us lhc accelerator research program roadmap to e-cloud driven emittance growth calculations us lhc...

US LHC Accelerator Research Program

Roadmap to e-cloud driven emittance growth calculations


Lawrence Berkeley National Laboratory - April 26-28, 2006

Jean-Luc Vay, Miguel Furman

Lawrence Berkeley National Laboratory

US LHC Accelerator Research Program2Vay - 04/28/06

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)


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.


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

1. Posinst mode (time-dependent)

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, …).

2-D slab of electrons

3-D beam: stack of 2-D slab

benddrift driftquad

s

s0lattice



2. Slice mode (s-dependent)

2-D beam slab

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.

benddrift driftquad

s

s0 s0+s0lattice



3. Three-dimensional fully self-consistent (t-dependent)

Beam bunches (macroparticles) and electrons (macroparticles) evolve self-consistently with self-field + external field (dipole, quadrupole, …).

QuadrupolesDriftsBends

WARP/POSINST-3DT = 300.5ns

1 LHC FODO cell (~107m) - 5 bunches - periodic BC


WARP/POSINST benchmarked against High-Current Experiment (HCX)

INJECTOR

MATCHINGSECTION ELECTROSTATIC

QUADRUPOLESMAGNETIC

QUADRUPOLES

Focus of CurrentGas/Electron Experiments

1 MeV, 0.18 A, t ≈ 5 s, 6x1012 K+/pulse

(a) (b) (c)CapacitiveProbe (qf4)

Clearing electrodes Suppress

or

Q1 Q2 Q3 Q4

200mA K+

e-

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


1.Good test of secondary module - no secondary electrons:

2.run time ~3 days, - without new electron mover and MR, run time would be ~1-2 months!

1.Good test of secondary module - no secondary electrons:

2.run time ~3 days, - without new electron mover and MR, run time would be ~1-2 months!

Wavelength of ~5 cm, growing from near center of 4th quad. magnet

WARP-3DT = 4.65s

OscillationsElectrons bunching

Beam ions hit end plate

(a)

(b)

(c)

e-

0V 0V 0V/+9kV 0V

MA4MA3MA2MA1

200mA K+

200mA K+

Electrons

~6 MHz signal in (C) in simulation AND experiment

(c)0. 2. time (s) 6.

WARP HCX

0.

-20.

-40.

I (m

A)

Potential contours

WARP HCX

(c)0. 2. time (s) 6.

I (m

A) 0.

-20.

-40.


For emittance growth study, we will add a 4th mode

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).

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

4. “Quasi-static” mode (s-dependent for e-, t-dependent for beam)-- more efficient when electrons can be treated as

steady-flow --

(Courtesy T. Katsouleas - QuickPIC)

2-D electron Plasma Slab


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


Backups


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 PoissonElectrons: 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)


Problem: Electron gyro timescale

<< other timescales of interest

brute-force integration very slow due to small t

Solution*: Interpolation between full-particle dynamics (“Boris mover”) and drift kinetics (motion along B plus drifts)

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

quadrupole

Sample electron motion in a quad

beam

quad

*R. Cohen et. al., Phys. Plasmas, May 2005; ROPA009, Thursday, Ballroom A, 16:45

small t=0.25/c

Standard Boris mover(reference case)

large t=5./c

New interpolated mover

large t=5./c

Standard Boris mover(fails in this regime)

Test: Magnetized two-stream instability


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+(ct/2)2]1/2 gives, at both small and large ct, – physically correct “gyro” radius– correct drift velocity– Correct parallel dynamics.

• Incorrect “gyration frequency” at large ct (same as pure Boris mover)

• Time step constraint set by next longer time scale -- typically electron cross-beam transit time.


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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