September 23, 2005 Second MAD-X Day 1

PTC Modules in Mad-XPTC Modules in Mad-X

• PTC for the Module Writer

• Goal of the PTC Module Duplicates

• PTC_twiss module

• PTC_track

• PTC_normal

September 23, 2005 Second MAD-X Day 2

PTC for the Module PTC for the Module WriterWriter

• PTC is basically a symplectic particle tracker and it provides a library of Normal Form techniques.

• A large fraction of an actual module are features (“decorations”) rather than physics that means how input/output is prepared etc. These “decorations” are of course very relevant to the MAD-X user!

• PTC will not provide these services and the PTC module keeper will have to learn the specific PTC syntax to provide them. (Example: PTC does not provide beta functions per se as output. However, the tools are at hand to calculate them PTC_twiss) .

• In building the PTC_track module which has many features it proved essential to know subtle

details of PTC.

• To this end Etienne has provide a checklist of FPP/PTC utilities including examples. More such documentation is needed and will be provided ( EF & FS).

• One should remember that PTC is object oriented which makes life easy for the PTC module keeper, since the “physics” can be separated from the “decorations”. (Example: Introducing a new element or upgrading an old one will require no modification whatsoever to the procedure to calculate the beta functions)

September 23, 2005 Second MAD-X Day 3

Goal of the PTC Goal of the PTC Module DuplicatesModule Duplicates

• The MAD-X proper modules usually have a large amount of features. An attempt is being made to provide all those features in the PTC modules.

• New features are added when PTC allows to do so.

• Some of the first PTC modules have a large overlap with standard modules.

• This gives confidence that both modules give proper results in cases where they should be the same.

• On the other hand when differences are expected (delta dependence, small machines etc) the applicability limits of MAD-X can be tested.

• The PTC modules are bound to be slower than the MAD-X proper ones. Therefore, there is an incentive to stay with the standard modules if their results can be trusted.

September 23, 2005 Second MAD-X Day 4

PTC_twiss ModulePTC_twiss Module

• Provides 3D Twiss parameters à la the late Gerhard Ripken. This is a replacement of the TWISS3 command of MAD8.

• Results will agree with the normal twiss (Teng/Edwards style) command in the absence of coupling.

• Twiss with initial conditions

• Documentation in preparation

• Examples available

• Desirable but missing features: Twiss summary, Eigenvectors

Help needed

September 23, 2005 Second MAD-X Day 5

! Example 2: Input twiss parameters manually!ptc_twiss,icase=5,no=1,!betx=177.6823337,bety=32.05718846,alfx=-

2.411683347,alfy=0.4797516839,!

dx=2.176379444,dpx=0.02964538223,mux=1.254518853,muy=1.25446531,

!x= 8.897806712109201E-05,px=7.283918352660537E-07,y=5.216050332314255E-05,

!py=-6.748041062611770E-07,

! Example 3: Read transfer matrix from table

!ptc_twiss,icase=5,no=1,initial_matrix_table,

! Example 4: Input transfer matrix coef manually

! ptc_twiss,icase=5,no=1,initial_matrix_manual,

!re11=-2.4571122533365,re12=176.79612000630,re13=0.23000824922475E-01,

!re14=1.0688611352549,re16=2.3391750911139,re21=-.38675166732927E-01,

!re22=2.3757451844819,re23=0.59429549540250E-03,re24=0.21234193844153E-01,

!re26=0.44298917404022E-01,re31= -.13869369418419E-01,re32=1.1108843741365,

!re33=0.44540891438146,re34=32.763919904586,re36=0.23713296091797E-02,

!re41=-.10425674606620E-03,re42=0.18936158169385E-01,re43=-.37799347979450E-01,

!re44=-.53503193709587,re46=-.94686370477940E-03,file=ptc_twiss;ptc_end;stop;

!TITLE,'Test input for PTC_TWISS';

call, file = "ring.seq";

SAVEBETA, label=TWSSip, place=#E,sequence=fivecell;select,flag=twiss,column=name,s,betx,bety,dx,dy;TWISS,file=twiss_fv9;SHOW,TWSSip;

ptc_create_universe;ptc_create_layout,model=2,method=6,nst=10,exact;ptc_align;select,flag=ptc_twiss,column=name,s,beta11,beta21,beta12,beta22,disp1,disp3,x,px,y,py;ptc_twiss,closed_orbit,icase=5,file=twiss_toy,no=1;ptc_normal,closed_orbit,maptable,icase=5,no=1;ptc_end;write,table="map_table",file="map_table";

call, file = "line.seq";

select,flag=ptc_twiss,clear;select,flag=ptc_twiss,column=name,s,beta11,beta21,beta12,beta22,disp1,disp3;ptc_create_universe;ptc_create_layout,model=2,method=6,nst=5,exact;

! Example 1: BETA0 block !!!active!!!

