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Jean-Luc Vay Heavy Ion Fusion Science Virtual National Laboratory

Self-consistent simulations of particle beam/plasma interaction with its environment. Jean-Luc Vay Heavy Ion Fusion Science Virtual National Laboratory Lawrence Berkeley National Laboratory DOE OFES Theory Seminar Series June 5, 2007. Collaborators.

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Jean-Luc Vay Heavy Ion Fusion Science Virtual National Laboratory

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  1. Self-consistent simulations of particle beam/plasma interaction with its environment Jean-Luc Vay Heavy Ion Fusion Science Virtual National Laboratory Lawrence Berkeley National Laboratory DOE OFES Theory Seminar Series June 5, 2007

  2. Collaborators • M. A. Furman, C. M. Celata, P. A. Seidl, K. Sonnad • Lawrence Berkeley National Laboratory • R. H. Cohen, A. Friedman, D. P. Grote, • M. Kireeff Covo, A. W. Molvik, W. M. Sharp • Lawrence Livermore National Laboratory • P. H. Stoltz, S. Veitzer • Tech-X Corporation • J. P. Verboncoeur • University of California - Berkeley

  3. Outline • Context • Simulation tools • Benchmarking against experiments • Application to high energy physics • Summary

  4. Context

  5. Today’s HIFS program is directed at beam & Warm Dense Matter physics in the near term, and IFE in the longer term • Heavy Ion Fusion Science experiments: • The physics of compressing beams in space and time • -- Drift compression and final focus • -- High brightness beam preservation • -- Electron cloud, beam halo, non-linear processes • Warm Dense Matter (WDM) experiments • -- Equation of state • -- Two-phase regime and droplet formation • -- Insulator and metals at WDM conditions • Hydrodynamics experiments relevant to HIF targets • -- Hydrodynamic stability, volumetric ion energy deposition, and Rayleigh-Taylor mitigation techniques

  6. It is highly desirable to minimize the space between the beam and the accelerating structure. This elevates the likelihood of "halo" (outlier) ions hitting structures, ... … so that a detailed understanding is needed. (from a WARP movie; see http://hif.lbl.gov/theory/simulation_movies.html)

  7. e- g e- e- i+ halo i+ g e- e- e- e- Sources of electron clouds e- • i+ = ion • e-= electron • g = gas • = photon = instability  Positive Ion Beam Pipe • Ionization of • background gas • desorbed gas Primary: Secondary: • ion induced emission from • expelled ions hitting vacuum wall • beam halo scraping • photo-emission from synchrotron radiation (HEP) • secondary emission from electron-wall collisions

  8. Simulation goal - predictive capability Source-through-target self-consistent time-dependent 3-Dsimulations of beam, electrons and gas with self-field + external field (dipole, quadrupole, …). HCX Electrons 200mA K+ From source… WARP-3D T = 4.65s …to target.

  9. Simulation tools

  10. WARP is our main tool • 3-D accelerator PIC code • Geometry: 3D, (x,y), or (r,z) • Field solvers:FFT, capacity matrix, multigrid • Boundaries:“cut-cell” --- no restriction to “Legos” • Bends: “warped” coordinates; no “reference orbit” • Lattice: general; takes MAD input • solenoids, dipoles, quads, sextupoles, … • arbitrary fields, acceleration • Diagnostics: Extensive snapshots and histories • Parallel:MPI • Python and Fortran: “steerable,” input decks are programs

  11. + new e-/gas modules quad beam 1 2 Key: operational; partially implemented (4/28/06) + Novel e- mover + Adaptive Mesh Refinement Allows large time step greater than cyclotron period with smooth transition from magnetized to non-magnetized regions concentrates resolution only where it is needed R Speed-up x10-104 e- motion in a quad Speed-up x10-100 3 4 Z WARP-POSINST has unique features merge of WARP & POSINST

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

  13. We have benefited greatly from collaborations • ion-induced electron emission and cross-sections from the TxPhysics* module from Tech-X corporation (http://www.txcorp.com/technologies/TxPhysics), • ion-induced neutral emission developed by J. Verboncoeur (UC-Berkeley).

  14. Benchmarking against experiments

  15. Benchmarked against dedicated experiment on HCX (b) (c) (a) Q1 Q2 Q3 Q4 Location of Current Gas/Electron Experiments MATCHING SECTION ELECTROSTATIC QUADRUPOLES INJECTOR MAGNETIC QUADRUPOLES 1 MeV, 0.18 A, t ≈ 5 s, 6x1012 K+/pulse, 2 kV space charge, tune depression ≈ 0.1 Retarding Field Analyser (RFA) Clearing electrodes Capacitive Probe (qf4) Suppressor GESD e- K+ End plate Short experiment => need to deliberately amplify electron effects: let beam hit end-plate to generate copious electrons which propagate upstream.

  16. Suppressor on Suppressor off experiment Comparison sim/exp: clearing electrodes and e- supp. on/off 200mA K+ e- (a) (b) (c) 0V 0V 0V V=-10kV, 0V • Time-dependent beam loading in WARP from moments history from HCX data: • current • energy • reconstructed distributionfrom XY, XX', YY' slit-plate measurements simulation measurement reconstruction Good semi quantitative agreement.

