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Recent advances in modeling advanced accelerators: plasma based acceleration and e-clouds
W.B.Mori , C.Huang, W.Lu, M.Zhou, M.Tzoufras, F.S.Tsung, V.K.Decyk (UCLA)D.Bruhwiler, J. Cary, P. Messner, D.A.Dimtrov, C. Neiter (Tech-X)
T. Katsouleas, S.Deng, A.Ghalam (USC) E.Esarey, C.Geddes (LBL)
J.H.Cooley, T.M.Antonsen (U. Maryland)
Particle Accelerators Why Plasmas?
• Limited by peak power and breakdown
• 20-100 MeV/m
• No breakdown limit
• 10-100 GeV/m
Conventional Accelerators Plasma
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
Physics necessitates the use of particle based methods:Many length and time scales for fields + particles--grand challenge!
Wake excitation is nonlinear: Trajectory crossingRosenzweig et al. 1990 Puhkov and Meyer-te-vehn 2002
Ion column provides ideal accelerating and focusing forces
Plasma Accelerator Progress and the “Accelerator Moore’s Law”
LOA,RAL
LBL ,RALOsaka
Slide 2
Courtesy of Tom Katsouleas
• Maxwell’s equations for field solver
• Lorentz force updates particle’s position and momentum
Interpolate to particles
Particle positions
Lorentz Force
push
partic
les weight to grid
z vi i,
ρn m n mj, ,,r
dpdt
E v B cr r r r= + ×
r rE Bn m n m, ,,
t
Computational cycle (at each step in time)
What Is a Fully Explicit Particle-in-cell Code?Not all PIC codes are the same!
Typical simulation parameters:~108-109 particles ~10-100 Gbytes~105 time steps ~104-105 cpu hours
Advanced accelerators:Before SciDAC
Beam-driven wake* Fully Explicitz ≤ .05 c/ωp
y, x ≤ .05 c/ωp
t ≤ .02 c/ωp
# grids i n z ≥350
# grids i n x, y ≥150# s tep s ≥2 x 105
Npar ticles ~.25 -1. x 10 8 (3D)
Part icle s x st ep s ~.5 x 10 13 (3D) - ≥ 50 00 h rs
*Laser -driven Ge V stage re quire s o n the orde r of (ωo/ωp)2=100 0 x longe r, however, the the re solution can us ua lly be re laxed (~200, 000 ho urs ).
5000+ node
hours for
each GeV of
energy
One 3D PIC
code
Accomplishments and highlights:Code development
• Four independent high-fidelity particle based codes– OSIRIS: Fully explicit PIC– VORPAL: Fully explicit PIC + ponderomotive guiding center– QuickPIC: quasi-static PIC + ponderomotive guiding center– UPIC: Framework for rapid construction of new
codes--QuickPIC is based on UPIC: FFT based
• Each code or Framework is fully parallelized. They each have load
balancing and particle sorting. Each production code has ionization packages for more realism. Effort was made to make codes scale to 1000+ processors.
OSIRIS:full parallel PIC for plasma accelerators
• Successfully applied to various LWFA and PWFA problems
– Mangles et al., Nature 431, 538 (2004).– Tsung et al., Phys. Rev. Lett., 93, 185002 (2004)– Blue et al., Phys. Rev. Lett., 90 214801 (2003)
• Code– Moving window– Parellized using domain decompostion– Two charge conserving deposition schemes– Current and field smoothing– Field + Impact Ionization– Static load balance.– Well tested
• Modern (object-oriented, Fortran 95 techniques)– Parallel (general domain decomposition) or Serial– Cross-platform (UNIX, Linux, AIX, OS X, MacMPIC)– Based on a well proven Fortran 77 code – Sophisticated 3D data diagnostics
• OSIRIS development team– UCLA(F. S. Tsung, J. W. Tonge), USC (S. Deng), IST (R. A.
Fonseca and L. O. Silva), Ecolé Polytechnique (J. C. Adam), and RAL (R. G. Evans).
– See http://exodus.physics.ucla.edu/
VORPAL – parallel PIC & related algorithms for advanced accelerators
• Successfully applied to various LWFA problems– Geddes et al., Nature 431, 538 (2004).– Cary et al., Phys. Plasmas (2005), in press (invited).
