A computer modeling of ionization is necessary for
the simulation of gaseous detectors of fast charged particles. Despite
the wide use of gas-filled detectors their computer modeling still
represents a difficult problem. Ionization deposited by incident
particle in a gas volume drift to electrodes and produces electric
signals on them. To calculate reliably the signals it needs to know the
initial amount of
ionization and its space location. A photoabsorption ionization (PAI)
model, which have been proposed by Allison and Cobb [2] and also by
many other
authors with various small differences and modifications, allows us to
compute the ionization amount, and location of primary clusters along
the
track. We will call the ionization deposited after the absorption of
all
delta-electrons "initial ionization", as opposed to "primary
ionization", which involves only atoms directly ionizated by the
incident particle. The total amount of initial ionization in each
cluster can be estimated with the use of the mean work per pair
production w and the Fano factor F. This allows one to estimate
the approximate longitudinal distribution of initial ionization along
the track provided that the small spreading of
ionization around each cluster is negligible. But this assumption is
not
justified in many circumstances, in particular when one studies the
gaseous
detectors with extremely good space resolution. The transverse
distribution of initial ionization aside from the track can be
important, but it cannot be obtained from PAI since PAI does not
discriminate the shells absorbing the energy and does not allow to
estimate the range of delta-electrons knocked out from the atoms. To
solve this problem the cross section of this model was modified, which
resulted in shell separation and gave the possibility to model atomic
relaxation cascades and the paths of delta-electrons and fluorescent
photons. The improved model was called photoabsorption ionization and
relaxation (PAIR) model.
2. HEED
A flexible computer program was created in FORTRAN
77 approximately in 1994-97, which was able to model various gas
mixtures. It was called "HEED", which was promted by the book "High
Energy ElectroDynamics", written by Akhiezer and Shulga [1]. They
proposed this title as a generic name of this science domain, namely
science studying the electromagnetic interactions of fast charged
particles with matter and including the transition and Cherenkov
radiations and many other effects which are explained by similar
approaches. However this book does not describe ionization in great
details and the HEED does not take anything from it (except the title).
PAIR was derived from the paper of Allison and Cobb [2], which gives
the most consistent description of PAI. The notation PAI is also
proposed by these authors.
In order to simulate the initial ionization in a
detector realistically, it needs to model geometrical volumes with
materials (gases) in them and to trace particles through the volumes
with modeling random interactions with matter and possibly with taking
into account fields
(presumably magnetic field). Put another way, it is a generic Monte
Carlo
problem of particle penetration through matter with modeling ionization
and photoabsorption processes. This is what the program HEED does.
3. Article in NIM
Although the program HEED-F77 based on this model was used during many
years in Garfield simulation package, the consistent description was
not published up to now (2005). Now the description is published. It
is available as
preprint
of a paper and as the paper in NIM A554 (2005) 474-493. But please note
that the
paper is based on and focused on the hew version of HEED, which is
written in C++. Mechanism of the shell separation is the same, but the
delta-electron absorption is slightly different.
Errata:
1. The first statement in section 3.1 (page 481 in the journal
paper format)
"The integral over E of eq. (7), multiplied by the electron density,
gives the number of energy transfers ... ."
should be read as
"The integral over E of eq. (7), multiplied by the atomic
concentration, gives the number of energy transfers ... ."
(But in the program eq. (7) is normalized to one electron of the media
and should be multiplied by the electron density anyway.)
2. The first sentence in caption to fig. 2 (the same page 481 in the journal
paper format)
"The number of primary clusters for minimum-ionizing
particles for various gases at NTP
according to calculations by
HEED (circles) and a number of measurements: ref. [57]
(squares), the average of numbers from ref. [18] and seven
other works quoted in table 5 of ref. [18]
(stars), and ref. [58]
(triangles)."
should be read as
"The number of primary clusters for minimum-ionizing
particles for various gases at NTP (Normal Temperature
293 K and Pressure 1 atm) according to calculations by
HEED (circles) and a number of measurements: ref. [57]
(squares), the average of numbers from ref. [18] and seven
other works quoted in table 5 of ref. [18] (triangles),
and ref. [58](crosses)."
3.
The remark about NTP is included in the correction above, because
it was recently understood that ref. [18] apparently used 273 K (0 C) as the
normal temperature. HEED assumed 20 C, as it is almost everywhere else.
Therefore, the data from ref. [18] should be corrected by the factor of 273/293
when compared to other data.
This is a minor correction which practically
does not have any visible effect for this figure
(and does not affect the other content of this
paper), but here is a
corrected plot.
4.
The notations of molecular formulas drawn above plot (a) in the journal
paper turn out to be shifted slightly if compared with a carefully adjusted
original plot (similar to what is given above).
This is unexpected, because this
plot was supplied to the journal in "eps"-format displayed identically with
the "ps"-figure,
modification of which is given above (this is made with the same
"kumac" file and PAW program, only the data for ref. [18]
are corrected according to item 3).
The vertical dashed lines in figure (a) are drawn to guide the eye
and to recognize the numbers of clusters of particular moleculas.
After the shift a couple of the molecular notations appear slightly apart from
the corresponing lines.
Therefore it perhaps needs to remark
that the order of vertical dashed lines which show molecular weights
is identical with
molecular notations except C02 and C3H6, which are merging because
of similar molecular weights.
It was not written, but can be easily understood that
comparison of this plot with plot (b)
allows the reader to understand that
the points grouping around 33 clusters per cm. show CO2 and
the points around 70 clusters show C3H8.
7.03.2022:
5.
It turns out the the value of Z_molecular_total/Z_atomic_mean^power
for iC4H10 was either calculated or input in my programs with embarrassing
error or typo 28.4 instead of true 23.8.
Since this point is at the end, the correction changes the fit.
The good thing is that now all numbers of clusters can be fit by a straight
line.
This leads to the following
new corrected plot.
6. Averaging of experimental data for the numbers of primary clusters,
was remade, description is to be given later.
At the previous plot, as well as in the paper, the fit was done
through the calculated by HEED numbers.
But the average experimental numbers could also be used.
This is presented in the following
picture.
Here squares represent averaged experiments and circles are calculations by HEED.
4. HEED-F77
These simulations have a long story. The first "public" program
calculating ionization by PAIR and prepared in a form in which programs
can be used by other people was compiled in FORTRAN 77 in 1995-96. The
geometry was constrained by a parallel adjacent layers model. It allows
to identify the layer in which the particle is currently located by
looking for an interval, in which the particle coordinate occurs. This
simplifies the program greatly, but creates trouble when one models
straw tubes and other modern detectors which cannot be described
precisely by the parallel adjacent layers model. The magnetic field was
not included in original program, but it was included by R. Veenhof in
a derivative version of HEED, created and connected by him to the
Garfield program.
These versions of HEED-F77 was reportedly used in many detector R&D
works.
The
author's version of the old HEED program composed in car-format can be
taken from here. This program was assumed to be used with
a source code management system CMZ, which was a
dominated code managemant system that time (today I do not see an afficial
CMZ web-page, so I let the reader to search it himself, if he needs).
Some users have recently reported a problem of extracting source files
form heed.car occuring at certain systems. Some of the files
are just not extracted by CMZ. It is unknown, why this happened. Such
problems did not appear previously. The author is unable to reproduce
this problem at his computers. To help in the case when this problem
occurs the author has constructed a tar-archive , which is a snapshot
of author's directory with the old HEED remained in his computer,
please
get it
here.