  17. (a) (b) (c) Simulation Experiment Simulation Experiment Detailed exploration of dynamics of electrons in quadrupole 0V 0V 0V/+9kV 0V Potential contours WARP-3D T = 4.65s e- 200mA K+ Q1 Q2 Q3 Q4 WARP-3D T = 4.65s Electrons 200mA K+ Electrons bunching Importance of secondaries - if secondary electron emission turned off: 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. Oscillations I (mA) (c) I (mA) 0. -20. -40. ~6 MHz signal in (C) in simulation AND experiment 0. 2. time (s) 6. (c) 0. 2. time (s) 6.

  18. Quest - nature of oscillations Progressively removes possible mechanisms Not ion-electron two stream • Other mechanisms: • Virtual cathode oscillations • -Density-potential, feedbacks to drift velocity • Kelvin Helmholtz/Diocotron (plausible, shear in drift velocities) Fluid velocity vectors (length and color according to magnitude) Vortices? color according to magnitude of velocity Shear flow R (m) V(m/s)

  19. Application to high energy physics

  20. quad drift bend drift HEP e-cloud work currently uses “quasi-static” approximation 2-D slab of electrons s 3-D beam s0 lattice A 2-D slab of electrons (macroparticles) is stepped backward (with small time steps) through the beam field and 2-D electron fields are stacked in a 3-D array, that is used to push the 3-D beam ions (with large time steps) using maps (as in HEADTAIL-CERN) or Leap-Frog (as in QUICKPIC-UCLA), allowing direct comparison.

  21. 1 station/turn Emittances X/Y (-mm-mrad) WARP-QSM X,Y HEADTAIL X,Y WARP-QSM X,Y HEADTAIL X,Y Time (ms) 2 stations/turn Emittances X/Y (-mm-mrad) Time (ms) Quasi-static mode (QSM) has been added to WARP Rationale - we had the building blocks - we need to reproduce HEP codes results for meaningful comparisonsComparison WARP-QSM/HEADTAIL on CERN benchmark

  22. AMR essential X103-104 speed-up! WARP/POSINST applied to High-Energy Physics • LARP funding: simulation of e-cloud in LHC Proof of principle simulation: • Fermilab: study of e-cloud in MI upgrade (K. Sonnad) • ILC: study of e-cloud in positron damping ring wigglers (C. Celata) Quadrupoles Drifts Bends 1 LHC FODO cell (~107m) - 5 bunches - periodic BC (04/06) WARP/POSINST-3D - t = 300.5ns

  23. y y x x How can FSC compete with QS? Recent key observation:range of space and time scales is not a Lorentz invariant* • same event (two objects crossing) in two frames Consequences • there exists an optimum frame which minimizes ranges, • for first-principle simulations (PIC), costT/t ~2 (L/l*T/t ~ 4 w/o moving window), = (L/l, T/t) F0-center of mass frame FB-rest frame of “B” 0 space 0 0 0 space+time 0 Range of space/time scales =(L/l,T/t) vary continuously as 2 for large, potential savings are HUGE! *J.-L. Vay, PRL 98, 130405 (2007)

  24. A few systems which might benefit include… Laser-plasma acceleration In laboratory frame. longitudinal scale x1000/x1000000… Free electron lasers x1000 3cm 1m … so-called“multiscale”problems = very challenging to model! Use of approximations (quasi-static, eikonal, …). 3cm/1m=30,000. HEP accelerators (e-cloud) x1000000 x1000 10km 10m 1nm 10cm 10km/10cm=100,000. 10m/1nm=10,000,000,000.

  25. frame  ≈19 3cm 1.6mm 1m 30m Hendrik Lorentz compaction x560 1.6mm/30m=53. 3cm/1m=30,000. frame  ≈22 frame  ≈4000 2.5mm 450m 10km 10m 1nm 1nm 4m 10cm 4.5m compaction x103 compaction x3.107 450m/4.5m=100. 10km/10cm=100,000. 10m/1nm=10,000,000,000. 2.5mm/4m=625. Lorentz transformation => large level of compaction of scales Laser-plasma acceleration Free electron lasers HEP accelerators (e-cloud)

  26. Boosted frame calculation sampleproton bunch through a given e– cloud* electron streamlines beam • This is a proof-of-principle computation: • hose instability of a proton bunch • Proton energy: g=500 in Lab • L= 5 km, continuous focusing proton bunch radius vs. z CPU time: • lab frame: >2 weeks • frame with 2=512: <30 min Speedup x1000 *J.-L. Vay, PRL 98, 130405 (2007)

  27. Summary • WARP/POSINST code suite developed for HIF e-cloud studies • Parallel 3-D AMR-PlC code with accelerator lattice follows beam self-consistently with gas/electron generation and evolution, • Benchmarked against HCX • highly instrumented section dedicated to e-cloud studies, • Being applied outside HIF/HEDP, to HEP accelerators • found that cost of self-consistent calculation is greatly reduced in Lorentz boosted frame (with >>1), thanks to relativistic contraction/dilatation bridging space/time scales disparities, • 1000x speedup demonstrated on proof-of-principle case, • will apply to LHC, Fermilab MI, ILC.

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