1. SciDAC-II Compass SciDAC-II Compass 1 Vay - Compass 09 Boosted frame e-cloud simulations J.-L. Vay Lawrence Berkeley National Laboratory Compass 2009 all hands meeting - Beam Dynamics session Tech-X, Boulder, CO - Oct 5-6, 2009 SciDAC-II Compass SciDAC-II Compass

2. SciDAC-II Compass SciDAC-II Compass 2 Vay - Compass 09 Toward fully self-consistent e-cloud simulations To date, electron cloud distributions have been predicted using ‘build-up’ simulations (using Posinst, Ecloud, Cloudland, Warp,…) and provided as inputs to codes calculating their interaction with the beam. This mode of operation is dictated by the widely separate time scales associated with the beam and electrons dynamics: the quasistatic or the boosted frame* methods are used to bridge the time scales in codes like Headtail, QuickPIC, Pehts, CMAD, Warp,…. electron streamlines beam *J.-L. Vay, Phys. Rev. Lett. 98, 130405 (2007) quasistaticboosted frame build-up

3. SciDAC-II Compass SciDAC-II Compass 3 Vay - Compass 09 This model is appropriate for single bunch instability but fails to capture memory effects for multibunch instabilities. Toward integrating the build-up and interaction phases, we have modified routines related to electron build-up in Warp to accommodate calculations in a boosted frame: – calculation of velocity and angle of particles impacting surfaces, – generation of secondary electrons, – background gas ionization. Toward fully self-consistent e-cloud simulations bunch nbunch n+1

4. SciDAC-II Compass SciDAC-II Compass 4 Vay - Compass 09 Modified routines successfully benchmarked on SPS toy problem The build-up of electrons was simulated in a fully self-consistent simulation in a boosted frame (  =27). Electrons generated from gas ionization and secondary emission at walls. Assumed continuous focusing. One bunch was simulated, the bunch train being emulated by periodic BC. Excellent agreement with simulations: in the laboratory frame, from the LBNL build-up code Posinst (M. Furman), Warp running in build-up mode.

5. SciDAC-II Compass SciDAC-II Compass 5 Vay - Compass 09 Fully self-consistent simulation of e-cloud driven instability If not properly resolving the betatron frequency, the choice of the parameter  = time step/betatron frequency is critical. The background gas pressure was x10, to trigger a strong instability. At these high electron densities, the electron space charge is large, which may explains observed differences between build-up and full 3D calculations. This is under investigation.

6. SciDAC-II Compass SciDAC-II Compass 6 Vay - Compass 09 Plans Implement calls to gas ionization and secondary electrons generation in Warp’s quasistatic class, Compare fully self-consistent (build-up+beam tracking) simulations between full PIC in a Lorentz boosted frame and quasistatic, cross- benchmarking and assessing the pros and cons of each approach. Replace continuous focusing by FODO lattice and redo above. Modify photo-electron generation class to accommodate boosted frame calculations. Add Monte-Carlo generation of photons radiated by beam, and the generation of photo-electrons at wall. Pursue benchmarking with other ecloud codes (to complement extensive benchmarking done with Headtail and Posinst to date).

7. SciDAC-II Compass SciDAC-II Compass 7 Vay - Compass 09 Backup

8. Vay - Compass 098 Benchmarking of Warp vs Headtail-1 LHC –  =479.6 –N p =1.1  10 11 –continuous focusing  x,y =66.0,71.54  x,y =64.28,59.31 –longitudinal motion OFF –n e =10 12- 10 14 –N b ecloud station/turn=10-100 –dipole magnetic field effect: frozen x-motion of electrons –same initial distribution of macro-protons with initial offset of 0.1  y No dipole field e- motion frozen in x e- motion frozen in x

9. Vay - Compass 099 Benchmarking of Warp vs Headtail-2 LHC –  =479.6 –N p =1.1  10 11 –continuous focusing  x,y =66.0,71.54  x,y =64.28,59.31 –longitudinal motion ON –n e =10 12- 10 14 –N b ecloud station/turn=10-100 –No dipole magnetic –same initial distribution of macro-protons with initial offset of 0.1  y

10. Vay - Compass 0910 Benchmarking of Warp vs Headtail-3 LHC –  =479.6 –N p =1.1  10 11 –continuous focusing  x,y = 66.0, 71.54  x,y,z = 64.28, 59.31, 0.0059  = 3.47  10 -4  p/p = 4.68  10 -4 chrom x,y = 2., 2. –n e =10 11- 10 14 –N b ecloud station/turn=10-100 –dipole magnetic field effect: frozen x-motion of electrons –same initial distribution of macro-protons with initial offset of 0.1  y –threshold 2-particle model for TMCI n e =10 14 m -3 n e =10 13 m -3 n e =10 12 m -3 n e =10 11 m -3 ≈ 6.43  10 11

11. SciDAC-II Compass SciDAC-II Compass 11 Vay - Compass 09 E-cloud: benchmarking against quasistatic model for LHC scenario The “quasistatic” approximation uses the separation of time scales for pushing beam and e-cloud macro-particles with different “time steps”: used in QuickPIC (USC/UCLA), Headtail (CERN), PEHTS (KEK), CMAD (SLAC), Warp (LBNL), … Excellent agreement on emittance growth between boosted frame full PIC and “quasistatic” for e-cloud driven transverse instability in continuous focusing model of LHC: The 2 runs have similar computational cost, thus how to choose one method other another? –boosted frame method offers less approximation to the physics, which may matter in some cases, –parallelization of quasistatic codes more complicated due to pipelining in the longitudinal direction.

