kapin@fnal.gov Status of Space-Charge Simulations with MADX Valery KAPIN MEPhI - Moscow Engineering Physics Institute (State Univ.) ITEP - Institute for Theoretical and Experimental Physics, Moscow FNAL, Batavia, 23-Jan-2008
ITEP-CERN collaboration 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 organisation => Development Team: Custodian (F.Schmidt) + Module Keepers • “PTC-TRACK module” is a main feature of MAD-X developed by V.Kapin (ITEP) & F.Schmidt (CERN) MAD-X Home Page: “http://mad.home.cern.ch/mad/”
“MADX+S.C.” project • The whole idea is not a new one. See references, below. • All 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.
Initial plans for S.C. in 2006 From “V.Kapin: Plans for PTC modules in 2006”[1] . (MADX meeting 20 March 2006, CERN, Geneva) ……………………………………… • 6) Beam-beam element for PTC (coding with help from Etienne) • 7) MADX PTC tracking with a space-charge ("frozen-beam" approach): Two options are discussed: 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”) [1] http://frs.home.cern.ch/frs/MAD-X_minutes/ Meeting-20/Kapin_madx_20060320.ppt
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.);
The 2nd order ray tracing integrator for a number of S-C kicks
Self-consistent 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 Q x,y =int => (TWISS=ERR) • Tune value oscillates around a final value; => near Q=n iterations with steps for the beam current 2.5 1.5 Qx_formula Qx_num_I/2 Qx_num_I Iterations in 2.4 1.4 two steps Straight lines 2.3 1.3 shows analytical values Qy_formula 2.2 1.2 Qy_num_I/2 according to Qy_num_I the Laslett's 2.1 1.1 formula for tune shifts. 2 1 0 5 10 15 N_iter 20
Resulting beam sizes for a simple 4-bend FODO structure Non-zero Zero beam beam current current
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); • Since BB is not included into MADX-PTC yet, thin-lens tracking with MADX (similar to MAD8) with lattice conversion by MAKETHIN command
Application to real ring – ITEP’s TWAC DA-emittance for TWAC Nonlinear lattice Er_min_ave proton beam at 700MeV DELTAP=-0.005 Er_cross_ave Er, Er_min_min [m x rad] Dependence of Er_cross_min analytical (Laslett) and 5 10 -5 computed (MADX) 4 10 -5 betatron tunes on intensity. 3 10 -5 2 10 -5 9.35 TWAC Nonliner lattice results for protons 700MeV 1 10 -5 9.3 Number of particles 0 Qx_formula 9.25 1 10 13 2 10 13 3 10 13 4 10 13 5 10 13 6 10 13 0 Qx_num Qy_formula 9.2 Qy_num 9.15 Dependence of DA on the beam intensity for relative 9.1 momentum offset Number of particles 9.05 DELTAP= -0.005 1 10 13 2 10 13 3 10 13 4 10 13 5 10 13 6 10 13 0 V. V. Kapin, A. Ye. Boshakov, P. R. Zenkevich, “Influence of space charge on dynamical effects on dynamical aperture of TWAC storage ring”, ITEP preprint, 2008.
Applications: collaboration ITEP-GSI • Proposals for a new collaboration ITEP-GSI for FAIR-project (at new FAIR Russia Research Centre to be located on premises of ITEP in Moscow) • ITEP – “Accelerator Theory Group” (P. Zenkevich – leader, A. Bolshakov, V. Kapin) & GSI – “High-Current Beam Physics Group” (I. Hofmann - leader, G. Franchetti) • One of the proposed subjects “Benchmarking of space charge induced loss in SIS100 ring” (using MADX)
Future developments of MADX • BB in MADX-PTC => • Simulation of non-linear maps for Synch. Osc. – s.c. => non-linear Time-Modulation of all maps of a whole ring. BB’s (not difficult) => all the map formalism & • Arb. thin-element: Normal Forms. “user” or code PTC – developer inputs coefficients (E.Forest will visit into element’s series CERN in this spring) (under discussion)
Recommend
More recommend
