EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

TOUSCHEK: Touschek Lifetime and Scattering Rates

The TOUSCHEK module computes the Touschek lifetime and the scattering rates around a lepton or hadron storage ring, based on the formalism of Piwinski [A. Piwinski, "The Touschek Effect in Strong Focusing Storage Rings," DESY-98-179; see also Piwinski's article on Touschek lifetime in the Handbook of Accelerator Physics and Engineering (A. Chao, M. Tigner, eds.), World Scientific, 1999] .

The syntax of the TOUSCHEK command is: 

TOUSCHEK, FILE;
TOUSCHEK should be called after a TWISS command. One or several cavities with rf voltages should be defined prior to calling TWISS and TOUSCHEK. [Warning: Calling EMIT between the TWISS and TOUSCHEK commands leads to TOUSCHEK using wrong beam parameters, even if the BEAM command is reiterated.]

The momentum acceptance is taken from the bucket size taking into account the energy loss per turn U0 from synchrotron radiation. The value of U0 is computed from the second synchrotron radiation integral synch_2 in the TWISS summ table (synch_2 is calculated only when the TWISS option 'chrom' is invoked), using Eq. (3.61) in Matt Sands' report SLAC-121, which was generalized to the case of several harmonic rf systems. If synch_2=0, not defined, or not calculated, zero energy loss is assumed.

In the case of several  rf systems with nonzero voltages, it is assumed that the lowest frequency system defines the phase of the outer point on the separatrix when calculating the momentum acceptance, and that all higher-harmonic systems are either in phase or in anti-phase to the lowest frequency system. (Note: if a storage rings really uses a different rf scheme, one would need to change the acceptance function in the routine cavtousch for that ring.)
 

The arguments have the following meaning:

Example: 

BEAM,PARTICLE=PROTON,ENERGY=450,NPART=1.15e11,EX=7.82E-9,EY=7.82E-9,ET=5.302e-5,SIGE=7.164e-4,SIGT=0.1124,RADIATE=TRUE;

...

USE,PERIOD=FODO;	

... 	

VRF=400;

...

SELECT,FLAG=TWISS,CLEAR;
TWISS,CHROM,TABLE,FILE;

TOUSCHEK,FILE;

...

The first command defines the beam parameters. It is essential that the longitudinal emittances and bunch length are set. The command use selects the beam line or sequence. The next command assign a value to the cavity rf voltage vrf (example name). The select clear previous assignments to the twiss module, twiss calculates and saves the values of all twiss parameters for all elements in the ring; the touschek command computes the Touschek lifetime and writes it to the file 'touschek' (default name).

The results are stored in the TOUSCHEK tables, and can be written to a file (with the default name 'touschek' in the example above), or values can be extracted from the table using the value command as follows

value,table(touschek,name),table(touschek,s),table(touschek,tli),table(touschek,tliw),table(touschek,tlitot);

where 'name' denotes the name of a beamline element, s the position of the center of the element, tli the instanteneous Touschek loss rate within the element, and tliw the instantaneous rate weighted by the length of the element divided by the circumference (its contribution to the total loss rate), and tlitot the accumulated loss rate adding the rates over all beamline elements through the present position. The value of tlitot at the end of the beamline is the inverse of the Touschek lifetime in units of 1/s.

Also, all results can be printed to a file using the command

write,table=touschek,file;

The MADX Touschek module was developed by Catia Milardi and Frank Zimmermann .

frankz 11.03.2008