Roadmap to ecloud driven emittance growth calculations

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Roadmap to e-cloud driven emittance growth
calculations
Jean-Luc Vay, Miguel Furman Lawrence Berkeley
National Laboratory
US LHC Accelerator Research Program
Lawrence Berkeley National Laboratory - April
26-28, 2006
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E-cloud driven emittance growth concern for LHC

• We propose to use the WARP/POSINST tool to
  evaluate e-cloud driven beam instabilities,
  emittance growth and (possibly) halo formation,
• code suite issued from
• merging of WARP Posinst
  new modules

Key operational partially implemented (4/28/06)
Benedetto et al, PRST-AB 8, 124402 (2005)
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What makes WARP/POSINST unique

• Physics modules
• beam,
• electrons (photosecondary),
• accelerator lattice,
• arbitrary vacuum chamber geometry,
• State-of-the-art
• new electron mover to advance electrons in
  magnetic fields with large time steps,
• adaptive mesh refinement (speed-up x20,000 LHC 1
  bunch/1 FODO cell),
• parallel,
• modular, user programmable/steerable.

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At present, we can run WARP/Posinst in 3 modes
(1)

• Posinst mode (time-dependent)

2-D slab of electrons
s
3-D beam stack of 2-D slab
s0
lattice
A 2-D slab of electrons (macroparticles) sits at
a given station and evolves self-consistently
with its own field kick from beam slabs passing
through external field (dipole, quadrupole, ).
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At present, we can run WARP/Posinst in 3 modes
(2)

• Slice mode (s-dependent)

2-D beam slab
s
s0 s0?s0
lattice
A 2-D slab of beam (macroparticles) is followed
as it progresses forward from station to station
evolving self-consistently with its own field
external field (dipole, quadrupole, )
prescribed additional species, eventually.
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At present, we can run WARP/Posinst in 3 modes (3)

• Three-dimensional fully self-consistent
  (t-dependent)

Quadrupoles Drifts Bends
WARP/POSINST-3D T 300.5ns
1 LHC FODO cell (107m) - 5 bunches - periodic BC
Beam bunches (macroparticles) and electrons
(macroparticles) evolve self-consistently with
self-field external field (dipole, quadrupole,
).
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WARP/POSINST benchmarked against High-Current
Experiment (HCX)
Focus of Current Gas/Electron Experiments
INJECTOR
MATCHING SECTION
ELECTROSTATIC QUADRUPOLES
MAGNETIC QUADRUPOLES
1 MeV, 0.18 A, t 5 ?s, 6x1012 K/pulse
Experiment setup for code benchmarking beam
hits end-plate to generate copious electrons
which propagate upstream, leading to observable
currents in diagnostics and effects on the beam.
End plate
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Wavelength of 5 cm, growing from near center of
4th quad. magnet
0V 0V 0V/9kV
0V
Potential contours
e-
200mA K
MA4
MA3
MA2
MA1
WARP-3D T 4.65?s
Electrons
200mA K

• Good test of secondary module -
  no secondary electrons
• run time 3 days,
• - without new electron mover and MR, run time
  would be 1-2 months!

Beam ions hit end plate
0. -20. -40.
I (mA)
Oscillations
Electrons bunching
(c)

0. -20. -40.
0. 2. time (?s) 6.
6 MHz signal in (C) in simulation AND experiment
I (mA)
(c)
0. 2. time (?s) 6.
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For emittance growth study, we will add a 4th mode

• Quasi-static mode (s-dependent for e-,
  t-dependent for beam)
• -- more efficient when electrons can be treated
  as steady-flow --

2-D electron Plasma Slab
(Courtesy T. Katsouleas - QuickPIC)
A 2-D Poisson solver is used to calculate
potentials and update positions and velocities in
the electron plasma slab. After the slab is
stepped through the beam, the stored 2-D
potentials are stacked into a 3-D array and used
to push the 3-D beam. This is the mode of
operation for QuickPIC (UCLA) and HeadTail (CERN).
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Plan

• Implement new hybrid mode
• Run with 1 LHC FODO cell with periodic boundary
  conditions
• beam only
• beam photo-electrons secondary electrons
• Run with more realistic LHC lattice
• Add RF kicks/cavity
• beam only
• beam photo-electrons secondary electrons
• Preliminary results by Sept 06

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Backups
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WARP/POSINST compared with QUICKPIC

• All pieces needed to reproduce QUICKPIC framework
  available in WARP package (implementation in WARP
  of correction to ?0 for Boris would be trivial)

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We have invented a new mover that relaxes the
problem of short electron timescales in magnetic
field
Magnetic quadrupole

• Problem Electron gyro timescale
• ltlt other timescales of interest
• ? brute-force integration very slow due to small
  Dt
• Solution Interpolation between full-particle
  dynamics (Boris mover) and drift kinetics
  (motion along B plus drifts)

Sample electron motion in a quad
small ?t0.25/?c Standard Boris mover (reference
case)
large ?t5./?c New interpolated mover
large ?t5./?c Standard Boris mover (fails in
this regime)
Test Magnetized two-stream instability
R. Cohen et. al., Phys. Plasmas, May 2005
ROPA009, Thursday, Ballroom A, 1645
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We have developed an interpolation technique that
allows us to skip over electron-cyclotron
timescale

• Our solution interpolation between full-electron
  dynamics (Boris mover) and drift kinetics (motion
  along B plus drifts).
• Choice ??1/1(?c?t/2)21/2 gives, at both small
  and large ?c?t,
• physically correct gyro radius
• correct drift velocity
• Correct parallel dynamics.
• Incorrect gyration frequency at large ?c?t
  (same as pure Boris mover)
• Time step constraint set by next longer time
  scale -- typically electron cross-beam transit
  time.

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Frame 2nd passage of bunch through cell - 2

• We use actual LHC pipe shape beam size ltlt pipe
  radius
• Mesh Refinement provides speedup of x20,000 on
  field solve

beam
electrons