W.B.Mori UCLA

Orion Center: Computer Simulation

Simulation component of the ORION Center

Just as the ORION facility is a resource for the ORION Center, codes such as OSIRIS and quickPIC will be a resource for modeling experiments.

This will be accomplished by encouraging collaborative partnerships.

The proposed simulation research in within the ORION Center includes:

Developing high fidelity parallelized software: currently OSIRIS, quickPIC, and UPIC

Model the full-scale of current and planned experiments ~50MeV -1GeV

Lay the foundation for enabling full-scale modeling of 100+ GeV plasma-based colliders

Real-time feedback between experiment and simulation

A new paradigm of scientific research

Close coupling between experiment and full-scale, three-dimensional, high-fidelity particle based simulations

Refraction of an Electron Beam:Interplay Between Simulation & Experiment

Laser off Laser on

3-D OSIRIS

PIC Simulation

Experiment(Cherenkov

images)

1 to 1 modeling of meter-scale experiment in 3-D!

P. Muggli et al., Nature 411, 2001

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

Beam-driven wake* Fully Explicitz .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 ~.25-1. x 108 (3D)

Particles x steps ~.5 x 1013 (3D) - ~ 5,000 hrson SP3

Computational challenges for modeling plasma wakefield acceleration

(1 GeV Stage)

Parallel Full PIC OSIRIS UPIC

Parallel quasi-static PIC quickPIC

Other codes exist within the community, e.g.,

OOPIC/Vorpal

The parallel simulation facility of the center includes:

Modeling Plasma Wakefield Acceleration Modeling Plasma Wakefield Acceleration requires particle based modelsrequires particle based models

• Space charge of drive beam displaces plasma electrons

• Transformer ratio

• Wake Phase Velocity = Beam Velocity (like wake on a boat)

• Plasma ions exert restoring force => Space charge oscillations

E Ez acc dec beam. .

• Wake amplitude N b z 2 ( )fornz p

o2

1

++++++++++++++ ++++++++++++++++

----- --- ----------------

--------------

--------- ----

--- -------------------- - --

---- - -- ---

------ -

- -- ---- - - - - - ------ - -

- - - - --- --

- -- - - - - -

---- - ----

------

electron beam

+ + + + + + + + + + ++ + + + + + + + + + + + + + ++ + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + +-

- --

--- --

EzEz

• 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,

n m n mj, ,,

dpdt

E v B c

E Bn m n m, ,,

t

Computational cycle (at each step in time)

What Is a Fully Explicit Particle-in-cell Code?

Typical simulation parameters:~107-109 particles ~1-100 Gbytes~104 time steps ~102-104 cpu hours

OSIRIS.frameworkBasic algorithms are mature and well tested

• Fully relativistic

• Choice of charge-conserving current deposition algorithms

• Boris pusher for particles, finite field solver for fields

• 2D cartesian, 2D cylindrical and 3D cartesian

• Field and impact ionization models

• Arbitrary particle initialization and external fields

• Conducting and Lindman boundaries for fields; absorbing, reflective, and thermal bath for particles; periodic for both

• Moving window

• Launch EM waves: field initialization and/or antennas

• Launch particle beam

• particle sorting and ion subcycling

• Extended diagnostics using HDF file output:–Envelope and boxcar averaging for grid quantities–Energy diagnostics for EM fields–Phase space, energy, and accelerated particle selection diagnostics for particles

UCLA

Effort was made to improve speed while maintaining parallel efficiency:

2D 128x128 with 16 particles/cell per processor and Vth=.1c

CPU#

Speed

s/ps

Push

%

BCpart BCcurr Field

Solve

BC Field

other Efficiency

1 2.1 95 4.2 .03 .56 .03 .19 100

4 2.13 95 3.89 .09 .59 .1 .31 99.48

16 2.2 92.8 4.91 .53 .71 .38 .68 95.82

64 2.3 89.3 6.87 1.28 .57 1.09 1.09 91.82

256 2.29 88.7 6.97 1.29 .55 1.39 1.15 92.16

512 2.37 85.2 7.42 1.27 .54 1.87 3.72 88.52

1024 2.29 90 5.6 1.1 .56 1.3 1.4 92.1

Speed in 3D: 3.2s/ps with 80%efficiency on 512 processors and 60% on 1024 processors(323 cells and 8 particles/cell/processor)

quickPIC• Quasi-static approximation: driver evolves on a much

longer distances than wake wavelength· Frozen wakefield over time scale of the bunch length

·

· => and/or xR >> z (very good approximation!)

