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 densityPressure=Energy/VolumePressure=Power/Area/c

PetaWatt with 10mm spot3x1010 J/cm3300 GBar

Electric field in laser:TeV/cm

At SLAC:N=2x1010 e- or e+sr=1mm, sz =60mmE=50GeVPressure:15x1010J/cm31.5TBar

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

20-100 MeV/m

No breakdown limit

10-100 GeV/m

Conventional AcceleratorsPlasmaWhy 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 beamTrailing beamWake excitationEvolution of driver and wakeLoading the wake with particles*Tajima and Dawson PRL 1979

Plasma Accelerator Progress and the Accelerator Moores LawLOA,RALLBL ,RALOsakaSlide 2Courtesy of Tom Katsouleas

The blowout and bubble regimesRosenzwieg et al. 1990 Puhkov and Meyer-te-vehn 2002Ion column provides ideal accelerating and focusing forces

Typical simulation parameters:~109 particles~105 time steps Full scale 3D particle-in-cell modeling is now possible:OSIRISOther codes:VLPL, Vorpal, TurboWAVE, Z3 etc., but no all the same!

Progress in computer hardwareThe Dawson cluster at UCLA:

Progress in lasersCourtesy of G.Mourou

Progress in hardware and software EraMemoryparticlesspeedmax energy (full PIC)

80s16MByte105-1065ms/part-step100 MeV (2D)

Today~6TByte/3~109 1x10-3ms/part-step1-10GeV (3D(e.g., NERSC)(~7.5 Tflops/3)

Local~500GByte~109 2x10-3 ms/part-step 1-10GeV (3D)Clusters(2.3Tflops)1 TeV (3D)(e.g., DAWSON)

Future25-1000TByte>10115x10-5ms/part-step500 GeV (3D)150Tflops - 10Pflops?The simulations of Tajima and Dawsonwould take ~1 second on my laptop!

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

Beam-driven wake*

Fully Explicit

(z

( .05 c/(p

(y, (x

( .05 c/(p

t

( .02 c/(p

# grids in z

(350

# grids in x, y

(150

# steps

(2 x 105

Nparticles

~.25 x 108 (3D)

~1 x 106 (2D)

Particles x steps

~.5 x 1013 (3D) - ( 10,000 hrs

~1 x 1011 (2D) - ( 75 hrs

*Laser-driven GeV stage requires on the order of (o/p)2=1000 x longer,

however, the the resolution can usually be relaxed.

Full-scale modeling: Challenges and expectationsAs a laser propagates through the plasma it encounters ~1013-1014 electrons

There are ~106-109 self-trapped electrons

Need to model accuracy of 1 part in O(106)

Dont know exact plasma profile.Dont know laser intensity or spot size.Dont 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

Full scale 3D LWFA simulation using OSIRIS:6TW, 50fs

Simulation ParametersLaser:a0 = 1.1W0=15.6 l=12.5 mm wl/wp = 10Particles2x1x1 particles/cell500 million totalPlasma lengthL=.2cm50,000 timesteps

Laser propagationPlasma Backgroundne = 2x1019 cm-3Simulation ran for 6400 hours on DAWSON (~4 Rayleigh lengths)

Simulations: no fitting parameters!Nature papers, agreement with experimentIn experiments, the # of electrons in the spike is 1.4 108.

In our 3D simulations, we estimate of 2.4 108 electrons in the bunch.3D Simulations for: Nature V431, 541 (S.P.D Mangles et al)

Movie of Imperial RunPlasma density and laser envelope

3D PIC simulations:Tweak parametersParameters: E=1 J, 30 fs, 18 m waist, 61018 cm-3Scenario: self-focusing (intensity increases by 10) longitudinal compressionExcite 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

Full scale 3D LWFA simulation using OSIRISPredict the future: 200TW, 40fs

Simulation ParametersLaser:a0 = 4W0=24.4 l=19.5 mm wl/wp = 33Particles2x1x1 particles/cell500 million totalPlasma lengthL=.7cm300,000 timesteps

Laser propagationPlasma Backgroundne = 1.5x1018 cm-3Simulation ran for 75,000 hours on DAWSON (~5 Rayleigh lengths)

OSIRIS 200 TW simulation: Run on DAWSON ClusterA 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 pictureEvolution of the nonlinear structure The blowout radius remains nearly constant as long as the laser intensity doesnt 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 slabBeam (3-D):Laser or particlesWake (3-D)QuickPIC loop:

Maxells equations in Lorentz gaugeParticle pusher(relativistic)Full PIC(no approximation)QuickPICQuickPIC: Basic concepts

QuickPIC: Code structure

QuickPIC Benchmark: Full PIC vs. Quasi-static PICBenchmark 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.

100+ CPU savings with no loss in accuracy

A Plasma Afterburner (Energy Doubler) Could be Demonstrated at SLACAfterburners3 km30 mS. Lee et al., Phys. Rev. STAB, 20010-50GeV in 3 km50-100GeV 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 Loss64 MeV6510 MeVPeak Energy Gain78 MeV7915 MeV5x108 e+ in 1 ps bin at +4 psHeadTailHeadTailOSIRISE162 Experiment

Full-scale simulationof E-164xx is possible using a new code QuickPIC Identical parameters to experiment including self-ionization: Agreement is excellent!

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 designWe 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 simulationswill use 1 trillion particlesI see a day where theworld is fueledby fusion energy.I see a day when high energy acceleratorswill fit on a tabletop.

Wakefield equations:2D-electro and magneto-staticsMaxwell equations in Lorentz gaugeReduced Maxwell equationsQuasi-static approx.We defineAntonsen and Mora 1997Whittum 1997Huang et al., 2005 (QuickPIC)

Quasi-static Model including a laser driverLaser envelope equation:

Pipelining: scaling quasi-static PIC to 10,000+ processors

LWFA - Accelerating Field 512 cells40.95 mmIsosurface values:Blue : -0.9Cyan: -0.6Green: -0.3Red: +0.3Yellow: +0.6Electric Field in normalized units me c wp e-1

SimulationsThe 200 TW run: Dephasing ~ Pump depletionLaserplasma Given a we pick the density and we evaluate from our formulas:

Physical picture of an optimal regimeGeometry - fields The ponderomotive force of the laser pushes the electrons out of the lasers 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 pictureEvolution 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.

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, nb/np= 8.4, Ndrive = 3x1010, Ntrailing = 0.5x1010Bi-Gaussian shapez= 1.2 c/p, nb/np= 26

In this slide Ill show how we get the basic equations in QuickPIC from those of Full PIC by making quasi-static approximation.In Full pic, where no approximation is made, the maxel in gauge look like this. And the partice pusher which is basically equation of motion and drdt equals v looks like this.Afte we make substitution of variable z& t to s & kesi, at the same time make the approximation of quasi-static and vb=c. the maxwells equations look like this, where the dirivative is only in the transverse direction. If we further make variale substitution by defining sai=, well get equations of pai and sai whose source are only rou and j// in the same slice, and these two equations could be solved by a 2d poisson solver.Another thing to mention before we move on is that the particle pusher are relativistic for both beam and plasma particles.

not really electrostatic and 2d, actually its electromagnetic & 3d. The quasi-static approx. makes its form like 2d electromagnetic. The afterburner is important because it shows the dream as well as helps transition from current experiments to the need/mission of ORION.The cavity is a sphere.The cavity is a sphere.The cavity is a sphere.The cavity is a sphere.