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. 2 J.-L. Vay - CERN - 10/05/06 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. 3 J.-L. Vay - CERN - 10/05/06 Outline 1.Who we are and why we care about electron cloud effects 2.Our tools and recent selected results 3.Application to HEP accelerators 4.Future directions and conclusion 1.Who we are and why we care about electron cloud effects 2.Our tools and recent selected results 3.Application to HEP accelerators 4.Future directions and conclusion

4. 4 J.-L. Vay - CERN - 10/05/06 The U.S. Heavy Ion Fusion Science Program - Participation Lawrence Berkeley National LaboratoryMIT Lawrence Livermore National LaboratoryAdvanced Ceramics Princeton Plasma Physics LaboratoryAllied Signal Naval Research Laboratory National Arnold Los Alamos National LaboratoryHitachi Sandia National LaboratoryScientific 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. 5 J.-L. Vay - CERN - 10/05/06 Our near term goal is High-Energy Density Physics (HEDP)... Heavy Ion Inertial Fusion (HIF) goal is to develop an accelerator that can deliver beams to ignite an inertial fusion target DT Target requirements: 3-7 MJ x ~ 10 ns  ~ 500 Terawatts Ion Range: 0.02 - 0.2 g/cm 2  1-10 GeV dictate accelerator requirements: A~200  ~10 16 ions, 100 beams, 1-4 kA/beam Artist view of a Heavy Ion Fusion driver

6. 6 J.-L. Vay - CERN - 10/05/06 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) Dense, strongly coupled plasmas @ 10 -2 to 10 -1 x solid density are potentially interesting areas to test EOS models. % disagreement in EOS models little or no data

7. 7 J.-L. Vay - CERN - 10/05/06 Intense heavy ion beams provide an excellent tool to generate homogeneous high energy density matter. Ion beam Example: He Enter foil Exit foil Al target Warm dense matter (WDM) –T ~ 1,000 to 100,000 K –  ~ 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

8. 8 J.-L. Vay - CERN - 10/05/06 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. 9 J.-L. Vay - CERN - 10/05/06 Why do we care about electrons? We have a strong economic incentive to fill the pipe. (from a WARP movie; see http://hif.lbl.gov/theory/simulation_movies.html) Time-dependent 3D simulations of HCX injector reveal beam ions hitting structure

10. 10 J.-L. Vay - CERN - 10/05/06 e-e- i+i+ halo e-e- ion induced emission from - expelled ions hitting vacuum wall - beam halo scraping Sources of electron clouds Primary: Secondary: i + = ion e - = electron g = gas  = photon = instability Positive Ion Beam Pipe e-e- i+i+ g g Ionization of - background gas - desorbed gas secondary emission from electron-wall collisions e-e- e-e- e-e- e-e- e-e- photo-emission from synchrotron radiation (HEP) 

11. 11 J.-L. Vay - CERN - 10/05/06 Outline 1.Who we are and why we care about electron cloud effects 2.Our tools and recent selected results 3.Application to HEP accelerators 4.Future directions and conclusion 1.Who we are and why we care about electron cloud effects 2.Our tools and recent selected results 3.Application to HEP accelerators 4.Future directions and conclusion

12. 12 J.-L. Vay - CERN - 10/05/06 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. 13 J.-L. Vay - CERN - 10/05/06 1 WARP-POSINST code suite is unique in four ways merge of WARP & POSINST Key: operational; partially implemented (4/28/06) + new e - /gas modules 2 + Adaptive Mesh Refinement Z R concentrates resolution only where it is needed 3 Speed-up x10-10 4 beam quad e - motion in a quad + New e - mover Allows large time step greater than cyclotron period with smooth transition from magnetized to non- magnetized regions 4 Speed-up x10-100

14. Monte-Carlo generation of electrons with energy and angular dependence. Three components of emitted electrons: backscattered: rediffused: true secondaries: true sec. back-scattered elastic POSINST provides advanced SEY model. re-diffused I0I0 I ts IeIe IrIr 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

15. 15 J.-L. Vay - CERN - 10/05/06 We can run WARP/Posinst in different modes. 1.Slice mode (2-D1/2 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

16. 16 J.-L. Vay - CERN - 10/05/06 We can run WARP/Posinst in different modes. 2.Posinst mode (2-D1/2 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

17. 17 J.-L. Vay - CERN - 10/05/06 We can run WARP/Posinst in different modes. 3.Fully self-consistent (3-D time-dependent) Beam bunches (macroparticles) and electrons (macroparticles) evolve self-consistently with self-field + external field (dipole, quadrupole, …). WARP-3D T = 4.65  s 200mA K + Electrons From source… …to target. HCX

