1. High performance modeling tools for plasma-based accelerators High performance modeling tools for plasma-based accelerators Work supported by Office of Science, US DOE, Contract No. DE-AC02-05CH11231 C. Benedetti, J.-L. Vay, C.B. Schroeder, R. Lehe, C.G.R. Geddes, E. Esarey, & W.P. Leemans BELLA Center, LBNL FACET-II Science Opportunities Workshops SLAC, October 12-16, 2015

2. Overview Requirements for an end-to-end modeling of a laser-plasma accelerator (LPA)-based linear collider [or a driver for an advanced light source (e.g., LPA- based FEL)] BLAST (Berkeley Lab Accelerator Simulation Toolkit) modules as a comprehensive suite of numerical tools for efficient, detailed and predictive modeling of intense laser-plasma interactions: – Ultra-low emittance from two-color laser ionization injection [injector] – Current BELLA experiments: 4.3 GeV LPA (using 16 J) [LPA stage] – Future BELLA experiments: 10 GeV LPA stage [LPA stage] – Staging experiment [LPA staging] Summary 2

3. (10 GeV, 1 m) Many potential LPA applications require high repetition rate and high wall-plug efficiency All-optical setup (injection+acceleration) 100x10 GeV LPA modules (staging) Length: ≤1 Km (1-10 GV/m) VS ~30 Km of ILC (RF, ~50 MV/m) LPA-based collider* → End-to-end simulation of a plasma-based linear collider is an extremely challenging problem (multi-physics, multi-scale) *Leemans, Esarey, Physics Today (2009) Schroeder et al., PRSTAB (2010) LPA-stage: - gas dynamics - MHD - laser-plasma interaction Beam transport - vacuum propag. - lenses - interaction w/plasma mirror Injector: - gas dynamics - bunch self-injection Final focus Driver in-coupling 3 Positron generation - Montecarlo code

4. Many potential LPA applications require high repetition rate and high wall-plug efficiency LBNL is developing a suite of tools to addresses the diverse physics of interest to model an LPA-based collider Time scale PhysicsCodesExamples ~ms Gas target formation: capillaries and gas jets Gas dynamics: ANSYS, OpenFOAM, Collab. w/ John Bell’s group @ CRD, LBNL ~1 ns ↓ ~100 ns Plasma formation in capillary discharges MHD: Bobrova's (1D) Marple (3D) (collab. w/ Keldysh institute, Moscow) ~fs ↓ ~ns Laser-plasma interaction (laser evolution, wake formation, particle dynamics) Vlasov-Maxwel: WARP @ BLAST INF&RNO @ BLAST 4

5. Computational complexity in modeling an LPA stage depends on unbalance between physical scales involved in the simulation plasma waves λ0λ0 e-bunch λpλp laser pulse L *courtesy of B. Shadwick et al. 10 GeV LPA stage (n 0 =10 17 cm -3 ) laser wavelength (λ 0 ) ~ μm laser length (L) ~ few tens of μm plasma wavelength (λ p )~100 μm interaction length (D)~ m Simulation complexity scales ~ (D/λ 0 ) 4/3 → 3D full PIC simulation of a 10 GeV LPA stage (~10 9 grid points, >10 9 macroparticles, 10 7 time steps) requires: 10 7 -10 8 CPUh → UNFEASIBLE WITH CONVENTIONAL 3D PIC CODES ← Maxwell-Vlasov equations → Particle-In-Cell (PIC) scheme: spatial grid for EM fields + macroparticles for plasma 5

6. Understanding the physics of intense LPAs requires detailed numerical modeling What we need (from the computational point of view): run 3D simulations (dimensionality matters!) of cm/m-scale laser-plasma interaction in a reasonable time (a few hours/days) perform, for a given problem, different simulations (exploration of the parameter space, optimization, convergence check, etc.) Lorentz Boosted Frame → Different spatial/temporal scales in an LPA simulation do not scale the same way changing the reference frame. Simulation length can be greatly reduced going to an optimal (wake) reference frame. Reduced Models → Reducing the computational complexity by carefully selecting the amount of Information/physics to compute (e.g., by neglecting some aspects of the physics) Vay, PRL (2007) Mora & Antonsen, Phys. Plas. (1997) [WAKE] Huang, et al., JCP (2006) [QuickPIC] Lifshitz, et al., JCP (2009) [CALDER-circ] Benedetti, et al., AAC2010/PAC2011/ICAP2012 [INF&RNO] Mehrling, et al., PPCF (2014) [HiPACE] 6

7. Berkeley Lab Accelerator Simulation Toolkit (BLAST) provides comprehensive suite of numerical tools for detailed, efficient, and predictive modeling of advanced accelerators http://blast.lbl.gov Detailed modeling of: beams, plasmas, laser-plasma interaction, linacs, rings, injectors, LPAs, … Using state-of-the-art codes: BEAMBEAM3D, IMPACT, POSINST, INF&RNO, WARP With original advanced algorithms: boosted frame, IGF, advanced laser envelope, AMR, relativistic particle pusher, EM spectral, quasi-cylindrical, … 2014 & 2015 NERSC HPC Achievement award; 2013 USPAS Prize Reduced code tailored on LPAs: several orders of magnitude faster compared to 3D full PIC General purpose, full 3D PIC: more complete description. Large gain with boosted frame. 7

