Status of Space-Charge Simulations with MADX Valery KAPIN ITEP & MEPhI, Moscow GSI, 19-Feb-2009

ITEP-CERN collaboration on MADX in 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: “

Initial plans for S.C. in 2006 From “V.Kapin: Plans for PTC modules in 2006”[1].[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][1] Meeting-20/Kapin_madx_ 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 ……………………………………………………… 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.);

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

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 Q x,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.

Resulting beam sizes for a simple 4-bend FODO structure Zero beam current Non-zero beam 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); 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. Dependence of DA on the beam intensity for relative momentum offset DELTAP= 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”