Beam

Wake

UCLA

Basic equations for approximate QuickPIC

• Quasi-static or frozen field approximation converts Maxwell’s equations into electrostatic equations

(1

c2

2

t2 2 )A 4

cj

(1

c2

2

t2 2 ) 4

2 A 4

cj

2 4

Maxwell equations in Lorentz gauge Reduced Maxwell equations

j jb je jb cbˆ z • )ˆ( // zAA

Local-- at any z-slice depend only on j at that slice!

, A , A(z ct )

Quasi-static approx.

• A//

Forces :

plasma : Fe e

beam : Fb e

2-D plasma slab

Beam (3-D)Wake (3-D)

1. initialize beam

2. solve 2 ,

2 e Fp ,

3. push plasma, store 4. step slab and repeat 2.

5. use to giant step beam

QuickPIC loop (based on UPIC):

Parallelization of QuickPIC

zy

x

Node 3 Node 2 Node 1 Node 0

x

y

Node 3

Node 2

Node 1

Node 0

Benchmarking

Full PIC: OSIRIS and OOPIC

Full PIC vs. quasi-static PIC: OSIRIS and quickPIC

PIC against experiment: OSIRIS and quickPIC against E-157/E-162

quickPIC vs. OSIRIS

Positron driver

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

-10 -5 0 5 10

OsirisStandard QuickPICFull QuickPIC

(c/p)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-3 -2 -1 0 1 2 3

Full QuickPICStandard QuickPICOsiris

(c/p)

Lon

gitu

dina

l Wak

efie

ld (

mc

p/e)

Focu

sing

Fie

ld (

mc

p/e)

Plasma density = 2.1E14 cm-3, Beam Charge = 1.8E10 e+

Head Tail

Wakefield and focusing field from QuickPIC agree well with those from OSIRIS, and it is >100 times faster!

Full-scale modeling of experiments:A new paradigm of research

Plasma wakefield accelerator(PWFA) E-157/E-162electron acceleration/focusingpositron acceleration/focusing

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

Beyond planned experiments:Afterburner modeling

Nonlinear wakespreformedself-ionized

Nonliear beamloadingStability: hosingFinal focusing

OOPIC shows that a PWFA e- driver can ionize neutral Li

• OOPIC simulations show that tunneling ionization plays a key role in the PWFA afterburner concept– The self-fields of the bunch can ionize Li or Cs– High particle density (i.e. large self-fields) is required to drive a strong wake

• In Li, a shorter afterburner drive beam could ionize the plasma by itself– This approach would greatly simplify beam-driven wakefield accelerators– r=20 m; z=30 m; 2x1010 e- in the bunch; E0=11.4 GV/m

• We need to model evolution of the drive beam with TI effects included

Superposition cannot be used for nonlinear beamloading: 1+1 ≠ 2

2nd beam charge density

1st beam charge density

Linear superposition

Nonlinear wake

Nonlinear wake

Hosing can be studied for afterburner

parameters using quickPIC

Electron drive beam hoses as it propagate over a long distance in the plasma

3D image of the plasma charge density under blow-out regime

t = 0 t = 64,800 (1/p)

++ ++ ++ ++ ++ ++ + ++ + ++ ++ ++ ++ ++ ++ ++

-- -- -- - ---- -- --- ---- ----

- - -- - - - ---Er --

---------- --- --- - - - -- - -- -- -----------

-

----------

-- --- --

-- ---------- --- - ---

----- ----

-- ------

- - - --- - --

-- - ---

++++++++++++++++++++++++++ +++++++++++++++ +++++++++++++++

-

---

-- ---

EzEz

Focusing fieldAcceleration field

Simulations are a key piece of the ORION Center

Mature fully parallelized codes are a “facility” for the Center.

Codes have been benchmarked against each other and experiment.

One goal is to provide realtime feedback between experiment and theory.

Another goal is to lay the foundation for pushing advanced accelerators forward.

Role for this workshop:To discuss the simulation needs for new ideas: Can they be done with existing software?What new physics modules are needed?Applying methods in UPIC and OSIRIS.framework to LEAP and Sources.