8. Tunnel ionization implemented in BLAST modules and used to investigate novel concept to produce ultra-low emittance beam using two-color laser ionization injection* *Yu, et al., PRL (2014) Schroeder, et al., PRSTAB (2014) Schroeder, et al., SPIE Proc (2015) ε n ≈ 0.028 μm Transverse phase space Pump laser pulse Injection laser pulse Low emittance injected beam Plasma Simulations: Warp Visualization: VisIt Simulations: Warp Visualization: VisIt Wake >0=trapping Modeling injector → 8

9. INF&RNO is used to model current BELLA experiments: study of laser evolution in a 9 cm capillary* using realistic model for laser pulse 9 Accurate model of the BELLA laser has been constructed based on measurements 2013 measured long. laser intensity profile transverse intensity profile based on exp data – top-hat near field: I/I 0 =[2J 1 (r/R)/(r/R)] 2 – Gaussian 0369 Propagation distance (cm) 0369 1/e 2 intensity Simulation cost w/ INF&RNO: ~10 CPUh (reduction ~10 6 ) *Leemans, et al., PRL (2014) → features of INF&RNO allowed to run many simulations at a reasonable computational cost 9 U laser =15 J

10. Post-interaction laser optical spectra have been used as an independent diagnostic of the on-axis density * Comparison between measured and simulated post-interaction laser optical spectra → numerical modeling reproduces key features in the laser optical spectra: independent diagnostic for the plasma density *Leemans, et al., PRL (2014) Measurement INF&RNO simulation ← 30 simulation runs (each for a 9 cm long LPA) 10 *Simulations include instrumental response

11. Energy [GeV] divergence [mrad] e-beam spectrum [nC/SR/(MeV/c)] E=4.2 GeV dE/E=6% Q=6 pC x'=0.3 mrad E=4.3 GeV dE/E=13% Q=50 pC x'=0.2 mrad Simulation cost w/ INF&RNO: 300,000 CPUh (reduction >200) INF&RNO full PIC simulation allows for detailed investigation of particle self-injection and acceleration Simulated spectra Experiment *Leemans, et al., PRL (2014) 11

12. WARP allows for efficient modeling of meter long, 10 GeV LPA stages using Lorentz boosted frame* e - beam size (  m) e - beam energy gain (GeV) e - beam position (m) * J.-L. Vay, PRL (2007) Simulation cost 10 GeV LPA (3D) w/ WARP: 5,000 CPUh using LBF (reduction ~20,000) Simulation speed-up γ (Lorentz boost speed) → Theoretical speedups demonstrated numerically 12

13. INF&RNO is used to design and help the interpretation of the results of the STAGING experiment* INF&RNO is used to design and help the interpretation of the results of the STAGING experiment* Measurement* Modeling of e-bunch spectrum after LPA2 as a function of the delay between e-bunch and laser2 at the entrance of LPA2 Simulation cost w/ INF&RNO: ~15 CPUh (reduction ~60,000) ← 550 simulation runs (each for a 3.3 cm long LPA) LPA1 LPA2 Laser1 (1.3 J, 45 fs) Laser2 (0.45 J, 45 fs) bunch cap lens plasma mirror *background subtracted INF&RNO simulation *Steinke, et al., submitted (2015) +100 MeV energy gain, 3% capturing efficiency in LPA2 → 13

14. Many potential LPA applications require high repetition rate and high wall-plug efficiency ~10 GeV electron beams from STAGING experiment using BELLA (5 GeV+5 GeV): simulations show 100% capturing efficiency Laser1 =BELLA/2 (15 J, 80 fs) bunch Laser2 =BELLA/2 (15 J, 80 fs) cap lens 10 cm 8 cm1 cm 20 cm ~30 cm LPA1 [n 0 =(2-3)x10 17 cm -3 ] injector delay=-434.6 fs delay=-430.8 fs delay= -426.9 fs Bunch energy Relative energy spread Bunch dynamics in LPA1 Bunch dynamics in LPA2 LPA2 [n 0 =(2-3)x10 17 cm -3 ] 5 GeV bunch from LPA1 refocused: 100% bunch captured in LPA2 cap lens Bunch transport LPA1 → LPA2 Bunch energy ← injector after LPA1 after LPA2 Energy spectra 14

15. Continuous development of new modules within BLAST for improved accuracy/physical fidelity Continuous development of new modules within BLAST for improved accuracy/physical fidelity New WARP Module* (R. Lehe) = spectral + quasi-cylindrical PIC *Lehe et al., submitted to CPC (2015) Two-fold improvement in the physical fidelity/accuracy: Quasi-cylindrical: possibility to model non-axisymmetric physics Spectral: strongly reduces spurious Cherenkov radiation (e.g., better description of beam emittance) Numerical error (eqs. solved in Fourier space) (addition of a few azimuthal modes) → Ported on GPU (40x speed-up) 15

16. Summary and future research directions BLAST modules will allow modeling all the aspects of an LPA-based collider – Our numerical tools are accurate: we are benchmarking/validating our simulation tools against current experiments at LBNL – Our numerical tools are efficient: our codes provides computational speed-ups of several orders of magnitude compared to conventional 3D PIC codes Modeling using BLAST modules guides the design of current experiments and enables testing of new advanced accelerator concepts Future research directions: – Exploring and developing reduced models to capture relevant physics – Continue developing numerical schemes for improved efficiency/fidelity – Combine different approaches to increase speedup – Improving the parallel efficiency exploiting new hardware (GPUs, many-cores) 16