1. W.B.Mori UCLA Orion Center: Computer Simulation

2. Simulation component of the ORION Center Just as the ORION facility is a resource for the ORION Center, codes such as OSIRIS and quickPIC will be a resource for modeling experiments. This will be accomplished by encouraging collaborative partnerships. The proposed simulation research in within the ORION Center includes: Developing high fidelity parallelized software: currently OSIRIS, quickPIC, and UPIC Model the full-scale of current and planned experiments ~50MeV -1GeV Lay the foundation for enabling full-scale modeling of 100+ GeV plasma-based colliders Real-time feedback between experiment and simulation

3. A new paradigm of scientific research Close coupling between experiment and full-scale, three- dimensional, high-fidelity particle based simulations

4. Refraction of an Electron Beam: Interplay Between Simulation & Experiment Laser off Laser on 3-D OSIRIS PIC Simulation Experiment (Cherenkov images) l 1 to 1 modeling of meter-scale experiment in 3-D! P. Muggli et al., Nature 411, 2001

5. One goal is to build a virtual accelerator: A 100 GeV-on-100 GeV e - e + Collider Based on Plasma Afterburners Afterburners 3 km 30 m

6. Computational challenges for modeling plasma wakefield acceleration (1 GeV Stage)

7.  Parallel Full PIC  OSIRIS  UPIC  Parallel quasi-static PIC  quickPIC Other codes exist within the community, e.g., OOPIC/Vorpal The parallel simulation facility of the center includes:

8. Modeling Plasma Wakefield Acceleration requires particle based models Space charge of drive beam displaces plasma electrons Transformer ratio Wake Phase Velocity = Beam Velocity (like wake on a boat) Plasma ions exert restoring force => Space charge oscillations Wake amplitude

9. Maxwell’s equations for field solver Lorentz force updates particle’s position and momentum Interpolate to particles Particle positions Lorentz Force push particles weight to grid tt Computational cycle (at each step in time) What Is a Fully Explicit Particle-in-cell Code? Typical simulation parameters : ~10 7 -10 9 particles~1-100 Gbytes ~10 4 time steps~10 2 -10 4 cpu hours

10. OSIRIS.framework Basic algorithms are mature and well tested Fully relativistic Choice of charge-conserving current deposition algorithms Boris pusher for particles, finite field solver for fields 2D cartesian, 2D cylindrical and 3D cartesian Field and impact ionization models Arbitrary particle initialization and external fields Conducting and Lindman boundaries for fields; absorbing, reflective, and thermal bath for particles; periodic for both Conducting and Lindman boundaries for fields; absorbing, reflective, and thermal bath for particles; periodic for both Moving window Launch EM waves: field initialization and/or antennas Launch particle beam particle sorting and ion subcycling Extended diagnostics using HDF file output: –Envelope and boxcar averaging for grid quantitiesEnvelope and boxcar averaging for grid quantities –Energy diagnostics for EM fieldsEnergy diagnostics for EM fields –Phase space, energy, and accelerated particle selection diagnostics for particlesPhase space, energy, and accelerated particle selection diagnostics for particles UCLA

11. Effort was made to improve speed while maintaining parallel efficiency: 2D 128x128 with 16 particles/cell per processor and V th =.1c CPU # Speed  s/ps Push % BCpartBCcurrField Solve BC Field otherEfficiency 12.1954.2.03.56.03.19100 42.13953.89.09.59.1.3199.48 162.292.84.91.53.71.38.6895.82 642.389.36.871.28.571.09 91.82 2562.2988.76.971.29.551.391.1592.16 5122.3785.27.421.27.541.873.7288.52 10242.29905.61.1.561.31.492.1 Speed in 3D: 3.2  s/ps with 80%efficiency on 512 processors and 60% on 1024 processors(32 3 cells and 8 particles/cell/processor)

12. quickPIC Quasi-static approximation: driver evolves on a much longer distances than wake wavelength ·Frozen wakefield over time scale of the bunch length · ·=>  and/or x R >>  z (very good approximation!) Beam Wake UCLA

13. Basic equations for approximate QuickPIC Quasi-static or frozen field approximation converts Maxwell’s equations into electrostatic equations Maxwell equations in Lorentz gauge Reduced Maxwell equations Local--  at any z-slice depend only on  j at that slice! Quasi-static approx.

14. 2-D plasma slab Beam (3-D) Wake (3-D) QuickPIC loop (based on UPIC):

15. Parallelization of QuickPIC z y x Node 3Node 2Node 1Node 0 x y Node 3 Node 2 Node 1 Node 0

16. Benchmarking Full PIC: OSIRIS and OOPIC Full PIC vs. quasi-static PIC: OSIRIS and quickPIC PIC against experiment: OSIRIS and quickPIC against E-157/E-162

17. quickPIC vs. OSIRIS Positron driver Longitudinal Wakefield (mc  p /e) Focusing Field (mc  p /e) Plasma density = 2.1E14 cm -3, Beam Charge = 1.8E10 e + Head Tail Wakefield and focusing field from QuickPIC agree well with those from OSIRIS, and it is >100 times faster!

18. Full-scale modeling of experiments: A new paradigm of research Plasma wakefield accelerator(PWFA) E-157/E-162 electron acceleration/focusing positron acceleration/focusing

19. Excellent agreement between simulation and experiment of a 28.5 GeV positron beam which has passed through a 1.4 m PWFA OSIRIS Simulation Prediction: Experimental Measurement: Peak Energy Loss 64 MeV 65±10 MeV Peak Energy Gain 78 MeV 79±15 MeV 5x10 8 e + in 1 ps bin at +4 ps HeadTailHeadTail OSIRISE162 Experiment

20. Beyond planned experiments: Afterburner modeling Nonlinear wakes preformed self-ionized Nonliear beamloading Stability: hosing Final focusing

21. OOPIC shows that a PWFA e- driver can ionize neutral Li OOPIC simulations show that tunneling ionization plays a key role in the PWFA afterburner concept –The self-fields of the bunch can ionize Li or Cs –High particle density (i.e. large self-fields) is required to drive a strong wake In Li, a shorter afterburner drive beam could ionize the plasma by itself –This approach would greatly simplify beam-driven wakefield accelerators –  r =20  m;  z =30  m; 2x10 10 e- in the bunch; E 0 =11.4 GV/m We need to model evolution of the drive beam with TI effects included

22. Superposition cannot be used for nonlinear beamloading: 1+1 ≠ 2 2nd beam charge density 1st beam charge density Linear superposition Nonlinear wake

23. Hosing can be studied for afterburner parameters using quickPIC Electron drive beam hoses as it propagate over a long distance in the plasma 3D image of the plasma charge density under blow-out regime t = 0 t = 64,800 (1/  p ) Focusing field Acceleration field

24. Simulations are a key piece of the ORION Center Mature fully parallelized codes are a “facility” for the Center. Codes have been benchmarked against each other and experiment. One goal is to provide realtime feedback between experiment and theory. Another goal is to lay the foundation for pushing advanced accelerators forward. Role for this workshop: To discuss the simulation needs for new ideas: Can they be done with existing software? What new physics modules are needed? Applying methods in UPIC and OSIRIS.framework to LEAP and Sources.