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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
Slide 2
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
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
(~4 Rayleigh lengths)
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
0
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
PIC
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
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
(~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 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.
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
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
(1c2
∂2
∂t2 −∇2)A =4πc
j
(1c2
∂2
∂t2 −∇2)φ =4πρ
−∇⊥2A =
4πc
j
−∇⊥2φ =4πρ
€
plasma e− :
dPe
d(ξ /c)=
qe
1− vez /c(E +
1
cve × B)
dXe
d(ξ /c)=
ve
1− vez /c
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
beam e− :
dPb
d(s /c)= qb (E +
1
cvb × B)
dXb
d(s /c)= vb
⎧
⎨ ⎪ ⎪
⎩ ⎪ ⎪
€
Let :
s = z,ξ = ct − z
Assume :
(1) ∂s << ∂ξ
(quasi − static
approximation)
(2) vb ≈ c€
plasma e− :
dPe
dt=qe (E +
1
cve × B)
dXe
dt= ve
⎧
⎨ ⎪
⎩ ⎪
beam e− :
dPb
dt= qb (E +
1
cvb × B)
dXb
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 −
j//
c)
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
QuickPIC: Code structure
-3
-2
-1
0
1
2
-5 0 5 10
OSIRISQuickPIC
ξ( /cωp)
-3
-2
-1
0
1
2
3
-8 -6 -4 -2 0 2 4 6 8
OsirisQuickPIC (l=2)QuickPIC (l=4)
ξ ( /cωp)
-0.1
-0.05
0
0.05
0.1
-10 -5 0 5 10
Osiris
QuickPIC (l=2)
ξ ( /cωp)
-1
-0.5
0
0.5
1
-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
3 km
30 m
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
are needed to see this picture.
0
+2
+4
-4
-2
0 +5-5X (mm)
Rel
ativ
e E
nerg
y (G
eV)
Full-scale simulationof E-164xx is possible using a new code QuickPIC
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
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.
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
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
π
4)1
(
4)
1(
22
2
2
22
2
2
=∇−∂
∂
=∇−∂
∂
tc
ctcjA
€
−∇⊥2 A =
4π
cj
−∇⊥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)
(1c2
∂2
∂t2 −∇2)A =4πc
j
(1c2
∂2
∂t2 −∇2)φ =4πρ
−∇⊥2A =
4πc
j
−∇⊥2φ =4πρ
€
quasi - static : ∂s ≈ 0
Maxwell equations in Lorentz gauge Reduced Maxwell equations
])([:
:
//⊥⊥
⊥ ×+−
=
⎥⎦
⎤⎢⎣
⎡ ×+−=
BV
EP
BV
EP
cVcq
dd
electronsplasmaFor
ccq
ds
delectronsbeamFor
e
e
ee
bbb
ξ
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
a
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
1 2 3 4
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
0
0.5
1
1.5
2
2.5
800 1200 1600 2000
f(E)
Energy (MeV)
f(E) (a.u.)
€
w0 = 20μm
€
τ =30 fs
€
a0 = 4
€
=0.8μm
€
P = 200TW
€
np =1.5 ×1018cm−3
€
P
Pc
≈10
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