Modeling narrow trailing beams and ion motion in PWFA

Chengkun Huang (UCLA/LANL)

and members of FACET collaboration

SciDAC COMPASS all hands meeting 2009

LA-UR 09-06300

a multi-stage PWFA-LC with 25GeV energy gain per stage in meter-long plasma

A few 10s nm beam size and emittance

PWFA Linear Collider concept

Radiation reaction effect can be observed in current generation experiments and it is in modeled in QuickPIC :

• Abraham-Lorentz-Dirac force: run-away solution and pre-acceleration• numerous other models exist• O’connell-Ford equation (Phys. Lett. A, 2003; Jackson 3rd ed.)

Synchrotron radiation

226 22

3loss

eP

c

Relativistic Larmor's formula

3/23

16 6

13.75 10

250 10 10nr

loaded loaded

E n

GeV m

Relative energy loss rate for a matched beam in PWFA:

Particle tracking in QuickPIC enable radiation diagnostics.

Radiation loss could be enhanced by ion motion.

• nonlinearity and local enhancement of the focusing force arise emittance growth• change longitudinal wakefield • increase radiation loss• effect of ion motion on main beam is of

major concern.

Ion collapse when nb/np > mi/me >>1 (Rosenweig PRL 2005),

PWFA Linear Collider concept

• Matched beam spot size shrinks at large γ, low n

• For future collider - eny down by 102 (e.g., 10nm-rad) - γ up by 10+- nb up by 102

- Ion motion must be included in design/models

nb x 1 y

1 1

nxny

2

p

c

ion motion for a future colliderion motion for a future collider

Drive beam

H+ ion

Reducing ion motionReducing ion motion

Analytical solutions are difficult, predictive quantitative study of the effects of ion motion on acceleration and beam quality requires accurate modeling.

• Possible solutions:

• Other possibilities:• emittance matching section?• weaker wake?

• estimate the computation requirements for the main beam. • collider beams are asymmetric, smallest emittance of the main beam in a

TeV collider is 0.04 mm·mrad. • the matched spot size of the main beam at 500 GeV in a plasma of

1×1017cm-3 will be 30 nm, which is three orders of magnitudes smaller than the longitudinal spot size or the plasma wavelength.

• transverse dimension of the beam is 6 nm at the final focus if a plasma lens is used.

• the transverse box size needs to be around 20 c/ωp, which is ~300 microns. This is 105 times larger than the required resolution.

• in the longitudinal direction, the plasma wavelength needs to be well resolved using O(1000) grids.

• a realistic 3D simulation of the accelerated beam would need 105×105×1000 = 1×1013 grids and 4×1013 particles (assuming 4 particles/cell).

• time step and the number of time steps for meter-long propagation distance are ~0.002 fs and 1×109 for a full PIC simulation, or ~ 16 ps and 208 for a quasi-static simulation.

Computation requirements for modeling ion motion

High resolution PWFA simulation

Milestone: Realistic 3D simulation of PWFA

• Drive beam: 2.91010 electrons, • Main beam: 11010 electrons, • Both are 25 GeV, modeled with ~4,200,000 macro-

particles.

Nominal PWFA-LC stage

• Main beam emittance: 0.093 mm·mrad• Matched spot sizes 100 nm for ne=11017 cm-3. • Drive beam emittance: 10 mm·mrad, typical for

current state-of-the-art linac.• Drive beam matched spot size 1 µm

High resoluton: required for TeV collider beam

• Simultion resolution: 49nm49nm304nm• 819281921024 grid points• 8192 processors on Franklin. • 4 particles per cell for plasma electron and ion

respectively. • Resolve real atom separation of ~20 nm at 11017

cm-3.

High resolution: required for ion dynamics

First PWFA PIC simulation to simulate nearly all the particles in a real plasma.