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Status of Space-Charge Simulations with MADX

kapin@itep.ru. 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).

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Status of Space-Charge Simulations with MADX

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  1. kapin@itep.ru Status of Space-Charge Simulations with MADX Valery KAPIN ITEP & MEPhI, Moscow GSI, 19-Feb-2009

  2. 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/”

  3. Initial plans for S.C. in 2006 From “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

  4. 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 dynamicssimulations without space-charge. M. Furman, 1987 PAC, pp. 1034-1036.………………………………………………………Y. Alexahin, 2007 PAC, report code THPAN105.

  5. 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.);

  6. The 2nd order ray tracing integrator for a number of S-C kicks

  7. 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;

  8. 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 Iterations in two steps Straight lines shows analytical values according to the Laslett's formula for tune shifts.

  9. Resulting beam sizes for a simple 4-bend FODO structure Non-zero beam current Zero beam current

  10. 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

  11. Application to real ring – ITEP’s TWAC Dependence of analytical (Laslett) and computed (MADX) betatron tunes on intensity. Dependence of DA on the beam intensity for relative momentum offset DELTAP=  -0.005 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.

  12. 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) Present Status With the option I -> for FAIR SIS100:“Benchmarking of sp.-charge induced loss in SIS100 ring”“DA with Octupoles (for Landau damping) in SIS100”

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