Transcript Roadmap to e-cloud driven emittance growth calculations Jean-Luc Vay, Miguel Furman

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
US LHC Accelerator Research Program
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 (photo+secondary),
– 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)
1. Posinst mode (time-dependent)
2-D slab of electrons
s
3-D beam: stack of 2-D slab
s0
lattice
quad
drift
bend
drift
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)
2. Slice mode (s-dependent)
2-D beam slab
s
s0
lattice
quad
drift
s0+s0
bend
drift
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)
3. Three-dimensional fully self-consistent (t-dependent)
WARP/POSINST-3D
T = 300.5ns
Quadrupoles
Drifts
Bends
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.
Clearing electrodes
(b)
(a)
(c)
Capacitive
Probe (qf4)
200mA K+
Suppressor
eQ1
Q2
Q3
Q4
End plate
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Wavelength of ~5 cm, growing from near center of 4th quad. magnet
0V
0V
0V/+9kV
0V
200mA K+
Potential contours
e-
MA1 (a) MA2 (b) MA3 (c) MA4
WARP-3D
T = 4.65s
Electrons
200mA
K+
I (mA)
Electrons bunching
Oscillations
WARP
HCX
0.
-20.
(c)
-40.
0.
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2.
time (s)
-20.
-40.
6.
~6 MHz signal in
(C) in simulation
AND experiment
WARP
HCX
0.
I (mA)
Beam ions
hit end
plate
1. Good test of secondary module
- no secondary electrons:
(c)
0.
2.
time (s)
6.
2. run time ~3 days,
- without new electron mover and MR, run
time would be ~1-2 months!
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For emittance growth study, we will add a 4th mode
4. “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
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
(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
Functionality
QUICKPIC
WARP/POSINST
Particles
Ions: x,y,z,px,py,pz
Electrons: x,y,px,py
All: x,y,z,px,py,pz
Particle pusher
Boris corrected for 0
Boris/drift hybrid for e- in magnetic
field (bridges ion/e- time scales)
Self-fields
Ions: 3-D from multiple 2-D Poisson
Electrons: 2-D Poisson
All: 3-D with AMR
(2-D XY and RZ available)
Lattice description
Uniform and constant focusing +
dispersion
MAD-like(+more) description includes
gaps, dipoles, quadrupoles, sext., …
Pipe geometry
Rectangle
Any
Particle/Wall
interaction
Specular reflection
Absorption, secondary emission,
neutral emission, gas model
Photoemission
No
Simple model
Parallel
Using MPI
Using MPI, different decomposition for
fields and particles
• 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
quad
Problem: Electron gyro timescale
<< 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)
Test:
Magnetized
two-stream
instability
small t=0.25/c
Standard Boris mover
(reference case)
large t=5./c
New interpolated mover
Sample electron
motion in a quad
large t=5./c
Standard Boris mover
(fails in this regime)
*R. Cohen et. al.,US
Phys.
Plasmas,
May 2005;
ROPA009,
Thursday, Ballroom A, 16:45
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Accelerator
Research
Program
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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+(cDt/2)2]1/2 gives, at both small and large cDt,
– physically correct “gyro” radius
– correct drift velocity
– Correct parallel dynamics.
• Incorrect “gyration frequency” at large cDt (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 << pipe radius
• Mesh Refinement provides speedup of x20,000 on field solve
beam
electrons
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