18. 18 J.-L. Vay - CERN - 10/05/06 (a) (b) (c) Capacitive Probe (qf4) Clearing electrodes Suppressor Q1Q2Q3Q4 K+K+ e-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 HCX dedicated setup for gas/electron effects studies Retarding Field Analyser (RFA) Location of Current Gas/Electron Experiments GESD 1 MeV, 0.18 A, t ≈ 5  s, 6x10 12 K + /pulse, 2 kV space charge, tune depression ≈ 0.1

19. 19 J.-L. Vay - CERN - 10/05/06 Diagnostics in two magnetic quadrupole bores, & what they measure. MA4 MA3 8 “paired” Long flush collectors (FLL): measures capacitive signal + collected or emitted electrons from halo scraping in each quadrant. 3 capacitive probes (BPM); beam capacitive pickup ((n b - n e )/ n b ). 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 BPM (3) BPM FLS(2) FLS GIC (2) GIC Not in service FLS GEC

20. 20 J.-L. Vay - CERN - 10/05/06 0V 0V 0V V=-10kV, 0V 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 May 2005 (PAC conference) 200mA K + (a)(b)(c) e-e- Suppressor offSuppressor on experiment Comparison sim/exp: clearing electrodes and e - supp. on/off Good qualitative agreement.

21. 21 J.-L. Vay - CERN - 10/05/06 simulation 200mA K + e-e- 0V 0V 0V V=-10kV, 0V Suppressor offSuppressor on experiment Comparison sim/exp: clearing electrodes and e - supp. on/off 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) August 2005 Agreement significantly improved! measurementreconstruction

22. 22 J.-L. Vay - CERN - 10/05/06 1.Importance of secondaries - if secondary electron emission turned off: 2.simulation run time ~3 days - without new electron mover and MR, run time would be ~1-2 months! 1.Importance of secondaries - if secondary electron emission turned off: 2.simulation run time ~3 days - without new electron mover and MR, run time would be ~1-2 months! Detailed exploration of dynamics of electrons in quadrupole WARP-3D T = 4.65  s Oscillations Beam ions hit end plate (a)(b)(c) e-e- 0V 0V 0V/+9kV 0V Q4Q3Q2Q1 200mA K + 200mA K + Electrons (c) 0. 2. time (  s) 6. Simulation Experiment 0. -20. -40. I (mA) Potential contours Simulation Experiment (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 = 4.65  s

23. 23 J.-L. Vay - CERN - 10/05/06 Outline 1.Who we are and why we care about electron cloud effects 2.Our tools and recent selected results 3.Application to HEP accelerators 4.Future directions and conclusion 1.Who we are and why we care about electron cloud effects 2.Our tools and recent selected results 3.Application to HEP accelerators 4.Future directions and conclusion

24. 24 J.-L. Vay - CERN - 10/05/06 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 WARP/POSINST-3D - t = 300.5ns 1 LHC FODO cell (~107m) - 5 bunches - periodic BC (04/06) AMR essential X10 3 -10 4 speed-up!

25. 25 J.-L. Vay - CERN - 10/05/06 “Quasi-static” mode added for codes comparisons. 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. 2-D slab of electrons 3-D beam benddrift quad s s0s0 lattice

26. 26 J.-L. Vay - CERN - 10/05/06 Time (ms) Emittances X/Y (  -mm-mrad) 2 stations/turn Comparison WARP-QSM/HEADTAIL on CERN benchmark Time (ms) Emittances X/Y (  -mm-mrad) 1 station/turn WARP-QSM X,Y HEADTAIL X,Y WARP-QSM X,Y HEADTAIL X,Y

27. 27 J.-L. Vay - CERN - 10/05/06 Can 3-D self-consistent compete with quasi-static mode? - computational cost of full 3-D run in two frames -  x =  x /n;  z = min(  z,L)/n  t < min[  x/max(v x ),  z/max(v z ) ]; T max = N units  L/V b N op = N e  T max /  t  x* =  x /n;  z* = min(  z *,L*)=  z  t* < min[  x*/max(v x *),  z*/max(v z *) ] = min[  x/(max(v x /  ),  z/v z ] =  t T* max = N units  L*/(V b -V f ) ~ T max /  N* op = N e  T* max /  t* ~ N op /   L* z*z* zz Lab frame Frame  VbVb VfVf VbVb VbVb => Computational cost greatly reduced in frame  L (1 unit) z x

28. 28 J.-L. Vay - CERN - 10/05/06 Comparison between quasi-static and full 3-D costs. if  z *=  S*,   = , N* op = N op,qs => cost of full 3-D run in frame  = cost of quasi-static mode in lab frame Quasi-static (HEADTAIL, QUICKPIC):  ~  S/  z N op,qs = N op /  Frame  z x Lab frame zz VbVb z*z* -V f VbVb SS

