Jean-Luc Vay Heavy Ion Fusion Science Virtual National Laboratory Lawrence Berke

Jean-Luc Vay Heavy Ion Fusion Science Virtual National Laboratory Lawrence Berke www.phwiki.com

Jean-Luc Vay Heavy Ion Fusion Science Virtual National Laboratory Lawrence Berke

Sugerman, Mike, Features Reporter has reference to this Academic Journal, PHwiki organized this Journal Jean-Luc Vay Heavy Ion Fusion Science Virtual National Laboratory Lawrence Berkeley National Laboratory DOE OFES Theory Seminar Series June 5, 2007 Self-consistent simulations of particle beam/plasma interaction with its environment 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 Cali as long as nia – Berkeley Outline Context Simulation tools Benchmarking against experiments Application to high energy physics Summary

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Context Today’s HIFS program is directed at beam & Warm Dense Matter physics in the near term, in addition to IFE in the longer term Heavy Ion Fusion Science experiments: The physics of compressing beams in space in addition to time – Drift compression in addition to final focus – High brightness beam preservation – Electron cloud, beam halo, non-linear processes Warm Dense Matter (WDM) experiments – Equation of state – Two-phase regime in addition to droplet as long as mation – Insulator in addition to metals at WDM conditions Hydrodynamics experiments relevant to HIF targets – Hydrodynamic stability, volumetric ion energy deposition, in addition to Rayleigh-Taylor mitigation techniques It is highly desirable to minimize the space between the beam in addition to the accelerating structure. (from a WARP movie; see http://hif.lbl.gov/theory/simulation-movies.html) This elevates the likelihood of “halo” (outlier) ions hitting structures, so that a detailed underst in addition to ing is needed.

Sources of electron clouds ion induced emission from expelled ions hitting vacuum wall beam halo scraping Primary: Secondary: i+ = ion e- = electron g = gas = photon = instability Positive Ion Beam Pipe Ionization of background gas desorbed gas secondary emission from electron-wall collisions e- photo-emission from synchrotron radiation (HEP) Simulation goal – predictive capability Source-through-target self-consistent time-dependent 3-D simulations of beam, electrons in addition to gas with self-field + external field (dipole, quadrupole, ). WARP-3D T = 4.65s 200mA K+ Electrons From source to target. HCX Simulation tools

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 in addition to histories Parallel: MPI Python in addition to Fortran: “steerable,” input decks are programs WARP-POSINST has unique features merge of WARP & POSINST re-diffused Monte-Carlo generation of electrons with energy in addition to angular dependence. Three components of emitted electrons: backscattered: rediffused: true secondaries: true sec. back-scattered elastic POSINST provides advanced SEY model. I0 Its Ie Ir Phenomenological model: based as much as possible on data as long as in addition to d/dE not unique (use simplest assumptions whenever data is not available) many adjustable parameters, fixed by fitting in addition to d/dE to data

We have benefited greatly from collaborations ion-induced electron emission in addition to 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). Benchmarking against experiments Capacitive Probe (qf4) Clearing electrodes Suppressor K+ e- Short experiment => need to deliberately amplify electron effects: let beam hit end-plate to generate copious electrons which propagate upstream. End plate INJECTOR MATCHING SECTION ELECTROSTATIC QUADRUPOLES MAGNETIC QUADRUPOLES Benchmarked against dedicated experiment on HCX Retarding Field Analyser (RFA) Location of Current Gas/Electron Experiments GESD 1 MeV, 0.18 A, t 5 s, 6×1012 K+/pulse, 2 kV space charge, tune depression 0.1

Comparison sim/exp: clearing electrodes in addition to e- supp. on/off simulation 200mA K+ e- 0V 0V 0V V=-10kV, 0V Time-dependent beam loading in WARP from moments history from HCX data: current energy reconstructed distribution from XY, XX’, YY’ slit-plate measurements (a) (b) (c) Good semi quantitative agreement. measurement reconstruction Detailed exploration of dynamics of electrons in quadrupole Importance of secondaries – if secondary electron emission turned off: run time ~3 days – without new electron mover in addition to MR, run time would be ~1-2 months! WARP-3D T = 4.65s Oscillations Beam ions hit end plate e- 0V 0V 0V/+9kV 0V Q4 Q3 Q2 Q1 200mA K+ 200mA K+ Electrons (c) 0. 2. time (s) 6. 0. -20. -40. I (mA) Potential contours (c) 0. 2. time (s) 6. I (mA) 0. -20. -40. Electrons bunching ~6 MHz signal in (C) in simulation AND experiment WARP-3D T = 4.65s Quest – nature of oscillations Progressively removes possible mechanisms Not ion-electron two stream R (m) V(m/s) Fluid velocity vectors (length in addition to color according to magnitude) Vortices Shear flow color according to magnitude of velocity Other mechanisms: Virtual cathode oscillations -Density-potential, feedbacks to drift velocity Kelvin Helmholtz/Diocotron (plausible, shear in drift velocities)

Application to high energy physics HEP e-cloud work currently uses “quasi-static” approximation A 2-D slab of electrons (macroparticles) is stepped backward (with small time steps) through the beam field in addition to 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. 2-D slab of electrons 3-D beam s s0 lattice Quasi-static mode (QSM) has been added to WARP Rationale – we had the building blocks – we need to reproduce HEP codes results as long as meaningful comparisons Comparison WARP-QSM/HEADTAIL on CERN benchmark

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 WARP/POSINST-3D – t = 300.5ns 1 LHC FODO cell (~107m) – 5 bunches – periodic BC (04/06) How can FSC compete with QS Recent key observation: range of space in addition to time scales is not a Lorentz invariant same event (two objects crossing) in two frames Consequences there exists an optimum frame which minimizes ranges, as long as first-principle simulations (PIC), costT/t ~ 2 (L/lT/t ~ 4 w/o moving window), J.-L. Vay, PRL 98, 130405 (2007) as long as large , potential savings are HUGE! = (L/l, T/t) 0 0 0 0 0 Range of space/time scales =(L/l,T/t) vary continuously as 2 space space+time F0-center of mass frame FB-rest frame of “B” A few systems which might benefit include Free electron lasers HEP accelerators (e-cloud) 1nm 10km 10m 10cm Laser-plasma acceleration x1000 3cm 1m In laboratory frame. longitudinal scale x1000/x1000000 so-called “multiscale” problems = very challenging to model! Use of approximations (quasi-static, eikonal, ). x1000000 x1000 10km/10cm=100,000. 10m/1nm=10,000,000,000. 3cm/1m=30,000.

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Lorentz trans as long as mation => large level of compaction of scales HEP accelerators (e-cloud) Laser-plasma acceleration Free electron lasers Boosted frame calculation sample proton bunch through a given e– cloud This is a proof-of-principle computation: hose instability of a proton bunch Proton energy: g=500 in Lab L= 5 km, continuous focusing electron streamlines beam 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) Summary WARP/POSINST code suite developed as long as HIF e-cloud studies Parallel 3-D AMR-PlC code with accelerator lattice follows beam self-consistently with gas/electron generation in addition to 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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