EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Initiating the Matching Module

• Cell matching:


In the first mode the matching routine is initiated only with one attribute specifying the sequence(s) the matching module will work on. In this matching mode the periodicity of the optics functions is enforced at the beginning and end of the selected range.

MATCH, SEQUENCE='name1', 'name2',..,nema-n';
 

• Insertion matching:


In the second mode, called insertion matching, the matching routine is initiated with two attributes: one specifying the sequence(s) the matching module will work on and one specifying the initial conditions of the optic functions for each sequence. In this case the initial values are assumed as exact.

• Specification of Initial Values: The initial values of the optical functions for the insertion matching can either be specified in form of a SAVEBETA command or by explicitly stating the individual optic function values after the 'MATCH' command. The two options can be entered as

MATCH,sequence='name1','name2',..,'name-n',BETA0='beta01','beta02',..,'beta0n';

or

MATCH,SEQUENCE='sequence-name', BETX=real,ALFX=real,MUX=real, 
                                BETY=real,ALFY=real,MUY=real,
                                X=real,PX=real,Y=real,PY=real,
                                DX=real,DY=real,DPX=real,DPY=real, 
                                DELTAP=real;

> Examples:
• Example 1:

CELL: SEQUENCE=(...) ;
INSERT: SEQUENCE=(...) ;
USE,PERIOD=cell;
SAVEBETA,LABEL=bini,place=#e;
TWISS,SEQUENCE=cell;
USE,PERIOD=insert;
MATCH,SEQUENCE=insert,BETA0=bini;
CONSTRAINT,SEQUENCE=insert,RANGE=#e,MUX=9.345,MUY=9.876;

This matches the sequence 'INSERT' with initial conditions to a new phase advance. The initial conditions are given by the periodic solution for the sequence CELL1.
• Example 2:

USE,PERIOD=INSERT; 
MATCH,SEQUENCE=insert;
CONSTRAINT,SEQUENCE=insert,RANGE=#e,MUX=9.345,MUY=9.876;

This matches the beam line 'INSERT' with periodic boundary conditions to a new phase advance.
The initial conditions can also be transmitted by a combination of a SAVEBETA command and explicit optic function specifications:

USE,CELL1;
SAVEBETA,LABEL=bini,PLACE=#E; 
TWISS,SEQUENCE=CELL1;
USE,PERIOD=LINE1; 
MATCH,SEQUENCE=LINE1,BETA0=bini,MUX=1.234,MUY=4.567;

This example transmits all values of the SAVEBETA array 'bini' as initial values to the MATCH command and overrides the initial phase values by the given values.
An additional CONSTRAINT may be imposed in other places, i.e. intermediate or end values of the optics functions at the transition point.
 
• More than one active sequence:


The matching module can act on more than one sequence simultaneously by specifying more than one sequence after the MATCH command:

MATCH,SEQUENCE=LINE1,CELL1,BETA0=bini1,bini2;

This example initiates the matching mode for the 'LINE1' and the 'CELL1' sequence. The Twiss module function of the two sequences are calculated with fixed initial conditions. The SAVEBETA array 'bini1' is used for calculating the optics functions of sequence 'LINE1' and the SAVEBETA array 'bini2' for calculating the optics functions of sequence 'CELL1'. Without the initial conditions the matching module will work in the CELL mode.




• Special speed flag:

The "slow" attribute enforces the old and slow matching procedure. Recently a number of parameter, like "RE56", have been added to list of matchable parameters. Nevertheless, some parameters might only be available when using the "slow" attribute.

Further attributes of the TWISS statements are:

• RMATRIX: If this flag is used the one-turn map at the location of every element is calculated and prepared for storage in the TWISS table.

Target values for the matrix elements at certain positions in the sequence can be specified with the help of the CONSTRAINT command and the keywords: RE, RE11...RE16...RE61...RE66, where REij refers to the "ij" matrix  component.
 
> Examples:

Example 1:
MATCH,RMATRIX,SEQUENCE='name',BETA0='beta-block-name';
CONSTRAINT,SEQUENCE=insert,RANGE=#e,RE11=-2.808058321,re22=2.748111197;
VARY,NAME=kqf,STEP=1.0e-6;
VARY,NAME=kqd,STEP=1.0e-6;

This matches the sequence 'name' with initial conditions to new values for the matrix elements 'RE11' and 'RE22' by varying the strength of the main quadrupole circuits.
• CHROM: If this flag is used the chromatic functions at the location of every element are calculated and prepared for storage in the TWISS table.

Target values for the chromatic functions at certain positions in the sequence can be specified with the help of the CONSTRAINT command and the keywords WX, PHIX, WY, PHIY,....

Leave Matching Mode

ENDMATCH;