BELLA and laser-driven e-/e+ collider concept

C.G.R. Geddes, E. Cormier-Michel, E. Esarey, C.B. Schroeder, C. Toth, W.P. Leemans

LOASIS program, LBNL, http://loasis.lbl.govJean-Luc Vay, LBNL

D.L. Bruhwiler, J.R. Cary, B.M. Cowan, C. Nieter, K. Paul Tech-X

COMPASS meeting, 2009

11

*cgrgeddes@lbl.gov

NA-22/Nonproliferation R&D

LOASIS team

StaffE. Esarey (T)C. Geddes (S+E)A. Gonsalves (E)W.Leemans(E)N. Matlis (E)C. Schroeder (T)C. Toth (E)J. Van Tilborg (E)

Eng/TechsD. SyversrudN. YbarrazaK. Sihler

AdminO. WongM. Condon (0.5)G. Rogers (0.1)

PostdocsE. Cormier-Michel (S)J. Osterhoff (E)

StudentsM. Bakeman (PhD)B. KesslerD. KimC. Lin (PhD)G. Plateau (PhD)S. Shiraishi (PhD)T. Le Corre (M) H. Vincente

Collaborators include:LBNL : K. Barat, M. Battaglia, W. Byrne, J. Byrd, R. Duarte, W. Fawley. K. Robinson, D. Rodgers, R. Donahue et al.Tech-X: J. Cary, D. Bruhwiler, et al.SciDAC team

Oxford: S. Hooker et al. MPQ: F. Krausz, F. Gruener et al.LOA: O. Albert, L. CanovaGSI: T. Stoehlker, D. Thorn

DOE Scientific Discovery through Advanced Computing:

UCLA: W.B. Mori, F.S. Tsung, C. Huang, M. Tzoufras, M. Zhou,

W. Lu, S. Martins, M. Tzoufras, V. Dycek + collaborators at IST

USC/Duke:T. Katsouleas, X. Wang

Simulation Collaboration

LOASIS: C.G.R. Geddes, E. Michel

E. Esarey, C.B. Schroeder, W.P. Leemans

Tech-X: D. Bruhwiler, B. Cowan, P. Messmer, P. Mullowney, K.Paul, V. Ranjbar

Tech - X & U. Colorado J. Cary

Oxford W. Andreas, S. Bajlekov, N. Bourgeois,

T. Ibbotson, S.M. Hooker

NERSC, visualization:W. Bethel, J. Jacobsen, Prabhat, O. Rubel,

D. Ushizima, G. Weber

LBNL AMAC, CBP: R. Ryne, J.L. Vay (LDRD), W. Fawley (LDRD)

Nebraska, B.A. Shadwick et al.;

Simulating modules for BELLA PW laser and towards a conceptual future LPLC

Simulation & Theory must address Collider requirements & design

Required suite of models 10 GeV meter-scale stages Parameters for efficient stages Wake load & shaping (Cormier- Michel) Low emittance injector – (Cormier-Michel) Low noise fluid simulations (Bruhwiler) Guiding experiments (Bruhwiler) Full scale stages & evolution

Envelope (Cowan), Lorentz (Vay, Mori)

Collider concept Leemans & Esarey, Phys. Today 2009

~10 GeV stages

p~100µm at 1017/cc

Laser

Trapped particles

Conceptual design of an LPLC

Linac length set by tradeoff of gradient vs. staging

Required luminosity L[1034 cm-2 s-2] ~ (Ecm[TeV])2 because (cross section ~g-2)

Beam power: Pb = fNEcm

AC wall-plug power: ~ 200 MW 2% efficiency

~10% laser to beam ~20% wall-plug to laser

Additional options include gamma-gamma collider**

N ~ 3x109

f ~ 15 kHzEcm~ 1 TeV

Pb ~ 4 MW

5TeV LPA length vs stage density

LPLC Concept at 1017 /cc

*Collider Details – Schroeder et al, AAC 2008; Leemans & Esarey Phys. Today 2009 **Schroeder et al, PAC 2009

10 GeVstage

Calculated synchrotron radiation and scattering emittance contributions tolerable

Michel, Schroeder, Esarey, Leemans, Phys. Rev. E (2006)

Betatron motion in high transverse fields (O[E0]) synchrotron radiation

Fx ~ 1 GV/m (for ne=1017 cm-3, r ~ μm)

