Full-scale particle simulations of high- energy density science experiments W.B.Mori, W.Lu, M.Tzoufras, B.Winjum, J.Fahlen,F.S.Tsung, C.Huang,J.Tonge M.Zhou, V.K.Decyk, C. Joshi (UCLA) L.O.Silva, R.A.Fonseca (IST Portugal) C.Ren (U. Rochester) T. Katsouleas (USC)

Directed high-energy density Pressure=Energy/Volume –Pressure=Power/Area/c PetaWatt with 10  m spot –3x10 10 J/cm 3 –300 GBar Electric field in laser: –TeV/cm At SLAC: –N=2x10 10 e - or e +  r =1  m,  z =60  m –E=50GeV Pressure: –15x10 10 J/cm 3 –1.5TBar Electric field of beam: –1.6TeV/cm LasersParticle beams

Radiation pressure and space forces of intense lasers and beams expel plasma electrons

Particle Accelerators Why Plasmas? Limited by peak power and breakdown MeV/m No breakdown limit GeV/m Conventional AcceleratorsPlasma Why lasers? Radiation pressure can excite longitudinal wakes

Laser Wake Field Accelerator(LWFA, SMLWFA, PBWA) A single short-pulse of photons Plasma Wake Field Accelerator(PWFA) A high energy electron bunch Concepts For Plasma Based Accelerators* Drive beam Trailing beam 1.Wake excitation 2.Evolution of driver and wake 3.Loading the wake with particles *Tajima and Dawson PRL 1979

Plasma Accelerator Progress and the “Accelerator Moore’s Law” LOA,RAL LBL,RAL Osaka Slide 2 Courtesy of Tom Katsouleas

The blowout and bubble regimes Rosenzwieg et al Puhkov and Meyer-te-vehn 2002 Ion column provides ideal accelerating and focusing forces

Typical simulation parameters: ~10 9 particles ~10 5 time steps Full scale 3D particle-in-cell modeling is now possible:OSIRIS Other codes:VLPL, Vorpal, TurboWAVE, Z3 etc., but no all the same!

Progress in computer hardware The “Dawson” cluster at UCLA: <$1,000,000 $50,000,000

Progress in lasers Courtesy of G.Mourou

Progress in hardware and software EraMemoryparticlesspeedmax energy (full PIC) 80’s 16MByte  s/part-step100 MeV (2D) Today ~6TByte/3~10 9 1x10 -3  s/part-step1-10GeV (3D (e.g., NERSC)(~7.5 Tflops/3) Local~500GByte~10 9 2x10 -3  s/part-step 1-10GeV (3D) Clusters(2.3Tflops)1 TeV (3D) (e.g., DAWSON) Future TByte> x10 -5  s/part-step500 GeV (3D) 150Tflops - 10Pflops? The simulations of Tajima and Dawson would take ~1 second on my laptop!

Computational challenges for modeling plasma-based acceleration (1 GeV Stage)

Full-scale modeling: Challenges and expectations As a laser propagates through the plasma it encounters ~ electrons There are ~ self- trapped electrons Need to model accuracy of 1 part in O(10 6 ) Don’t know exact plasma profile. Don’t know laser intensity or spot size. Don’t know laser transverse, longitudinal, or frequency profile (not a diffraction limited Gaussian beam). Challenges:What is excellent agreement?

Convergence of advances in laser technology and computer simulation

Simulation Parameters –Laser: a 0 = 1.1 W 0 =15.6  m  l /  p = 10 –Particles 2x1x1 particles/cell 500 million total –Plasma length L=.2cm 50,000 timesteps Full scale 3D LWFA simulation using OSIRIS: 6TW, 50fs 2340 cells  m 512 cells 100  m 512 cells 100  m State-of- the- art ultrashort laser pulse 0 = 800 nm,  t = 50 fs I = 2.5 x W/cm -2, W =12.5  m Laser propagation Plasma Background n e = 2x10 19 cm -3 Simulation ran for 6400 hours on DAWSON (~4 Rayleigh lengths) Simulation ran for 6400 hours on DAWSON (~4 Rayleigh lengths)

Simulations: no fitting parameters! Nature papers, agreement with experiment In experiments, the # of electrons in the spike is In our 3D simulations, we estimate of electrons in the bunch. 3D Simulations for: Nature V431, 541 (S.P.D Mangles et al)

Movie of Imperial Run Plasma density and laser envelope

3D PIC simulations: Tweak parameters Parameters: E=1 J, 30 fs, 18 µm waist, 6×10 18 cm -3 Scenario: self-focusing (intensity increases by 10) longitudinal compression  Excite highly nonlinear wakefield with cavitation: bubble formation trapping at the X point electrons dephase and self-bunch monoenergetic electrons are behind the laser field Propagation: 2 mm PIC Experiment

Simulation Parameters –Laser: a 0 = 4 W 0 =24.4  m  l /  p = 33 –Particles 2x1x1 particles/cell 500 million total –Plasma length L=.7cm 300,000 timesteps Full scale 3D LWFA simulation using OSIRIS Predict the future: 200TW, 40fs 4000 cells  m 256 cells 80.9  m 256 cells 80.9  m State-of- the- art ultrashort laser pulse 0 = 800 nm,  t = 30 fs I = 3.4 x W/cm -2, W =19.5  m Laser propagation Plasma Background n e = 1.5x10 18 cm -3 Simulation ran for 75,000 hours on DAWSON (~5 Rayleigh lengths) Simulation ran for 75,000 hours on DAWSON (~5 Rayleigh lengths)

