1 / 47

New self-consistent 3-D capabilities of electron clouds simulations

New self-consistent 3-D capabilities of electron clouds simulations. Jean-Luc Vay Lawrence Berkeley National Laboratory Heavy Ion Fusion Science Virtual National Laboratory CERN - October 5, 2006. Many thanks to collaborators. M. A. Furman, C. M. Celata, P. A. Seidl, M. Venturini

marly
Download Presentation

New self-consistent 3-D capabilities of electron clouds simulations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. New self-consistent 3-D capabilities of electron clouds simulations Jean-Luc Vay Lawrence Berkeley National Laboratory Heavy Ion Fusion Science Virtual National Laboratory CERN - October 5, 2006

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

  3. Outline Who we are and why we care about electron cloud effects Our tools and recent selected results Application to HEP accelerators Future directions and conclusion

  4. The U.S. Heavy Ion Fusion Science Program - Participation Lawrence Berkeley National Laboratory MIT Lawrence Livermore National Laboratory Advanced Ceramics Princeton Plasma Physics Laboratory Allied Signal Naval Research Laboratory National Arnold Los Alamos National Laboratory Hitachi Sandia National Laboratory Scientific Voss University of Maryland Georgia Tech University of Missouri General Atomic Stanford Linear Accelerator Center MRTI Advanced Magnet Laboratory Tech-X Idaho National Environmental and SciberQuest Engineering Lab University of California a. Berkeley b. Los Angeles c. San Diego Employees of LBNL, LLNL, and PPPL form the U.S. Virtual National Laboratory for Heavy Ion Fusion Sciences

  5. Heavy Ion Inertial Fusion (HIF) goal is to develop an accelerator that can deliver beams to ignite an inertial fusion target Artist view of a Heavy Ion Fusion driver DT Target requirements: 3-7 MJ x ~ 10 ns  ~ 500 Terawatts Ion Range: 0.02 - 0.2 g/cm2 1-10 GeV dictate accelerator requirements: A~200  ~1016 ions, 100 beams, 1-4 kA/beam Our near term goal is High-Energy Density Physics (HEDP)...

  6. High energy density physics (HEDP) is study of matter under extreme temperature, density, and pressure. • Diverse applications: HED astrophysics, HED laboratory plasmas, ICF, materials science • Accessible, open facilities with dedicated beam time are needed • HIFS-VNL workshops, study groups have explored possible contributions; outside collaborators include: R. More, R. Lee (LLNL), M. Murillo (LANL), N. Tahir (and others at GSI) % disagreement in EOS models little or no data Dense, strongly coupled plasmas @ 10-2 to 10-1x solid density are potentially interesting areas to test EOS models.

  7. Intense heavy ion beams provide an excellent tool to generate homogeneous high energy density matter. • Warm dense matter (WDM) • T ~ 1,000 to 100,000 K • r~ 0.01 -1 * solid density • P ~ kbar, Mbar • Techniques for generating WDM • High explosives • Powerful lasers • Exploding wire (z-pinch) • Some advantages of intense heavy ion beams • Volumetric heating: uniform physical conditions • High rep. rate and reproducibility • Any target material Al target Ion beam Example: He Enter foil Exit foil

  8. Program Objectives • OFES/OMB endorses the 2005 Fusion Energy Science Advisory Committee top priority for the heavy ion program: “How can heavy ion beams be compressed to the intensities required for high energy density physics and fusion?” • OFES has two targets (objectives) for HIFS-VNL FY06 research: Priority 1:"Conduct experiments and modeling on combined transverse and longitudinal compression of intense heavy ion beams.” Priority 2: "Extend electron cloud effects studies to include experiments with mitigation techniques with improved computational models".