12. SciDAC-II Compass SciDAC-II Compass 12 Vay - Compass 09 Other possible complication: inputs/outputs z’,t’=LT(z,t) frozen active Often, initial conditions known and output desired in laboratory frame –relativity of simultaneity => inject/collect at plane(s)  to direction of boost. Injection through a moving plane in boosted frame (fix in lab frame) –fields include frozen particles, –same for laser in EM calculations. Diagnostics: collect data at a collection of planes –fixed in lab fr., moving in boosted fr., –interpolation in space and/or time, –already done routinely with Warp for comparison with experimental data, often known at given stations in lab.

13. SciDAC-II Compass SciDAC-II Compass 13 Vay - Compass 09 space+time  x/t = ( L/l, T/  t)* 00 00 00 00 00 *J.-L. Vay, Phys. Rev. Lett. 98, 130405 (2007) Range of space and time scales spanned by two identical beams crossing each other space F 0 -center of mass frame x y x y F B -rest frame of “B”  is not invariant under the Lorentz transformation:  x/t  . There exists an “optimum” frame which minimizes it. Result is general and applies to light beams too.

14. SciDAC-II Compass SciDAC-II Compass 14 Vay - Compass 09 boosted frame 10km 10cm 10km/10cm=100,000. 10m 10m/1nm=10,000,000,000. 1nm 3cm 3cm/1  m=30,000. 1  m compaction x10 3 450m 4.5m frame  ≈ 22 450m/4.5m=100. 1nm compaction x3.10 7 2.5mm 4m4m 2.5mm/4  m=625. frame  ≈ 4000 compaction x560 1.6mm 30  m 1.6mm/30  m=53. frame  ≈ 19 Lorentz transformation => large level of compaction of scales range HEP accelerators (e-cloud) Laser-plasma acceleration Hendrik Lorentz Free electron lasers

15. SciDAC-II Compass SciDAC-II Compass 15 Vay - Compass 09 # of computational steps grows with the full range of space and time scales involved Choosing optimum frame of reference to minimize range can lead to dramatic speed-up for relativistic matter-matter or light-matter interactions. Consequence for computer simulations Calculation of e-cloud induced instability of a proton bunch* Proton energy:  = 500 in Lab L=5 km, continuous focusing Code: Warp (Particle-In-Cell) electron streamlines beam (from Warp movie) proton bunch radius vs. z CPU time (2 quad-core procs): lab frame: >2 weeks frame with  2 =512: <30 min Speedup x1000 *J.-L. Vay, Phys. Rev. Lett. 98, 130405 (2007)

16. SciDAC-II Compass SciDAC-II Compass 16 Vay - Compass 09 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  t -- no issue –Velocity push:  n+1 V n+1 =  n V n + (E n+1/2 +  B n+1/2 ) issue: E+v  B=0 implies E=B=0 => large errors when E+v  B  0 (e.g. relativistic beams). Solution –Velocity push:  n+1 V n+1 =  n V n + (E n+1/2 +  B n+1/2 ) Not used before because of implicitness. We solved it analytically* q tq t m  n+1 V n+1 +  n V n 2  n+1/2 *J.-L. Vay, Phys. Plasmas 15, 056701 (2008) (with,,, q tq t m V n+1 + V n 2,,, ).

17. Vay - Compass 09LARP CM12, Napa, Apr. 8- 10, 2009 ec feedback simulations - JL Vay, et al. 17 Simulations of e-cloud instability in SPS comparison Warp-Headtail  SPS – N p =1.1  10 11 – n e =1.  10 12 m -3 (uniform) –  :continuous focusing  x,y = 33.85, 71.87 x,y = 26.13, 26.185 chrom. x,y =0.1,0.1 – // : z = 0.00323 Warp/HT (isyn=1): continuous focusing HT (isyn=4): focusing more localized – 10 stations/turns – 512 turns E b =26 GeV (at injection) E b =120 GeV Good agreement between Warp and Headtail on emittance growth and tune shift using continuous focusing models at 26GeV and 120GeV.

18. Vay - Compass 09LARP CM12, Napa, Apr. 8- 10, 2009 ec feedback simulations - JL Vay, et al. 18 Simulations of e-cloud instability in SPS closer look at tune shift E b =26 GeV E b =120 GeV Warp Headtail (isyn=1) Headtail (isyn=4) tail head

19. Vay - Compass 09LARP CM12, Napa, Apr. 8- 10, 2009 ec feedback simulations - JL Vay, et al. 19 Simulations of e-cloud instability in SPS at injection - higher electron density  SPS at injection (E b =26 GeV) – N p =1.1  10 11 – n e =3  10 12 m -3 (uniform) – continuous focusing  x,y = 33.85, 71.87 x,y = 26.12, 26.185 chrom. x,y =0.,0. z = 0.0059 Warp Headtail Fractional emittance growth horizontal vertical tail head