29. 29 J.-L. Vay - CERN - 10/05/06 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 ( ) or or… quadrupole; bend

30. 30 J.-L. Vay - CERN - 10/05/06 Outline 1.Who we are and why we care about electron cloud effects 2.Our tools and recent selected results 3.Application to HEP accelerators 4.Future directions and conclusion 1.Who we are and why we care about electron cloud effects 2.Our tools and recent selected results 3.Application to HEP accelerators 4.Future directions and conclusion

31. 31 J.-L. Vay - CERN - 10/05/06 Point source of electrons to simulate synchrotron radiation photoelectrons Electron gun operates over range ~10 eV to 2000 eV (cathode & grid indep.) <1 mA to 1000 mA Electron gun enables quantitatively controlled injection of electrons

32. 32 J.-L. Vay - CERN - 10/05/06 Signal from clearing electrode B depends on surface. (a)(b)(c) e-e- +9kV +9kV 0V 0V Q4Q3Q2Q1 200mA K + time (  s) I (mA) HCX experiment Sim. - stainless steel Sim. - copper 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. current in (b) 0. 2. time (  s) 6. Simulation Experiment 0. -20. -40. I (mA) current in (c) (a)(b)(c) e-e- +9kV +9kV +9kV 0V Q4Q3Q2Q1 200mA K + Case A: all clearing electrodes biased at +9kV Case B: clearing electrode (C) grounded Uses default Posinst SEY parameters for stainless steel. Experimental result well recovered.

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

34. 34 J.-L. Vay - CERN - 10/05/06 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. 36 J.-L. Vay - CERN - 10/05/06 Study of virtual cathode using axisymmetric XOOPIC 1 model Ion beam injected from left edge 1 Verboncoeur et al., Comp. Phys. Comm. 87, 199 (1995) t=200 ns. v z (m/s) z (m) t=2000 ns. v z (m/s) z (m) z r Beam - K +, 972 kV, 174 mA, r b =2.2 cm, emitted electrons reflected electrons 0 26 cm 0 11 cm Phase space hole eventually collapses due to VC oscillations right boundary: absorbing, with emission of electrons. left edge: reflects electrons with coefficient R

37. 37 J.-L. Vay - CERN - 10/05/06 Spurious oscillations observed when VC is not resolved Potential in vicinity of virtual cathode region (t=2  s,  t=0.2ns) oscillation high resolution (200x780) low resolution (40x156) Mesh refinement very helpful for modeling of HCX magnetic section!

38. 38 J.-L. Vay - CERN - 10/05/06 Quest - nature of oscillations Progressively removes possible mechanisms Not ion-electron two stream

39. 39 J.-L. Vay - CERN - 10/05/06 Increasing beam diameter in direction of maximum electron cloud radius, reduces oscillations. Vary beam section

40. 40 J.-L. Vay - CERN - 10/05/06 Replace Q1-4 with 1 quad. 1  s2  s 1  s Looks like vortices developing and propagating upstream… R (m) V(m/s) e-e- 200mA K +

41. 41 J.-L. Vay - CERN - 10/05/06 Is this a Kelvin-Helmholtz instability? Fluid velocity vectors (length and color according to magnitude) Vortices? Shear flow

42. 42 J.-L. Vay - CERN - 10/05/06 Replace quadrupole field by azimuthal field 1  s 2  s System is axisymmetric: much simpler to study analytically…

43. 43 J.-L. Vay - CERN - 10/05/06 Example of application of the quasi-static module

44. 44 J.-L. Vay - CERN - 10/05/06 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 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

45. 45 J.-L. Vay - CERN - 10/05/06 code of M. Furman and M. Pivi 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) POSINST calculates the evolution of the electron cloud Under SBIR funding, POSINST SEY module implemented into CMEE library distributed by Tech-X corporation. POSINST has been used extensively for e-cloud calculations TxPhysics Library

46. 46 J.-L. Vay - CERN - 10/05/06 HEDP:  - T regime accessible by beam driven experiments lies square in the interiors of gas planets and low mass stars Accessible region using beams in near term Figure adapted from “Frontiers in HEDP: the X-Games of Contemporary Science:” Terrestial planet

47. 47 J.-L. Vay - CERN - 10/05/06 Wavelength of ~5 cm, growing from near center of 4th quad. magnet Array of BPMs in HCX Quad 4 verified WARP simulation results Centre of 4th magnet Beam Position Monitor (BPM): electrode capacitively coupled to beam upstream (a)(b)(c) e-e- 0V 0V 0V/+9kV 0V Q4Q3Q2Q1 200mA K + Experiment and simulations agree quantitatively on oscillation –frequency –Wavelength –amplitude RMS Power (arbitrary units) Experiment Simulation