OSIRIS 200 TW simulation: Run on DAWSON Cluster A 1.3 GeV beam! The trapped particles form a beam. Normalized emittance:The divergence of the beam is about 10mrad. Energy spread: Beam loading

Physical picture Evolution of the nonlinear structure The blowout radius remains nearly constant as long as the laser intensity doesn’t vary much. Small oscillations due to the slow laser envelope evolution have been observed. Beam loading eventually shuts down the self injection. The laser energy is depleted as the accelerating bunch dephases. The laser can be chosen long enough so that the pump depletion length is longer than the dephasing length.

2-D plasma slab Beam (3-D): Laser or particles Wake (3-D) QuickPIC loop:

Solved by 2D field solver Maxell’s equations in Lorentz gauge Particle pusher(relativistic) Full PIC (no approximation) QuickPIC QuickPIC: Basic concepts

QuickPIC: Code structure

e - drivere + driver e - driver with ionization laser driver QuickPIC Benchmark: Full PIC vs. Quasi-static PIC Benchmark for different drivers  Excellent agreement with full PIC code.  More than 100 times time- savings.  Successfully modeled current experiments.  Explore possible designs for future experiments.  Guide development on theory CPU savings with “no” loss in accuracy

A Plasma Afterburner (Energy Doubler) Could be Demonstrated at SLAC Afterburners 3 km 30 m S. Lee et al., Phys. Rev. STAB, GeV in 3 km GeV in 10 m!

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

Full-scale simulationof E-164xx is possible using a new code QuickPIC Identical parameters to experiment including self- ionization: Agreement is excellent! X (mm) Relative Energy (GeV)

Full-scale simulationof E-164xx is possible using a new code QuickPIC

5000 instead of 5,000,000 node hours We use parameters consistent with the International Linear Collider “design” We have modeled the beam propagating through ~25 meters of plasma. Full-scale simulation of a 1TeV afterburner possible using QuickPIC

I see a day where particle simulations will use 1 trillion particles I see a day where the world is fueled by fusion energy. I see a day when high energy accelerators will fit on a tabletop.

Maxwell equations in Lorentz gauge Reduced Maxwell equations Quasi-static approx. We define Wakefield equations: “2D-electro and magneto-statics Antonsen and Mora 1997 Whittum 1997 Huang et al., 2005 (QuickPIC)

Maxwell equations in Lorentz gauge Reduced Maxwell equations Initialize beam Call 2D routine Deposition 3D loop end Push beam particles 3D loop begin Initialize plasma Field Solver Deposition 2D loop begin 2D loop end Push plasma particles Iteration Quasi-static Model including a laser driver Laser envelope equation:

Pipelining: scaling quasi-static PIC to 10,000+ processors beam solve plasma response update beam Initial plasma slab Without pipelining: Beam is not advanced until entire plasma response is determined solve plasma response update beam solve plasma response update beam solve plasma response update beam solve plasma response update beam Initial plasma slab beam With pipelining: Each section is updated when its input is ready, the plasma slab flows in the pipeline.

LWFA - Accelerating Field 512 cells  m Isosurface values: Blue : -0.9 Cyan: -0.6 Green: -0.3 Red: +0.3 Yellow: +0.6 Electric Field in normalized units m e c  p e -1 Isosurface values: Blue : -0.9 Cyan: -0.6 Green: -0.3 Red: +0.3 Yellow: +0.6 Electric Field in normalized units m e c  p e -1

Simulations The 200 TW run: Dephasing ~ Pump depletion Laserplasma Given a we pick the density and we evaluate from our formulas: After 5 Z r / 7.5 mm Total charge = 1.1 nC

Physical picture of an “optimal” regime Geometry - fields The ponderomotive force of the laser pushes the electrons out of the laser’s way. The particles return on axis after the laser has passed. The region immediately behind the pulse is void of electrons but full of ions. The result is a sphere (bubble) moving with the speed of (laser) light, supporting huge accelerating fields. The ponderomotive force of the laser pushes the electrons out of the laser’s way. The particles return on axis after the laser has passed. The region immediately behind the pulse is void of electrons but full of ions. The result is a sphere (bubble) moving with the speed of (laser) light, supporting huge accelerating fields.

Physical picture Evolution of the nonlinear structure The front of the laser pulse interacts with the plasma and loses energy. As a result the front etches back. The shape and size of the accelerating structure slightly change. Electrons are self-injected in the plasma bubble due to the accelerating and focusing fields. The trapped electrons make the bubble elongate. The front of the laser pulse interacts with the plasma and loses energy. As a result the front etches back. The shape and size of the accelerating structure slightly change. Electrons are self-injected in the plasma bubble due to the accelerating and focusing fields. The trapped electrons make the bubble elongate.

PIC Simulations of beam loading in blowout regime: Used the new code QuickPIC (UCLA,USC,U.Maryland) Wedge shape w/ beam load beam length = 6 c/  p, n b /n p = 8.4, N drive = 3x10 10, N trailing = 0.5x10 10 Bi-Gaussian shape  z = 1.2 c/  p, n b /n p = 26