure in Torr and e.g. the E/p tables are therefore in V/cm.Torr, no matter the pressure unit you used on input. Also the unit with which the pressure is displayed is not affected by the unit with which you enter it.

The following pressure units are accepted:

[The default pressure input unit is the Torr.]

Section 5.20: REPLACE

Section 5.21: RESET

A selective reset is performed if any items are listed, otherwise all gas data is deleted.

Format:

RESET [item1] [item2] ...

5.21.1: item

ATTACHMENT-COEFFICIENTS

Resets the attachment coefficient and resets the interpolation and extrapolation methods for this item to their defaults.

CLUSTERING-DATA

Resets the cluster size distribution, whether derived from Heed, from a Landau distribution or from a table of cluster sizes. Also resets the mean number of clusters per cm as entered with the PARAMETERS statement.

DIFFUSION

Equivalent to LONGITUDINAL-DIFFUSION, TRANSVERSE-DIFFUSION and DIFFUSION-TENSOR combined.

DIFFUSION-TENSOR

Resets all 6 components of the diffusion covariance matrix and resets the interpolation and extrapolation methods for this item to their defaults.

DRIFT-VELOCITY

Resets all 3 drift velocity components, i.e. the component parallel with E, the component parallel with the part of B transverse with respect to E and the component parallel with E\&times;B. Also resets the interpolation and extrapolation methods for these items to their defaults.

EXCITATION-RATES

Resets all excitation rates and resets the the interpolation and extrapolation methods for this item to their defaults.

GAS-IDENTIFIER

Sets the gas identifier to a blank string.

ION-DISSOCIATION

Resets the ion dissociation coefficients and resets the interpolation and extrapolation methods for this item to their defaults.

ION-MOBILITY

Resets the ion mobility and resets the interpolation and extrapolation methods for this item to their defaults.

IONISATION-RATES

Resets all ionisation rates and resets the the interpolation and extrapolation methods for this item to their defaults.

LONGITUDINAL-DIFFUSION

Resets the longitudinal diffusion and resets the interpolation and extrapolation methods for this item to their defaults.

LORENTZ-ANGLES

Resets the Lorentz angles and resets the interpolation and extrapolation methods for this item to their defaults.

TABLES

Equivalent to combining ATTACHMENT-COEFFICIENTS, DIFFUSION, DRIFT-VELOCITY, LORENTZ-ANGLES and TOWNSEND-COEFFICIENTS, EXCITATION-RATES and IONISATION-RATES..

TOWNSEND-COEFFICIENTS

Resets the Townsend coefficient and sets the interpolation and extrapolation methods for this item to their defaults.

TRANSVERSE-DIFFUSION

Resets the transverse diffusion and sets the interpolation and extrapolation methods for this item to their defaults.

Section 5.22: SRIM

In order to estimate electron deposition from the SRIM model, Garfield will need the A and Z of the gas to be entered with the PARAMETERS statement. The SRIM files do not seem to contain this information.

SRIM files contain a density estimate and, when reading such a file, the gas density, if entered on beforehand with the PARAMETERS statement, would be overwritten. It is therefore advisable to issue the PARAMETERS command after the SRIM command if the density as estimated by SRIM is not considered reliable. Please note that the a density entered with the PARAMETERS statement will not affect the range estimated by SRIM.

The energy loss, range and straggling parameters will be plotted, when the gas section is being left, if the GAS-PLOT option is switched on.

The SRIM tables are included in the files that are written by the WRITE command and read by the GET command.

Use the SRIM option of the TRACK command to produce clusters based on this model.

Comments, and in particular comparisons with experimental data, as well as suggestions for improvement are invited.

Format:

SRIM FILE file ...
     WORK-FUNCTION work ...
     FANO-FACTOR fano

Example:

srim file="SRIMHeInCF.dat" work=40

5.22.1: file

The energy range of the table should at least extend up to the kinetic energy of the incoming particle, and should extend as far down as SRIM will allow so as to simulate the final absorption. The Garfield interface extrapolates to higher and lower energies by taking resp. the last and first tabulated values.

