Novel Simulation Methods in the code-framework Warp

Transcription

1 Novel Simulation Methods in the code-framework Warp J.-L. Vay1,3, D.P. Grote2,3, R.H. Cohen2,3, A. Friedman2,3, S.M. Lund2,3, E. Cormier-Michel1, W.M. Fawley1, M.A. Furman1, C.G.R. Geddes1 1Lawrence Berkeley National Laboratory 2Lawrence Livermore National Laboratory 3Heavy Ion Fusion Science Virtual National Laboratory UMER 2009 Workshop University of Maryland, Oct , Vay UMER Workshop 09 1

2 Warp is a parallel framework combining features of plasma (Particle-In-Cell) and accelerator codes Geometry: 3D (x,y,z), 2D-1/2 (x,y), (x,z) or axisym. (r,z) Python and Fortran: steerable, input decks are programs Field solvers: Electrostatic - FFT, multigrid; AMR; implicit Red: <5 years Magnetostatic - FFT, multigrid; AMR; implicit Electromagnetic - Yee, Kark.; PML; AMR Parallel: MPI (1, 2 and 3D domain decomposition) Boundaries: cut-cell --- no restriction to Legos Lattice: general; non-paraxial; can read MAD files - solenoids, dipoles, quads, sextupoles, linear maps, arbitrary fields, acceleration Bends: warped coordinates; no reference orbit Particle movers: Boris, large time step drift-lorentz, new relativistic Leapfrog Reference frame: lab, moving-window, Lorentz boosted Surface/volume physics: secondary e - /photo-e - emission, gas emission/tracking/ionization Diagnostics: extensive snapshots and histories Parallel scaling of Warp 3D PIC-EM solver on Franklin supercomputer (NERSC) 32,768 cores Misc.: trajectory tracing; quasistatic & steady-flow modes; space charge emitted emission; equilibrium-like beam loads in linear focusing channels; maintained using CVS repository. 2

3 Electrostatic AMR simulation of ion source : speedup x10 Run Grid size Nb particles Low res. 56x640 ~1M Medium res. High res. Low res. + AMR 112x x x640 ~4M ~16M ~1M zoom R (m) R (m) Z (m) Emittance (mm.mrad) 1.0 Low res. Medium res. High res. Low res. + AMR Z (m) Z (m) Refinement of gradients: emitting area, beam edge and front Z(m) 3

4 Electromagnetic MR simulation of beam-induced plasma wake with Warp 2 levels of mesh refinement (MR) 2-D high resolution 2-D low resolution + MR 3-D There simulations used the same time steps for all refinement levels. The implementation of separate time steps for each refinement level is underway. 4

5 POSINST provides advanced SEY model. Monte-Carlo generation of electrons with energy and angular dependence. Three components of emitted electrons: Its I 0 I0 Ie I ts I e I r Ir backscattered: rediffused: true secondaries: Phenomenological model: based as much as possible on data for δ and dδ/de not unique (use simplest assumptions whenever data is not available) many adjustable parameters, fixed by fitting δ and dδ/de to data true sec. re-diffused back-scattered elastic

6 Ion-induced electron emission and ionization cross-sections from the TxPhysics* library (Tech-X corporation) ion-induced neutral emission developed by J. Verboncoeur (UC-Berkeley). 6

7 New Drift-Lorentz mover that relaxes the problem of short electron timescales in magnetic field* Magnetic quadrupole Problem: Electron gyro timescale << other timescales of interest brute-force integration very slow due to small Δt Solution*: Interpolation between full-particle dynamics ( Boris mover ) and drift kinetics (motion along B plus drifts) beam quad correct gyroradius with Sample electron motion in a quad Test: Magnetized two-stream instability small δt=0.25/ω c Standard Boris mover (reference case) large δt=5./ω c Standard Boris mover (fails in this regime) large δt=5./ω c New interpolated mover *R. Cohen et. al., Phys. Plasmas, May

8 Modeling of the interaction of beam with electrons in a quadrupole 200mA K + Q1 0V 0V 0V/+9kV 0V (a) Q2 (b) Q3 (c) Q4 e - WARP-3D T = 4.65µs Potential contours WARP-3D T = 4.65µs Electrons 200mA K + I (ma) (c) Simulation Experiment time (µs) 6. Electrons bunching Oscillations Beam ions hit end plate ~6 MHz signal in (C) in simulation AND experiment run time ~3 days would be ~1-2 months without new electron mover and MR. 8

9 Warp electromagnetic field descriptions Electrostatic: Δφ=ρ Magnetostatic: ΔA=J Fully electromagnetic: E/ t = B-J; B/ t = - E ( E = ρ; B = 0) longitudinal Darwin for ultra-relativistic beams* (v z >>v x,v y ) * J.-L. Vay, Phys. Plasmas 15, (2008) 9

10 Applications of Warp to High-Energy Physics projects Electron cloud driven beam instabilities Beam + γ e - e - e - e - e - Pipe (collaboration with M. Furman, CBP, LBNL) Laser-plasma wakefield accelerators Plasma wake e- beam Laser pulse E // (GV/m) (collaboration with LBNL s LOASIS group, lead by Wim Leemans) Free electron lasers/coherent synchrotron radiation (collaboration with W. Fawley, CBP, LBNL) 10

11 Large scale range renders simulation of some HEP problems very difficult, if not impractical, in lab frame Laser-plasma acceleration laboratory frame 1µm 3cm HEP accelerators (e-cloud) 3cm/1µm=30,000. Free electron lasers 10cm 10km 1nm 10m 10km/10cm=100, m/1nm=10,000,000,

