DYNAP

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

DYNAP: Tunes, Tune Footprints, Smear and Lyapunov Exponent

DYNAP can be called instead of RUN inside a TRACK command:

DYNAP,TURNS=real, FASTUNE=logical,LYAPUNOV=real,MAXAPER:={..,..,..,..,..,..},ORBIT=logical;

For each previously entered start command, DYNAP tracks two close-by particles over a selected number of turns, from which it obtains the betatron tunes with error, the action smear, and an estimate of the lyapunov exponent. Many such companion particle-pairs can be tracked at the same time, which speeds up the calculation. The smear is defined as 2.0 (wxy_max - wxy_min) / (wxy_max + wxy _min), where the wxy_min,max refer to the miminum and maximum values of the sum of the transverse betatron invariants wx+wy during the tracking. The tunes are computed by using an FFT and either formula (18) or formula (25) of CERN SL/95-84 (AP), depending on whether the number of turns is less-equal or larger than 64.

The arguments have the following meaning:

TURNS: The number of turns to be tracked (default: 64, present maximum: 1024).
FASTUNE: A logical flag. If set, the tunes are computed (default: false).
MAXAPER: If the particle phase-space coordinates exceed certain maximum values, the particle is considered lost. The maximum aperture is a vector of 6 real numbers (default: (0.1, 0.01, 0.1,0.01, 1.0, 0.1) ).
LYAPUNOV: The launch distance between two companion particles added to the x coordinate (default: 1.e-7 m).
ORBIT: A logical flag. If set, the flag orbit is true during the tracking and its initialization (default: true). This flag should be set to be true, if normalized coordinates are to be entered.

Example:

BEAM,PARTICLE=ELECTRON,ENERGY=50,EX=1.E-6,EY=1.E-8,ET=0.002,SIGT=1.E-2;
...
USE,PERIOD=FODO;
...
TRACK;
START,X=0.0010,Y=0.0017,PT=0.0003;
DYNAP,FASTUNE,TURNS=1024,LYAPUNOV=1.e-7;
ENDTRACK;
...

The first command defines the beam parameters. It is essential that the longitudinal emittance ET is set. The command use selects the beam line or sequence. The track activates the tracking module, start enters the starting coordinates (more than one particle can be defined), dynap finally tracks two nearby particles with an initial distance lyapunov for each start definition over turns revolutions, and endtrack terminates the execution of the tracking module.

The results are stored in the DYNAP and DUNAPTUNE tables, and can be obtained by the commands

value,table(dynap,smear);

resp.

value,(dynaptune,tunx),(dynaptune,tuny),(dynaptune,dtune);

More generally, all results can be printed to a file, using the commands

write,table=dynap,file;
write,table=dynaptune,file;

The output file 'lyapunov.data' lists the turn number and phase distance between the two Lyapunov partners, respectively, allowing for visual inspection of chaoticity.

frankz 20.03.2006