  9. Why do we care about electrons?We have a strong economic incentive to fill the pipe. Time-dependent 3D simulations of HCX injector reveal beam ions hitting structure (from a WARP movie; see http://hif.lbl.gov/theory/simulation_movies.html)

  10. 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

  11. Outline Who we are and why we care about electron cloud effects Our tools and recent selected results Application to HEP accelerators Future directions and conclusion

  12. Unique simulation/experimental tools to study ECE • WARP/POSINST code suite • Parallel 3-D PlC-AMR code with accelerator lattice follows beam self-consistently with gas/electrons generation and evolution • collaborative effort • LBNL Center for Beam Physics (M. Furman) - secondary emission • Tech-X (P. Stoltz, S. Veitzer) - ion-induced electron emission, ionization cross-sections • UC-Berkeley (J. Verboncoeur) - neutrals generation • HCX experiment adresses ECE fundamentals relevant to HEP • trapping potential ~2kV with highly instrumented section dedicated to e-cloud studies • The combination forms a unique set for careful study of the fundamental physics of ECE and extensive methodical benchmarking

  13. + new e-/gas modules quad beam 1 2 Key: operational; partially implemented (4/28/06) + New 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 code suite is unique in four ways merge of WARP & POSINST

  14. 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

  15. quad drift bend drift We can run WARP/Posinst in different modes. • Slice mode (2-D1/2 s-dependent) 2-D beam slab s s0 s0+s0 lattice 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.

  16. quad drift bend drift We can run WARP/Posinst in different modes. • Posinst mode (2-D1/2 time-dependent) 2-D slab of electrons s 3-D beam: stack of 2-D slab s0 lattice 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, …).

  17. We can run WARP/Posinst in different modes. • Fully self-consistent (3-D time-dependent) HCX Electrons 200mA K+ From source… WARP-3D T = 4.65s …to target. Beam bunches (macroparticles) and electrons (macroparticles) evolve self-consistently with self-field + external field (dipole, quadrupole, …).

  18. HCX dedicated setup for gas/electron effects studies (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.

  19. MA3 Diagnostics in two magnetic quadrupole bores, & what they measure. Not in service MA4 FLS(2) GIC (2) BPM (3) 8 “paired” Long flush collectors (FLL): measures capacitive signal + collected or emitted electrons from halo scraping in each quadrant. GEC GEC BPM FLS FLS GIC 3 capacitive probes (BPM); beam capacitive pickup ((nb- ne)/ nb). 2 Short flush collector (FLS); similar to FLL, electrons from wall. 2 Gridded e- collector (GEC); expelled e- after passage of beam 2 Gridded ion collector (GIC): ionized gas expelled from beam

  20. 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 May 2005 (PAC conference) • Time-dependent beam loading in WARP from moments history from HCX data: • current • energy • assuming semi-gaussian distribution • RMS envelopes • RMS emittances • average slopes • beam centroids simulation Good qualitative agreement.

  21. 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 August 2005 • Time-dependent beam loading in WARP from moments history from HCX data: • current • energy • reconstructed distributionfrom XY, XX', YY' slit-plate measurements simulation Agreement significantly improved! measurement reconstruction

  22. (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: simulation 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) 0. -20. -40. ~6 MHz signal in (C) in simulation AND experiment I (mA) 0. 2. time (s) 6. (c) 0. 2. time (s) 6.

  23. Outline Who we are and why we care about electron cloud effects Our tools and recent selected results Application to HEP accelerators Future directions and conclusion

  24. AMR essential X103-104 speed-up! WARP/POSINST applied to High-Energy Physics • LARP funding: simulation of e-cloud in LHC • Fermilab: study of e-cloud in MI upgrade • ILC: start work in FY07 Quadrupoles Drifts Bends 1 LHC FODO cell (~107m) - 5 bunches - periodic BC (04/06) WARP/POSINST-3D - t = 300.5ns

  25. quad drift bend drift “Quasi-static” mode added for codes comparisons. 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.