ptc_twiss,icase=5,no=1,BETA0=TWSSip,

September 23, 2005 Second MAD-X Day 6

PTC_track ModulePTC_track Module

• Goal: Same functionality as the thinlens tracking module• BUT: Using thick elements in PTC• Features:

– Start, Run command– Tracking Data in TFS tables– Plotting– Normal Coordinates– Observation Points– Documentation– Examples

• Features in Preparation:– Radiation– Aperture

September 23, 2005 Second MAD-X Day 7

Input for MADX Input for MADX-PTCtrack, dump,onepass;start, x=1e-3, px=0, y=1e-3, py=0;start, x=1e-3, px=0, y=1e-3, py=0;start, x=2e-3, px=0, y=2e-3, py=0;start, x=3e-3, px=0, y=3e-3, py=0;start, x=4e-3, px=0, y=4e-3, py=0;start, x=5e-3, px=0, y=5e-3, py=0;start, x=6e-3, px=0, y=6e-3, py=0;start, x=7e-3, px=0, y=7e-3, py=0;run, turns=1000, ffile=1;

plot, file="apr07ktr", table=track, haxis=x, vaxis=px, particle=1,2,3,4,5,6,7, colour=100, multiple, symbol=3;

plot, file="apr07ktr", table=track, haxis=y, vaxis=py,

particle=1,2,3,4,5,6,7, colour=100, multiple, symbol=3;

endtrack;

ptc_create_universe;ptc_create_layout,

model=2, method=6, nst=10,exact;ptc_start, x= 3e-3, px=0, y= 3e-3, py=0;ptc_start, x= 6e-3, px=0, y= 6e-3, py=0;ptc_start, x= 9e-3, px=0, y= 9e-3, py=0;ptc_start, x=12e-3, px=0, y=12e-3, py=0;ptc_start, x=15e-3, px=0, y=15e-3, py=0;ptc_start, x=18e-3, px=0, y=18e-3, py=0;ptc_track,icase=4,closed_orbit,dump, // ptc_radiation, radiation, // radiation_energy_loss, radiation_quad, turns=1000,ffile=1, norm_out, norm_no=1;

plot, file="apr07ktrptc", table=track, haxis=x,vaxis=px,particle=1,2,3,4,5,6, colour=1000, multiple, symbol=3;plot, file="apr07ktrptc", table=track, haxis=y,vaxis=py,particle=1,2,3,4,5,6, colour=1000, multiple, symbol=3;ptc_end;

September 23, 2005 Second MAD-X Day 8

NORMAL FORM for small amplitudes: Input in STANDARD coordinates; 1000 turns; 4 particles;

Output in STANDARD coords;

Example for fv9.madx;ptc_create_layout, model=2,method=6,nst=10,exact

September 23, 2005 Second MAD-X Day 9

Input in STANDARD coordinates; 1000 turns; 4 particles; no=1 (linear);

Output in NORMALIZED coords;

Example for fv9.madx;ptc_create_layout, model=2,method=6,nst=10,exact

September 23, 2005 Second MAD-X Day 10

Input in STANDARD coordinates; 1000 turns; 4 particles; no=4 ;

Output in NORMALIZED coords;

Example for fv9.madx;ptc_create_layout, model=2,method=6,nst=10,exact

September 23, 2005 Second MAD-X Day 11

Input in STANDARD coordinates; 1000 turns; 4 particles; no=8 (CPU time 4 min);

Output in NORMALIZED coords;

Example for fv9.madx;ptc_create_layout, model=2,method=6,nst=10,exact

September 23, 2005 Second MAD-X Day 12

PTC_normal ModulesPTC_normal Modules

• Provides Nonlinear Terms to any Order:– Dispersion– Chromaticity– Anharmonicity– Hamiltonian Terms

• Put to tables for ready use in the matching module (yet to be used!)

• Documentation in Preparation• Example available• Important: Parameter Dependence yet to be

explored!!

September 23, 2005 Second MAD-X Day 13

ptc_create_universe; ptc_create_layout,model=1,method=2,nst=1;!,exact;

select_ptc_normal, dx=1, dpx=1;select_ptc_normal, dy=1, dpy=1;select_ptc_normal, haml=1,0,0;select_ptc_normal, q1, q2;select_ptc_normal, dq1=1, dq2=1;select_ptc_normal, dq1=2, dq2=2;select_ptc_normal, haml=1,-2,0;select_ptc_normal, anhx=1,0,0;select_ptc_normal, anhy=1,0,0;select_ptc_normamb1l, anhx=1,0,1;select_ptc_normal, haml=-5,0,0;select_ptc_normal, anhy=1,0,1;select_ptc_normal, anhx=0,0,2;select_ptc_normal, anhy=0,0,2;select_ptc_normal, anhx=2,0,0;select_ptc_normal, haml=1,2,0;select_ptc_normal, anhy=2,0,0;select_ptc_normal, anhx=1,1,0;select_ptc_normal, anhy=1,1,0;

ptc_normal,closed_orbit,normal,icase=5,no=7; ptc_end; write, table=normal_results;