status of space-charge simulations with madx valery kapin itep & mephi, moscow gsi, 19-feb-2009...
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Status of Space-Charge Simulations with MADX
Valery KAPIN
ITEP & MEPhI, Moscow
GSI, 19-Feb-2009
ITEP-CERN collaboration on MADX in 2004-2006
• MAD => code for the beam dynamics in accelerators.
• MAD-X is the successor of MAD-8 (frozen in 2002).
• MAD-X has a modular organization =>Development Team:
Custodian (F.Schmidt) + Module Keepers
• “PTC-TRACK module” is developed by V.Kapin (ITEP) & F.Schmidt (CERN)
MAD-X Home Page: “http://mad.home.cern.ch/mad/”
Initial plans for S.C. in 2006From “V.Kapin: Plans for PTC modules in 2006”[1] .
(MADX meeting 20 March 2006, CERN, Geneva)
Two options are discussed – “inserting BB-kicks” & with PTC-library:I.a) usage a “linear” kick-matrix for Twiss parameters (b);I.b) a space-charge kicks from "frozen beam" during tracking;
II) Model using a new PTC elements (many “Beam-Beam”)
For the option II:• Beam-beam element for PTC (coding by E.Forest)
• MADX PTC tracking with a space-charge kicks inside thick elements (even with fill-turn maps)
[1] http://frs.home.cern.ch/frs/MAD-X_minutes/Meeting-20/Kapin_madx_20060320.ppt
Thin-lens (option I) “MADX+S.C.”
• The whole idea is not a new one. For example, references below.
• Presented methods had been already implemented in other beam dynamics codes.
• Our task is a step-by-step adaptation some of them to MADX, which is presently one of the most advanced code for nonlinear beam dynamics simulations without space-charge.
M. Furman, 1987 PAC, pp. 1034-1036.………………………………………………………Y. Alexahin, 2007 PAC, report code THPAN105.
Features & Algorithm of Direct S.C Simulations with MADX
• all work is done using macros of MADX input
scripts
• Now only 4D
• "Frozen" charge distribution either linear (MATRIX) or Gaussian (BB);
• Several space-charge kicks within every thick element (bends, quads, drifts etc.);
Self-consistent (linear) beam-sizes
• Space-charge kicks simulated by the 1st order MATRIX for
linear TWISS calculations;
• Linearly self-consistent beam sizes calculated by iterations with the TWISS;
• Analytical Laslett's formula and numerical iterations provide
near the same tune shifts;
Iterations to find beam sizes at non-zero beam current
• No Equilibrium solution for Qx,y=int => (TWISS=>stops)
• Tune value oscillates around a final value;
=> near Q=n iterations with steps for the beam current
2
2.1
2.2
2.3
2.4
2.5
1
1.1
1.2
1.3
1.4
1.5
0 5 10 15 20
Qx_formulaQx_num_I/2Qx_num_I
Qy_formulaQy_num_I/2Qy_num_I
N_iter
Iterations in two steps
Straight lines shows
analytical values
according to the Laslett's formula for tune shifts.
Tracking with many BB Example for a simple lattice
• S.C kicks by BB-elements for non-linear tracking; (C.O. shifts are included; a total number BB-elements is not limited);
• Thin-lens tracking with MADX (similar to MAD8)
with lattice conversion by MAKETHIN command
Application to real ring – ITEP’s TWAC
V. V. Kapin, A. Ye. Boshakov, P. R. Zenkevich, “Influence of space charge on dynamical
effects on dynamical aperture of TWAC storage ring”, RuPAC’08.
9.05
9.1
9.15
9.2
9.25
9.3
9.35
0 1 1013 2 1013 3 1013 4 1013 5 1013 6 1013
TWAC Nonliner lattice results for protons 700MeV
Qx_formula
Qx_num
Qy_formula
Qy_num
Number of particles
0
1 10-5
2 10-5
3 10-5
4 10-5
5 10-5
0 1 1013 2 1013 3 1013 4 1013 5 1013 6 1013
DA-emittance for TWAC Nonlinear lattice proton beam at 700MeV DELTAP=-0.005
Er_min_aveEr_cross_aveEr_min_minEr_cross_min
Er, [m x rad]
Number of particles
Dependence of DA on the beam intensity for relative
momentum offset DELTAP= -0.005
Dependence of analytical (Laslett) and
computed (MADX) betatron tunes on intensity.
Present Status
• BB in MADX-PTC (option II) => non-linear maps including s.c. (inside “thick elements”)
=> non-linear maps of a whole ring. => all the map formalism & Normal Forms.
Status: 1) BB are in PTC-library (done by E.Forest) 2) interfacing with MADX -> ??? (manpower required)
With the option I -> for FAIR SIS100: “Benchmarking of sp.-charge induced loss in SIS100 ring” “DA with Octupoles (for Landau damping) in SIS100”