12 Range of space and time scales spanned by two identical beams crossing each other F 0 -center of mass frame F B -rest frame of B Γ x/t = (L/l, T/δt)* space y x y x γ 0 space+time γ 0 γ 0 γ 0 γ 0 Γ is not invariant under the Lorentz transformation: Γ x/t γ 2 There exists an optimum frame which minimizes it. Result is general and applies to light beams too. *J.-L. Vay, Phys. Rev. Lett. 98, (2007) 12

13 Lorentz transformation => large level of compaction of scales range Hendrik Lorentz boosted frame Laser-plasma acceleration 30µm 1µm frame γ mm 3cm HEP accelerators (e-cloud) 4.5m 10cm frame γ 22 10km 450m 3cm/1µm=30, mm/30µm=53. Free electron lasers 1nm 4µm frame γ 4000 compaction x mm 10m 10km/10cm=100, m/4.5m=100. compaction x m/1nm=10,000,000, mm/4µm=625. compaction x

14 Seems simple but!. Algorithms which work in one frame may break in another. Example: the Boris particle pusher. Boris pusher ubiquitous In first attempt of e-cloud calculation using the Boris pusher, the beam was lost in a few betatron periods! Position push: X n+1/2 = X n-1/2 + V n Δt -- no issue q Δt γ n+1 V n+1 + γ n V n Velocity push: γ n+1 V n+1 = γ n V n + (E n+1/2 + B n+1/2 ) m 2 γ n+1/2 issue: E+v B=0 implies E=B=0 => large errors when E+v B 0 (e.g. relativistic beams). Solution q Δt V n+1 + V n Velocity push: γ n+1 V n+1 = γ n V n + (E n+1/2 + B n+1/2 ) m 2 Not used before because of implicitness. We solved it analytically* (with,,,,,, ). * J.-L. Vay, Phys. Plasmas 15, (2008) 14

15 Application to modeling of e-cloud driven instability Warp Calculation of e-cloud induced instability of a proton bunch* Proton energy: γ=500 in Lab L=5 km, continuous focusing beam electron streamlines proton bunch radius vs. z (from Warp movie) CPU time (2 quad-core procs): lab frame: >2 weeks frame with γ 2 =512: <30 min Speedup x1000 Recently conducted fully self-consistent (including gas ionization and secondary e- emission) simulation of e-cloud driven instability for toy SPS problem. Will soon apply to bunch train: bunch n+1 bunch n *J.-L. Vay, Phys. Rev. Lett. 98, (2007) 15

16 2D scaled simulations of a 10 GeV class LWFA stage (λ=0.8µm, a 0 =1, k p L=2, L p =1.5mm in lab) Snapshots of surface plot of // electric field in lab frame and boosted frame at γ=10 arp 2-D E // (GV/m) arp 2-D Plasma wake Laser imprint E // (GV/m) 2D Lab frame Station z=0.154mm e- beam Boosted frame (γ=10) and // electric field history in lab frame Station z=1.354mm 2D Average beam energy and CPU time vs position in lab frame 1,500s speedup x75 20s 16

17 % level agreement obtained between Warp simulations with γ=1-10 instability observed at front of plasma for higher γ 3D scaled simulations of a 10 GeV LWFA stage (λ=0.8µm, a0=1, kpl=2, ne=1019cc, Lp=1.5mm in lab) Average beam energy and CPU time vs position in lab frame 3D 30,000s speedup x75 400s Max γframe achieved in 2D and 3D limited by instability developing at front of plasma 2D full scale simulation 10 GeV LWFA stage (ne=1017cc, γ=130) 17

18 Widening the band of the digital filter improves significantly filter applied to current density and gathered field, NOT on Maxwell EM field Smoothing 1 Smoothing 2 Smoothing 3 Smoothing 4 E // (GV/m) E // (GV/m) E // (GV/m) E // (GV/m) Z Z Z Z Result is only slightly affected, even with most aggressive filtering tested. wideband filter applied along longitudinal direction only 18

19 Filtering allows max speedup for simulations of 10 GeV LWFA stage Simulations in 1D/2D/3D at plasma densities of cc, cc and cc show good agreement on (scaled) beam energy gain: cc: max γ frame = 130 speedup > 10,000 In 3D, 3h using 256 CPUs > 1 year x 256 CPUs in lab frame! cc: max γ frame = 400 speedup > 100,000 In 2D, 4h using 24 CPUs > 50 years x 24 CPUs in lab frame! 2D n e = cc γ frame = 13 19

20 FEL in Boosted-Frame E&M Code Standard FEL codes use slowly-varying envelope (Eikonal) and wiggler-period averaring approximations; Physics ignored by Eikonal codes but accessible to boosted frame approach Backward wave emission Wide-angle emission (generally highly red-shifted) CSE for all undulator, e-beam configurations (very short beams; beams with rapidly-varying envelope properties, beams bunched with multiple colors ) Properties of very high gain systems (L G /λ u < 5) FEL emission from beams in multiple harmonic undulators (biharmonic or triharmonic undulators; effects of adiabatic match sections) FEL emission in waveguides where v group strongly varying with ω (normally relevant to microwave FEL s operating near cutoff) Benchmarking of BF with Eikonal code Ginger*: impressive speedup compared to full E&M but much slower than standard eikonal method Not likely to become dominant paradigm for short wavelength FEL s but might be useful for very high gain microwave/far-ir devices or situations with wideband spectral output *W.M. Fawley et al, Proc AAC 08; Proc. PAC 09 20