Status of Space-Charge Simulations with MADX Valery KAPIN MEPhI - - - PowerPoint PPT Presentation

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 kapin@fnal.gov

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 Qx,y=int => (TWISS=ERR)
• 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 5 10 15 20 Qx_formula Qx_num_I/2 Qx_num_I Qy_formula Qy_num_I/2 Qy_num_I N_iter

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);

• 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

• 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.

9.05 9.1 9.15 9.2 9.25 9.3 9.35 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

1 10-5 2 10-5 3 10-5 4 10-5 5 10-5 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_ave Er_cross_ave Er_min_min Er_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.

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 =>

non-linear maps for s.c. => non-linear maps of a whole ring. => all the map formalism & Normal Forms. PTC – developer (E.Forest will visit CERN in this spring)

• Simulation of
• Synch. Osc. –

Time-Modulation of all BB’s (not difficult)

• Arb. thin-element:

“user” or code inputs coefficients into element’s series (under discussion)