The file for \&alpha; particles traversing a mixture of He and CF\<SUB\>4\</SUB\> would look as follows:

 ==================================================================
              Calculation using SRIM-2003
              SRIM version ---> SRIM-2003.26
              Calc. date   ---> October 24, 2005
 ==================================================================

 Disk File Name = SRIM Outputs\\Helium in He- C- F

 Ion = Helium [2] , Mass = 4.003 amu

 Target Density =  1.9000E-03 g/cm3 = 1.1026E+20 atoms/cm3
 ======= Target  Composition ========
    Atom   Atom   Atomic    Mass
    Name   Numb   Percent   Percent
    ----   ----   -------   -------
     He      2    053.12    020.49
      C      6    009.38    010.86
      F      9    037.50    068.65
 ====================================
 Bragg Correction = 0.00%
 Stopping Units =  MeV / (mg/cm2)
 See bottom of Table for other Stopping units

   Ion        dE/dx      dE/dx     Projected  Longitudinal   Lateral
  Energy      Elec.      Nuclear     Range     Straggling   Straggling
-----------  ---------- ---------- ----------  ----------  ----------
  10.00 keV   2.629E-01  6.037E-02  128.41 um    52.40 um    46.05 um
  11.00 keV   2.760E-01  5.715E-02  140.80 um    55.57 um    49.42 um
  12.00 keV   2.885E-01  5.431E-02  153.00 um    58.53 um    52.63 um
(...)
   7.00 MeV   5.985E-01  3.596E-04   39.51 mm     1.44 mm   790.64 um
   8.00 MeV   5.416E-01  3.196E-04   48.75 mm     1.96 mm   931.02 um
   9.00 MeV   5.000E-01  2.879E-04   58.85 mm     2.44 mm     1.09 mm
  10.00 MeV   4.604E-01  2.622E-04   69.81 mm     2.91 mm     1.25 mm
-----------------------------------------------------------
 Multiply Stopping by        for Stopping Units
 -------------------        ------------------
  1.8999E-02                 eV / Angstrom
  1.8999E-01                keV / micron
  1.8999E-01                MeV / mm
  1.0000E+00                keV / (ug/cm2)
  1.0000E+00                MeV / (mg/cm2)
  1.0000E+03                keV / (mg/cm2)
  1.7231E+01                 eV / (1E15 atoms/cm2)
  1.5537E+00                L.S.S. reduced units
 ==================================================================
 (C) 1984,1989,1992,1998,2003 by J.P. Biersack and J.F. Ziegler

Recipe to be provided ... Berta !

[No default; mandatory argument.]

5.22.2: work

The work function depends on the gas and is typically a factor 2 larger than the ionisation energy.

[No default; mandatory argument.]

5.22.3: fano

The Fano factor equals the RMS\&sup2;/average of the number of electrons produced by a given amount of electromagnetic energy. The factor depends on the electromagnetic energy - it tends to decrease from 1 at threshold to the asymptotic value which needs to be specified.

If set to NONE (or 0), the energy used for an electron will be equal to the work function, without fluctuations.

[By default: 0.17.]

Section 5.23: TABLE

Each of the table entries can either be tabulated or be computed from a parametrisation. In either case, the quantities that obey simple pressure scaling laws, have to be entered multiplied by the appropriate power of the pressure.

All tabulated entries must be specified at a common set of E/p values, which must itself be listed in the table if at least one transport property is tabulated. Use ADD if the data that you wish to use for one or more entries, is tabulated at a different set of E/p values.

The order of the tabulated entries is indicated on the TABLE line by listing the names of the entries in the same sequence as in the table. The entry names should not be followed by parametrisations. The place of the E/p values in the table should be indicated by 'E/P'. There is no preferred order of the entries.

If you opt for a parametrised form for one or more entries, then functions have to follow the names of the entries that are to be parametrised. The parametrisations that you enter are not stored as functions, rather they are evaluated at the E/p, angle(E,B) and B values of the table. The list thus obtained will be interpolated when transport properties are required, like for tabulated entries.

If all entries are entered in a parametrised form, then you can either establish the list of E/p values by tabulating them or by specifying an electric_field range.

