Full-scale particle simulations of high- energy density science experiments W.B.Mori, W.Lu,...

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 10m spot– 3x1010 J/cm3

– 300 GBar

• Electric field in laser:– TeV/cm

• At SLAC:– N=2x1010 e- or e+

r=1m, z =60m

– E=50GeV

• Pressure:– 15x1010J/cm3

– 1.5TBar

• Electric field of beam:– 1.6TeV/cm

Lasers Particle 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 Accelerators Plasma

a0 ≡eA

mc 2= 8.5x1010 I(W /cm2)λ μm

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 excitation2. Evolution of driver and wake3. Loading the wake with particles

*Tajima and Dawson PRL 1979

Plasma Accelerator Progress and the “Accelerator Moore’s Law”

LOA,RAL

LBL ,RALOsaka

Courtesy of Tom Katsouleas

The blowout and bubble regimesRosenzwieg et al. 1990 Puhkov and Meyer-te-vehn 2002

Ion 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: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

• Era Memory particles speed max energy (full PIC)

•80’s 16MByte 105-106 5s/part-step 100 MeV (2D)

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

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

•Future 25-1000TByte >1011 5x10-5s/part-step 500 GeV (3D)

150Tflops - 10Pflops?

The simulations of Tajima and Dawsonwould take ~1 second on my laptop!

Beam-driven wake* Fully ExplicitΔz ≤ .05 /cωp

Δy, Δx ≤ .05 /cωp

Δt ≤ .02 /cωp

# grids in z ≥350

# grids in x , y ≥150# s teps ≥2 x 10 5

Npa rticles ~.25 x 1 08 (3D)~1 x 10 6 (2D)

Pa rticles x s teps ~.5 x 1013 (3D) - ≥ 10,000 h rs~1 x 10 11 (2D) - ≥ 75 h rs

*Lase r-driven GeV st age re quires on the o rder of (ωo/ωp)2=1000 x longer , however , the the res olution ca n usua lly be re laxed.

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 ~1013-1014

electrons

• There are ~106-109 self-trapped electrons

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

• 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:

• a0 = 1.1• W0=15.6 25 m• ωl/ωp = 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 cells56.18 m

512 cells100 m

State-of- the- art ultrashort laser pulse

0 = 800 nm, Δt = 50 fs

I = 2.5x1018 W/cm-2, W =12.5 m

Laser propagation

Plasma Backgroundne = 2x1019 cm-3

Simulation ran for 6400 hours on DAWSON

(~4 Rayleigh lengths)

Simulation ran for 6400 hours on DAWSON

Simulations: no fitting parameters!Nature papers, agreement with experiment

• In 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)

-2 1011

2 1011

4 1011

6 1011

8 1011

1 1012

1.2 1012

1.4 1012

-50 0 50 100 150 200

Imperial Data #( /((dE/E) Ω)3 D OSIRIS

( )Energy MeV

Movie of Imperial RunPlasma density and laser envelope

QuickTime™ and aMPEG-4 Video decompressor

are needed to see this picture.

3D PIC simulations:Tweak parameters

Parameters: E=1 J, 30 fs, 18 µm waist, 6×1018 cm-3

Scenario:• 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

Experiment

•Simulation Parameters–Laser:

• a0 = 4• W0=24.4 5 m• ωl/ωp = 33

–Particles• 2x1x1 particles/cell• 500 million total

–Plasma length• L=.7cm• 300,000 timesteps

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

4000 cells101.9 m

256 cells80.9 m

State-of- the- art ultrashort laser pulse

0 = 800 nm, Δt = 30 fs

I = 3.4x1019 W/cm-2, W =19.5 m

Laser propagation

Plasma Backgroundne = 1.5x1018 cm-3

Simulation ran for 75,000 hours on DAWSON

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 pictureEvolution 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)

1. initialize beam

2. solve ∇⊥2ϕ =ρ, ∇⊥

2ψ =ρe ⇒ Fp,ψ

3. pushplasma, storeψ

4. stepslabandrepeat2.

5. useψ togiantstepbeam

QuickPIC loop:

Solved by 2D field solver

∂t2 −∇2)A =4πc

∂t2 −∇2)φ =4πρ

−∇⊥2A =

−∇⊥2φ =4πρ

plasma e− :

d(ξ /c)=

1− vez /c(E +

cve × B)

d(ξ /c)=

1− vez /c

⎨ ⎪ ⎪

⎩ ⎪ ⎪

beam e− :

d(s /c)= qb (E +

cvb × B)

d(s /c)= vb

⎨ ⎪ ⎪

⎩ ⎪ ⎪

s = z,ξ = ct − z

Assume :

(1) ∂s << ∂ξ

(quasi − static

approximation)

