Status of SpaceCharge Simulations with MADX

1
Status of Space-Charge Simulations with MADX
kapin_at_itep.ru

• Valery KAPIN
• ITEP MEPhI, Moscow

GSI, 19-Feb-2009
2
ITEP-CERN collaboration on MADX in 2004-2006

• MAD gt code for the beam dynamics in
  accelerators.
• MAD-X is the successor of MAD-8 (frozen in 2002).
• MAD-X has a modular organization gtDevelopment
  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 20061
  .
• (MADX meeting 20 March 2006, CERN, Geneva)
• Two options are discussed inserting BB-kicks
  with PTC-libraryI.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/ M
  eeting-20/Kapin_madx_20060320.ppt

4
Thin-lens (option I) MADXS.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.
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,yint gt
  (TWISSgtstops)
• Tune value oscillates around a final value
• gt near Qn 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 ITEPs 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,
RuPAC08.
12
Present Status
With the option I -gt for FAIR SIS100
Benchmarking of sp.-charge induced loss in
SIS100 ring DA with Octupoles (for Landau
damping) in SIS100

• BB in MADX-PTC (option II) gt non-linear maps
  including s.c. (inside thick elements) gt
  non-linear maps of a whole ring. gt all the
  map formalism Normal Forms. Status 1) BB are
  in PTC-library (done by E.Forest) 2)
  interfacing with MADX -gt ??? (manpower required)