You have the possibility to create tables with a dependence on the angle between E and B, as well as on the magnetic_field, provided a magnetic field is present in the chamber.

Format:

TABLE [ E/P ] ...
      [ DRIFT-VELOCITY [ function ] ] ...
      [ BTRANSVERSE-VELOCITY [ function ] ] ...
      [ ExB-VELOCITY [ function ] ] ...
      [ ION-MOBILITY [ function ] ] ...
      [ ION-DISSOCIATION-COEFFICIENT [ function ] ] ...
      [ LORENTZ-ANGLE [ function ] ] ...
      [ LONGITUDINAL-DIFFUSION-COEFFICIENT [ function ] ] ...
      [ TRANSVERSE-DIFFUSION-COEFFICIENT [ function ] ] ...
      [ TOWNSEND-COEFFICIENT [ function ] ] ...
      [ ATTACHMENT-COEFFICIENT [ function ] ] ...
      [ DUMMY [ function ] ] ...
      [ E/P-RANGE epmin epmax ] [ N-E/P nep ] ...
        [ LOGARITHMIC-E/P-SCALE | LINEAR-E/P-SCALE ] ...
      [ [ B-RANGE bmin bmax ] [ N-B nb ] | ...
        [ B-FIELD b ] ] ...
      [ [ ANGLE-RANGE amin amax ]  [ N-ANGLE nangle ] | ...
        [ ANGLE angle ] ]

This line is followed by tables for those items that are not functions. The end of the table is signalled by a blank line.

Example:

table  drift=100*ep, diff, e/p
0.3 0.1
0.1 0.2
0.1 0.5
0.2 1.0
0.3 2.0

// Note that the preceding line is intentionally left blank

The drift velocity is entered as the function 100*E/p which is evaluated at the E/p values listed in the second column. The longitudinal diffusion is listed in the first column. The ion mobility, the Lorentz angle and the Townsend and attachment coefficients are not specified. Note the blank line at the end of the table.

5.23.1: E/P

This is an optional keyword. If the E/P keyword is not used, then all transport properties must be specified by means of functions.

5.23.2: ATTACHMENT-COEFFICIENT

The attachment coefficients are computed from the function if the keyword is followed by a function. The coefficients should not be part of the listing in this case.

With a view to pressure scaling, one should in either case enter the attachment coefficients divided by the pressure. The quantity to be entered thus has the unit of 1/(cm.Torr).

Access to the data is provided with the ATTACHMENT procedure.

[Entering attachment coefficients is optional.]

5.23.3: BTRANSVERSE-VELOCITY

This velocity component is computed from the function if the keyword is followed by a function. The velocity component should not be part of the listing in this case.

In either case, one should enter the velocity component in units of cm/\&mu;sec.

This component should only be included in the table if a magnetic field has been defined. Although you do not have to enter this component if a magnetic field has been defined, you're strongly advised to do so if you dispose of the relevant data. If the component has not been entered, but is needed for a calculation, then the missing velocity components will be computed using the Lorentz angle, if available, otherwise from the Langevin equation.

Access to the data is provided with the VELOCITY_BTRANSVERSE procedure.

[Entering this component of the velocity is optional.]

5.23.4: DRIFT-VELOCITY

• In case a magnetic field is present:

  If not followed by a function, the keyword indicates the location, in the listing that follows the command, of the component of the electron velocity parallel with E. If you do not enter both the component parallel with E\&times;B and the component parallel with the part of B that is transverse with respect to E, then you should enter here the norm of the drift velocity.

  A function following this keyword should return the quantity described above. There should not be a corresponding item in the table if a function is specified.

• In case there is no magnetic field:

  If not followed by a function, the keyword indicates the location, in the listing that follows the command, of the norm of the electron drift velocity.

  The velocity is computed from the function if the keyword is followed by a function. The velocity should not be part of the listing in this case.

  The other components of the electron velocity vector should not be entered if there is no magnetic field.

In all cases, one should enter the velocity (component) in units of cm/\&mu;sec.