(2) vb ≈ c€

plasma e− :

dt=qe (E +

cve × B)

dt= ve

⎨ ⎪

⎩ ⎪

beam e− :

dt= qb (E +

cvb × B)

dt= vb

⎨ ⎪

⎩ ⎪

Maxell’s equations in Lorentz gauge Particle pusher(relativistic)

Full PIC(no approximation)

Let : Ψ = φ − A//

QuickPIC

QuickPIC: Basic concepts

−∇⊥2 φ = 4πρ

−∇⊥2 Ψ = 4π (ρ −

QuickTime™ and aTIFF (LZW) decompressor

QuickPIC: Code structure

-5 0 5 10

OSIRISQuickPIC

ξ( /cωp)

-8 -6 -4 -2 0 2 4 6 8

OsirisQuickPIC (l=2)QuickPIC (l=4)

ξ ( /cωp)

-10 -5 0 5 10

Osiris

QuickPIC (l=2)

ξ ( /cωp)

-6 -4 -2 0 2 4 6

Osiris QuickPIC (l=2)

ξ ( /cωp)

e- driver e+ 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.

100+ CPU savings with “no” loss in accuracy

A Plasma Afterburner (Energy Doubler) Could be Demonstrated at SLAC

Afterburners

S. Lee et al., Phys. Rev. STAB, 2001

0-50GeV 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 MeV

65±10 MeV

Peak Energy Gain78 MeV

79±15 MeV

5x108 e+ in 1 ps bin at +4 ps

Head Tail Head Tail

OSIRIS E162 Experiment

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

• Identical parameters to experiment including self-ionization: Agreement is excellent!

QuickTime™ and aYUV420 codec decompressor

0 +5-5X (mm)

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 theworld is fueled

by fusion energy.

I see a day when high energy

acceleratorswill fit on a

tabletop.

πρφ

=∇−∂

−∇⊥2 A =

−∇⊥2 φ = 4πρ

−∇⊥2ψ = 4π (ρ − jz /c)

∂(ρ − j /c)

∂ξ+∇⊥⋅ j⊥ = 0

Maxwell equations in Lorentz gaugeReduced Maxwell equations

φ,A = ϕ (ct − z = ξ ,x⊥),A(ξ ,x⊥)

Quasi-static approx.

ψ =φ−Az

We define

Wakefield equations:“2D-electro and magneto-statics

Antonsen and Mora 1997

Whittum 1997

Huang et al., 2005 (QuickPIC)

∂t2 −∇2)A =4πc

∂t2 −∇2)φ =4πρ

−∇⊥2A =

−∇⊥2φ =4πρ

quasi - static : ∂s ≈ 0

Maxwell equations in Lorentz gauge Reduced Maxwell equations

//⊥⊥

⊥ ×+−

⎥⎦

⎤⎢⎣

⎡ ×+−=

electronsplasmaFor

delectronsbeamFor

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

s =z, ξ =ct−z

2∂∂s

−ik0 +∂∂ξ

⎝⎜

⎠⎟a−∇⊥

2a=k02χ pa=−k0

2 ωp2

ω02γp

Quasi-static Model including a laser driver

Laser envelope equation:

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

solve plasma response

update beam

Initial plasma slab

Without pipelining: Beam is not advanced until entire plasma response is determined

update beam

Initial plasma slab

1 2 3 4

With pipelining: Each section is updated when its input is ready, the plasma slab flows in the pipeline.

LWFA - Accelerating Field

512 cells40.95 m

•Isosurface values:

•Blue : -0.9

•Cyan: -0.6

•Green: -0.3

•Red: +0.3

•Yellow: +0.6

•Electric Field in normalized units me c ωp e-1

•Isosurface values:

•Blue : -0.9

•Cyan: -0.6

•Green: -0.3

•Red: +0.3

•Yellow: +0.6

•Electric Field in normalized units me c ωp e-1

SimulationsThe 200 TW run: Dephasing ~ Pump depletion

LT ≈1.0cm

Ldp ≈1.3cm

ΔE ≈1.5GeV

Laser plasma Given a we pick the density and we evaluate from our formulas:

After 5 Zr / 7.5 mm

Total charge = 1.1 nC

800 1200 1600 2000

Energy (MeV)

f(E) (a.u.)

w0 = 20μm

τ =30 fs

a0 = 4

=0.8μm

P = 200TW

np =1.5 ×1018cm−3

Physical picture of an “optimal” regimeGeometry - 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 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.

• 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/ωp, nb/np= 8.4, Ndrive = 3x1010, Ntrailing = 0.5x1010

Bi-Gaussian shapez= 1.2 c/ωp, nb/np= 26

Full-scale particle simulations of high- energy density science experiments W.B.Mori, W.Lu,...

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