• Recently implemented algorithms– Ponderomotive guiding center treatment of laser pulses– PML (perfectly matched layer) absorbing BC’s– implicit 2nd-order & explicit 4th-order EM
• Many other capabilites/algorithms (only a sample here):– Impact & field ionization; secondary e- emission– Fluid methods for plasmas; hybrid PIC/fluid
• Modern (object-oriented, C++ template techniques)– Parallel (general domain decomposition) or Serial– Cross-platform (Linux, AIX, OS X, Windows)
• VORPAL development team– J. Cary (Tech-X/CU), C. Nieter, P. Messmer, D. Dimitrov,
J. Carlson, D. Bruhwiler, P. Stoltz, R. Busby, W. Wang, N. Xiang (CU), P. Schoessow, R. Trines (RAL)
– See http://www.txcorp.com/technologies/VORPAL/• Highly leveraged via SBIR funds: DOE, AFOSR, OSD
104
s(N)
VORPAL scales well to 1,000’s of processors
Colliding laser pulses
Particle beams
Code development:QuickPIC
Code features:• Based on UPIC parallel object-oriented plasma simulation Framework.• Underlying Fortran library is reliable and highly efficient• Multi-platform, Mac OS 9/X, Linux/Unix.• Dynamic load balancing
Model features:• Highly efficient quasi-static model for beam drivers• Ponderomotive guiding center + envelope model for laser drivers.• Can be 100+ times faster than conventional PIC with no loss in accuracy.• ADK model for field ionization.
Applications:• Simulations for PWFA experiments, E157/162/164/164X/167• Study of electron cloud effect in LHC.• Plasma afterburner design
Scalability:• Currently scales to ~32 processors• With pipelining should scale to 10,000+ processors
afterburner
hosing
E164X
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:
(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:
Parallelization for QuickPIC
zy
x
Node 3 Node 2 Node 1 Node 0
3D domain decompositionCommunication
Beam
xy
2D domain decomposition with dynamic load balancing
Node 3
Node 2
Node 0
Node 1
Beam
Plasma
2D loop timing
10
100
1000
1 10 100
CPUs
Excution time (Sec)
Dawson diff. nodes
Dawson same node
Nersc diff. nodes
Nersc same node
Dawson diff. nodes -- overhead removed
Dawson same node -- overhead removed
Network Overhead
• Scales up to 16-32 CPUs for small problem size.
• Network overhead dominates on Dawson cluster (GigE).
• 4 times performance boost with infiniband hardware.
• With pipelining should scale to 10,000+ processors
Accomplishments and highlights:Physics
• Development of new reduced models (QuickPIC) and benchmarking of codes (OSIRIS vs. Vorpal, QuickPIC vs. OSIRIS, Vorpal vs. Vorpal PG)
• Code validation (by adding more realism):– Modeling of PWFA experiments at SLAC in 3D: 4GeV energy gain in ~10cm
(OSIRIS and QuickPIC).– Identified self-ionization as a plasma source option in PWFA (OOPIC, Vorpal,
OSIRIS)– Modeling LWFA experiments at LBNL and RAL: 100MeV monoenergetic
beams in ~1mm (OSIRIS and VORPAL).
• New physics:– Modeling PWFA Afterburner (energy doubler) stages: From 50 to 100 GeV
and from 500 to 1000 GeV (QuickPIC).– Modeling possible 1GeV mono-energetic LWFA stages: with and without
external optical guiding (OSIRIS and VORPAL).
-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
Code benchmarking:Vorpal fully explicit vs. ponderomotive
guiding center
• Removes fast time-scale of laser pulse– orders of magnitude faster than full
PIC– can simulate 3 cm LBNL plasma
channel in 2D in a few processor-hours
• Excellent comparison w/ 2D PIC
– good agreement seen for a0~1
• accelerating wake fields (upper fig.)• normalized particle velocities
(lower fig.)– particle trapping seen at larger values
of a0
€
Emax ~ 4GeV
(initial energy chirp
considered)
Modeling self-ionized PWFA experiment with QuickPIC
E164X experiment
QuickPIC simulation
-4
-2
0
2
4
6
8
0
2
4
6
8
10
12
0 100 200 300 400 500
(z μ )m
€
Emax ~ 5− 0.5(β − tron radiation) = 4.5GeV
Located in the FFTB
e-
N=1-2· 1010
σz=0.1 mm=30 E GeV
Ionizing Laser Pulse
(193 )nm Li Plasma
ne≈6 · 10 15 cm-3
L≈30 cm
CerenkovRadiator
Streak Camera(1 )ps resolution
-X RayDiagnostic
Optical TransitionRadiators Dump
25 m
∫Cdt
!Not to scale
Spectrometer
25 m
FFTB
Full-scale simulation with ionization of E-164xx is possible using a new code QuickPIC• Identical parameters to experiment including self-ionization: Agreement is very good!
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)
3 Nature papers (September 2004) where mono-energetic electron beams with energy near 100 MeV were measured. Supporting PIC simulations were presented.