The magnitude of the drift velocity can be accessed through the DRIFT_VELOCITY procedure. To obtain only the part parallel with E, one uses VELOCITY_E.

[Although entering the drift velocity is optional, one would normally do so since very few calculations can be performed if velocity data is absent.]

5.23.5: ExB-VELOCITY

This velocity component is computed from the function if the keyword is followed by a function. The velocity component should not be part of the listing in this case.

In either case, one should enter the velocity component in units of cm/\&mu;sec.

This component should only be included in the table if a magnetic field has been defined. Although you do not have to enter this component if a magnetic field has been defined, you're strongly advised to do so if you dispose of the relevant data. If the component has not been entered, but is needed for a calculation, then the missing velocity components will be computed using the Lorentz angle, if available, otherwise from the Langevin equation.

Access to the data is provided with the VELOCITY_ExB procedure.

[Entering this component of the velocity is optional.]

5.23.6: ION-DISSOCIATION-COEFFICIENT

The dissociation coefficients are computed from the function if the keyword is followed by a function. The coefficients should not be part of the listing in this case.

With a view to pressure scaling, one should in either case enter the dissociation coefficients divided by the pressure. The quantity to be entered thus has the unit of 1/(cm.Torr).

Access to the data is provided with the ION_DISSOCIATION procedure.

[Entering dissociation coefficients is optional.]

5.23.7: ION-MOBILITY

The ion mobility is computed from the function if the keyword is followed by a function. The ion mobility should not be part of the listing in this case.

In either case, one should enter the ion mobility in units of cm\&sup2;/(\&mu;sec.V).

Access to the data is provided with the ION_MOBILITY procedure.

[Entering the ion mobility is optional.]

5.23.8: LONGITUDINAL-DIFFUSION-COEFFICIENT

The longitudinal diffusion coefficients are computed from the function if the keyword is followed by a function. The longitudinal diffusion coefficients should not be part of the listing in this case.

With a view to pressure scaling, one should in either case enter the amount of longitudinal diffusion over 1\&nbsp;cm of drift, multiplied with the square root of the pressure. This quantity has the unit of \&radic;(cm.Torr).

Access to the data is provided with the LONGITUDINAL_DIFFUSION procedure.

[Entering the longitudinal diffusion is optional.]

5.23.9: LORENTZ-ANGLE

The Lorentz angle is computed from the function if the keyword is followed by a function. The Lorentz angle should not be part of the listing in this case.

In either case, the Lorentz angle should be entered in degrees.

This component can only be included in the table if a magnetic field has been defined. If you have included all 3\&nbsp;components of the drift velocity vector, then you do not have to enter the Lorentz angle since this information will not be used. If however you enter only the velocity component parallel with E, then you're strongly advised to tabulate the Lorentz angle if you dispose of the relevant data. If neither Lorentz angles nor transverse velocity components are available, then the velocity vector will be computed using the Langevin equation.

Access to the data is provided with the LORENTZ_ANGLE procedure.

[Entering Lorentz angles is is optional.]

5.23.10: TOWNSEND-COEFFICIENT

The Townsend coefficients are computed from the function if the keyword is followed by a function. The coefficients should not be part of the listing in this case.

With a view to pressure scaling, one should in either case enter the Townsend coefficient divided by the pressure. The quantity to be entered thus has the unit of 1/(cm.Torr).

Access to the data is provided with the TOWNSEND procedure.

[Entering Townsend coefficients is optional.]

5.23.11: TRANSVERSE-DIFFUSION-COEFFICIENT

The transverse diffusion coefficients are computed from the function if the keyword is followed by a function. The transverse diffusion coefficients should not be part of the listing in this case.

The coordinate_system aligns the longitudinal diffusion with the electric field, not necessarily with the drift velocity vector. The transverse diffusion is the average of the diffusion perpendicular to E.

With a view to pressure scaling, one should in either case enter the amount of transverse diffusion over 1\&nbsp;cm of drift, multiplied with the square root of the pressure. This quantity has the unit of \&radic;(cm.Torr).

Access to the data is provided with the TRANSVERSE_DIFFUSION procedure.

[Entering the transverse diffusion is optional.]

5.23.12: function