  26. WARP-QSM X,Y HEADTAIL X,Y WARP-QSM X,Y HEADTAIL X,Y Comparison WARP-QSM/HEADTAIL on CERN benchmark 1 station/turn Emittances X/Y (-mm-mrad) Time (ms) 2 stations/turn Emittances X/Y (-mm-mrad) Time (ms)

  27. Can 3-D self-consistent compete with quasi-static mode?- computational cost of full 3-D run in two frames - Vb Vb Lab frame z x z L (1 unit) x = x/n; z = min(z,L)/n t < min[ x/max(vx),z/max(vz) ]; Tmax = NunitsL/Vb Nop = NeTmax/t Frame  Vb L* Vf z* x* = x/n; z* = min(z*,L*)= z t* < min[ x*/max(vx*),z*/max(vz*) ] = min[ x/(max(vx/), z/vz] = t T*max = NunitsL*/(Vb-Vf) ~ Tmax / N*op = NeT*max/t* ~ Nop / => Computational cost greatly reduced in frame 

  28. Comparison between quasi-static and full 3-D costs. Vb Lab frame z x z S Quasi-static (HEADTAIL, QUICKPIC):  ~ S/z Nop,qs = Nop/ Frame  Vb -Vf z* if z *= S*,  =, N*op = Nop,qs => cost of full 3-D run in frame = cost of quasi-static mode in lab frame

  29. Application to rings • In bends, WARP uses warped coordinates with a logically cartesian grid. If solving in a frame moving at constant  along s, we need to extend existing algorithm to allow treatment of motion in relativistic rotating frame in bends. • Meanwhile, in order to study electron cloud effects, including bends, where effects are dominated by the magnitude of the bending field rather than its sign, we propose to substitute a ring by a linear lattice with bends of alternating signs. • For example, diagram 1 LHC FODO cell ( ) quadrupole; bend or or…

  30. Outline Who we are and why we care about electron cloud effects Our tools and recent selected results Application to HEP accelerators Future directions and conclusion

  31. Point source of electrons to simulate synchrotron radiation photoelectrons Electron gun enables quantitatively controlled injection of electrons Electron gun operates over range ~10 eV to 2000 eV (cathode & grid indep.) <1 mA to 1000 mA

  32. (a) (a) (b) (b) (c) (c) +9kV +9kV +9kV 0V e- 200mA K+ Q1 Q2 Q3 Q4 +9kV +9kV 0V 0V e- 200mA K+ Q1 Q2 Q3 Q4 I (mA) HCX experiment Sim. - stainless steel Sim. - copper time (s) Simulation Experiment Signal from clearing electrode B depends on surface. current in (c) Case A: all clearing electrodes biased at +9kV 0. -20. -40. I (mA) Uses default Posinst SEY parameters for stainless steel. Experimental result well recovered. 0. 2. time (s) 6. Case B: clearing electrode (C) grounded current in (b) Experimental result bracketed by simulation results when using default Posinst SEY parameters for stainless steel and copper. => Need to measure SEY for an actual sample.

  33. +10kV e- g 200mA K+ 0-D model Experiment Beam 0-D model Experiment Beam Q4 -10kV i+ g 200mA K+ Q4 Electron suppressor ring replaced by two plates. I (mA) Time (s) I (mA) • Simple 0D model: • electron and neutrals emission • gas ionization • beam stripping • electrons/H(2)+ are collected instantly at the plate Nb e- per beam ion: 1.5 (~8. was predicted) Nb H2 per beam ion: 15000. (~7000. was predicted) cross section K+ + H2 => K+ + H2+ + e- : 1.6e-16cm-2 cross section K+ + H2 => K++ + H2 + e- : 6.e-16cm-2 => Need to measure yields and cross-sections.

