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

US LHC Accelerator Research Program 2 Vay - 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, (2005)

US LHC Accelerator Research Program 3 Vay - 04/28/06 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.

US LHC Accelerator Research Program 4 Vay - 04/28/06 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 quad s s0s0 lattice

US LHC Accelerator Research Program 5 Vay - 04/28/06 At present, we can run WARP/Posinst in 3 modes (2) 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 quad s s 0 s 0 +  s 0 lattice

US LHC Accelerator Research Program 6 Vay - 04/28/06 At present, we can run WARP/Posinst in 3 modes (3) 3.Three-dimensional fully self-consistent (t-dependent) Beam bunches (macroparticles) and electrons (macroparticles) evolve self-consistently with self-field + external field (dipole, quadrupole, …). Quadrupoles Drifts Bends WARP/POSINST-3D T = 300.5ns 1 LHC FODO cell (~107m) - 5 bunches - periodic BC

US LHC Accelerator Research Program 7 Vay - 04/28/06 WARP/POSINST benchmarked against High-Current Experiment (HCX) INJECTOR MATCHING SECTION ELECTROSTATIC QUADRUPOLES MAGNETIC QUADRUPOLES Focus of Current Gas/Electron Experiments 1 MeV, 0.18 A, t ≈ 5  s, 6x10 12 K + /pulse (a) (b) (c) Capacitive Probe (qf4) Clearing electrodes Suppressor Q1Q2Q3Q4 200mA K + e-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

US LHC Accelerator Research Program 8 Vay - 04/28/06 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-3D T = 4.65  s OscillationsElectrons bunching Beam ions hit end plate (a)(b)(c) e-e- 0V 0V 0V/+9kV 0V MA4MA3MA2MA1 200mA K + 200mA K + Electrons ~6 MHz signal in (C) in simulation AND experiment (c) time (  s) 6. WARP HCX I (mA) Potential contours WARP HCX (c) time (  s) 6. I (mA)

US LHC Accelerator Research Program 9 Vay - 04/28/06 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). 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

US LHC Accelerator Research Program 10 Vay - 04/28/06 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

US LHC Accelerator Research Program Backups

US LHC Accelerator Research Program 12 Vay - 04/28/06 WARP/POSINST compared with QUICKPIC FunctionalityQUICKPICWARP/POSINST ParticlesIons: x,y,z,p x,p y,p z Electrons: x,y,p x,p y All: x,y,z,p x,p y,p z Particle pusher Boris corrected for  0 Boris/drift hybrid for e- in magnetic field (bridges ion/e- time scales) Self-fieldsIons: 3-D from multiple 2-D Poisson Electrons: 2-D Poisson All: 3-D with AMR (2-D XY and RZ available) Lattice descriptionUniform and constant focusing + dispersion MAD-like(+more) description includes gaps, dipoles, quadrupoles, sext., … Pipe geometryRectangleAny Particle/Wall interaction Specular reflectionAbsorption, secondary emission, neutral emission, gas model PhotoemissionNoSimple model ParallelUsing MPIUsing 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)

US LHC Accelerator Research Program 13 Vay - 04/28/06 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

US LHC Accelerator Research Program 14 Vay - 04/28/06 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) 2 ] 1/2 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.

US LHC Accelerator Research Program 15 Vay - 04/28/06 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 beamelectrons