SciDAC members were collaborators on two of these Nature publications and SciDAC codes were used.
Cover is a Vorpal simulation
Phys. Rev. Lett. by Tsung et al. (September 2004) where a peak energy of 0.8 GeV and a mono-energetic beam with an central energy of 280 MeV were reported in full scale 3D PIC simulations.
Recent highlights: LWFA simulations using full PIC
3D PIC Simulations with no fitting parameters:Nature papers, “agreement” with experiment: What is the metric for agreement?
• In experiments, the # of electrons in the spike is 1.4 108.
• In our 3D simulations, we estimate of 0.9 108 electrons in the bunch.
3D Simulations for: Nature V431, 541 (S.P.D Mangles et al)
0
5 107
1 108
1.5 108
20 40 60 80 100 120 140
3D PICExperiment
Energy (MeV)
f(E) (a.u.)
•Simulation Parameters–Laser:
• a0 = 4• W0=24.4 l=19.5 mm• wl/wp = 33
–Particles• 2x1x1 particles/cell• 500 million total
–Plasma length• L=.7cm• 300,000 timesteps
Full scale 3D LWFA simulation using OSIRIS:200TW, 40fs
4000 cells101.9 μm
256 cells80.9 μm
256 cells80.9 μm
State-of- the- art ultrashort laser pulse
0 = 800 nm, t = 30 fs
I = 3.4x1019 W/cm-2, W =19.5 μm
Laser propagation
Plasma Backgroundne = 1.5x1018 cm-3
Simulation ran for 75,000 hours on 200 G5 x-serve processors on
DAWSON (~5 Rayleigh lengths)
Simulation ran for 75,000 hours on 200 G5 x-serve processors on
DAWSON (~5 Rayleigh lengths)
Simulations are leading experiments:200TW 30fs laser----1.5 GeV beam in ~cm
• Laser blows out all plasma electrons leading to an ideal accelerating structure
• Isolated beams are self-injected.
• Beams become mono-energetic as they outrun the wake.
QuickTime™ and aMPEG-4 Video decompressor
are needed to see this picture.
OSIRIS simulation
One goal is to build a virtual accelerator:
A 100+ GeV-on-100+ GeV e-e+ Collider
Based on Plasma Afterburners
Afterburners
3 km
30 m
Advanced accelerator milestone:Full-scale simulation of a 1TeV afterburner is possible using QuickPIC
• 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.
•Before SciDAC: 5,000,000+ node hours at NERSC (was not done)
•Because of SciDAC: 5,000 node hours on the DAWSON Cluster (2.3 Ghz x-serves)
Advanced accelerators:After SciDAC
• 3D modeling with realism-2 explicit PIC codes plus a parallel Framework• Code benchmarking• Code validation-Full scale 3D modeling of experiments• Efficient and high fidelity reduced description models: Rapid construction of
fully parallelized code• Extension of plasma techniques to conventional accelerator issues: e-cloud
• Rapid progress has resulted from:– Faster computers– New algorithms– Reuseable software
• Scientific discovery:• 3 Nature articles and 8 Phys. Rev. Lett.’s
Vision for the future:High fidelity modeling of .1 to 1TeV plasma accelerator stages
• Physics Goals:– A) Modeling 1to 10 GeV plasma accelerator stages: Predicting and designing near term
experiments.– B) Extend plasma accelerator stages to 250 GeV to 1TeV range: understand the physics and
scaling laws– C) Use plasma codes to definitively model e-cloud physics:
• 30 minutes of beam circulation time on LHC• ILC damping ring
• Software goals:– A) Add pipelining into QuickPIC: Allow QuickPIC to scale to 1000’s of processors.– B) Add self-trapped particles into QuickPIC and ponderomotive guiding center Vorpal packages.– C) Improve numerical dispersion* in OSIRIS and VORPAL.– D) Scale OSIRIS, VORPAL, QuickPIC to 10,000+ processors.– E) Merge reduced models and full models– F) Add circular and elliptical pipes* into QuickPIC and UPIC for e-cloud.– G) Add mesh refinement into* QuickPIC, OSIRIS, VORPAL,and UPIC.– H) Investigate the utility of fluid and Vlasov models.
* Working with APDEC ISIC
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.
Advanced accelerators:Goals
• Develop reusable software based on particle-in-cell methods that scales to 1000+ processors.
• Develop codes that use this reusable software and which include the necessary physics modules.
• Develop reduced description codes to reduce cpu and memory needs.
• Benchmark codes against each other and validate codes against experiments.
• Use validated codes to discover ways to scale plasma based accelerator methods to .1 to 1 TeV.