  34. Conclusion • We developed a unique combination of tools to study ECE • WARP/POSINST code suite • Parallel 3-D PlC-AMR code with accelerator lattice follows beam self-consistently with gas/electrons generation and evolution, • HCX experiment adresses ECE fundamentals (HIF/HEDP/HEP) • highly instrumented section dedicated to e-cloud studies, • extensive methodical benchmarking of WARP/POSINST, • Being applied outside HIF/HEDP, to HEP accelerators • LHC, Fermilab MI, ILC, • Implemented “quasi-static” mode for direct comparison to HEADTAIL/QUICKPIC, • fund that self-consistent calculation has similar cost than quasi-static mode if done in moving frame (with >>1), thanks to relativistic contraction/dilatation bridging space/time scales disparities (applies to FEL, laser-plasma acceleration, plasma lens,…).

  35. Backup Slides

  36. 11 cm reflected electrons emitted electrons r Beam -K+, 972 kV, 174 mA, rb=2.2 cm, 0 0 z 26 cm t=200 ns. t=2000 ns. vz (m/s) vz (m/s) z (m) z (m) Study of virtual cathode using axisymmetric XOOPIC1 model left edge: reflects electrons with coefficient R Ion beam injected from left edge right boundary: absorbing, with emission of electrons. Phase space hole eventually collapses due to VC oscillations 1 Verboncoeur et al., Comp. Phys. Comm.87, 199 (1995)

  37. Spurious oscillations observed when VC is not resolved Potential in vicinity of virtual cathode region (t=2s, t=0.2ns) high resolution (200x780) low resolution (40x156) oscillation Mesh refinement very helpful for modeling of HCX magnetic section!

  38. Quest - nature of oscillations Progressively removes possible mechanisms Not ion-electron two stream

  39. Vary beam section Increasing beam diameter in direction of maximum electron cloud radius, reduces oscillations.

  40. 1 s V(m/s) e- 200mA K+ R (m) Looks like vortices developing and propagating upstream… Replace Q1-4 with 1 quad. 1 s 2 s

  41. Is this a Kelvin-Helmholtz instability? Fluid velocity vectors (length and color according to magnitude) Vortices? Shear flow

  42. Replace quadrupole field by azimuthal field 1 s 2 s System is axisymmetric: much simpler to study analytically…

  43. Example of application of the quasi-static module

  44. Problem: Electron gyro timescale << other timescales of interest  brute-force integration very slow due to small Dt Solution*: Interpolation between full-particle dynamics (“Boris mover”) and drift kinetics (motion along B plus drifts) quad beam 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 large t=5./c Standard Boris mover (fails in this regime) small t=0.25/c Standard Boris mover (reference case) large t=5./c New interpolated mover • Test: Magnetized two-stream instability • *R. Cohen et. al., Phys. Plasmas, May 2005

  45. POSINST has been used extensively for e-cloud calculations code of M. Furman and M. Pivi POSINST calculates the evolution of the electron cloud Follows slice of electrons at one location along beam line 2-D PIC for e– self force analytical kick for force of beam on electrons Effect of electrons on beam -- minimally modeled dipole wake Good models for electron production by: synchrotron radiation residual gas ionization stray beam particles hitting vacuum wall secondary electron production (detailed model) TxPhysics Library Under SBIR funding, POSINST SEY module implemented into CMEE library distributed by Tech-X corporation.

  46. HEDP: r - T regime accessible by beam driven experiments lies square in the interiors of gas planets and low mass stars Figure adapted from “Frontiers in HEDP: the X-Games of Contemporary Science:” Accessible region using beams in near term Terrestial planet

  47. 0V 0V 0V/+9kV 0V (a) (b) (c) e- 200mA K+ Q1 Q2 Q3 Q4 Centre of 4th magnet Array of BPMs in HCX Quad 4 verified WARP simulation results • Wavelength of ~5 cm, growing from near center of 4th quad. magnet Experiment Simulation RMS Power (arbitrary units) Beam Position Monitor (BPM): electrode capacitively coupled to beam • Experiment and simulations agree quantitatively on oscillation • frequency • Wavelength • amplitude upstream

More Related