Energy spread induced < 10-4 for collider params

betatron motion

€

Prad =2e2γ 2

3m2c 3F⊥

2 ∝ γ 2rβ2

synchrotron radiation

Beam – beam interaction

(beamstrahlung) favors

short (micron) bunches

e- ion

€

dεn

dz=

γ

2kβ

d

dzθ 2 =

Zkp2re

kβ γln

bmax

bmin

⎛

⎝ ⎜

⎞

⎠ ⎟

Coulomb collisions

flat beam εx= 10-6

2 TeVf= 10 kHzN=109

n=1017 cm-3

Scattering between beam and background plasma ions:

Coulomb scattering emittance growth <nm for collider parameters

€

bmax ~ λ D = T 4πne2( )

1/ 2

*Details – Schroeder et al, AAC 2008; Leemans & Esarey Phys. Today 2009

Simulation + theory required to model self consistent laser, wake, and bunch

Explicit particle in cell simulates required physics – resolves laser period Mhours CPU time for cm-scale GeV simulations (VORPAL*)

Meter scale of 10 GeV stages – O[Ghours] explicit scaling + new models scaled simulation – change density, scale parameters envelope & quasistatic – average fast laser osc. see Ben Cowan’s talk Lorentz boosted – moving calculation frame Vay, Mori talks Combination of models for full solution

Require improved accuracy for collider emittances Cormier-Michel, Bruhwiler, Vay* Vorpal - Nieter & Cary, JCP 2004.

Tajima & Dawson PRL 1979;l Esarey et al. TPS 1996; Leemans et al., IEEE Trans. Plasma Science (1996); Phys. Plasmas (1998)

p~100µm at 1017/cc

Laser

Trapped particles

Energy gain ~ n-1 (10 GeV at 1017/cc)Length ~ n-3/2 (1m at 1017/cc)Gradient ~ n1/2 (10 GV/m at 1017/cc)

Laser w0&L ~ lp (100fs at 1017/cc)

Depletion ~ Dephasing for a0 > 1

Simulations of past expt.’s : Geddes et al JPCS 2008; ScDAC Review 2009

10 GeV stages in Quasilinear regime High gradient symmetric e+/e- acceleration

8

e- accel

e- focus

e+ focus

e+ accel

a0=4 Quasilinear - a0 ~1-2 e+/e- nearly symmetric high gradient Laser mode controls beam

matching to wake

Bubble regime wake curvature focuses e- defocuses e+

Linear, nonlinear scalings are of same order

e- accel

e- focus

e+ focus

e+ accel

a0=1Accel. field

Focus field

Density

Wake scales with densityScaled simulations at a=1

Scaling with density predicts wake structure for 10 GeV 40 J BELLA Stages

Use and verify linear theory predictions field ~ 1/p @ const. a0, kpLlaser, kpw0

Predict 10 GeV performance using short simulations at high density

Wake amplitude scales accurately: over 100-fold in density & 2D/3D between explicit, envelope and quasistatic codes

Simulation + scaling with theory predict: wake structure wake and laser evolution (details-Cowan,Vay)

* Cormier-Michel et al, Proc. AAC 2008

Field ~ 1/p

1019 cm-3 = 120 GV/m1018 cm-3 = 40 GV/m

Wake contoursVORPAL slab 1019/cc

WAKE Quasistatic cylindrical 1017/cc

14 kpX 0

-13

k pR

13

Spot size ~ lp optimizes quasilinear wake excitation and guiding

Small spot sizes

channel dispersion reduces Ldephase

energy depleted to transverse field

Large spot sizes

self focusing pinches focus

nonlinear wake results

Operate near kpw0 ~ 5

*Linear scaling: Esarey et al TPS 1996, simulations Geddes PAC 2009

Dephasing, focusing, efficiencyversus laser spot size

normalized simulations

Efficient stage obtained near kpL =1

Resolves laser depletion, broadening

0 /w w0 2

laser spectrum at depletion

Inte

nsity

(A

.U.)

Laser, Accelerating field evolution

Scan pulse length with fixed laser energy* stay on threshold of self focusing/nonlinearity

Characterized 0.5 < kpL < 3

kpL=1 optimal – laser depleted at dephasing

Depletion, field scale with density Numerically converged at percent level

Does not resolve focusing oscillations – requires envelope (Cowan), Lorentz (Vay)

*Geddes PAC 2009

kpL=2 laser energy

kpL=2 accelerating field

kpL=1 laser & accelerating fielddeplete at dephasing

ne (1/cm^3) 2.0e18a0 1lambda_p(um) 24kp*L_laser 2tau (fs) 25w0 (µm) 20kp*w0 5.3P(TW) 14P/Pc 0.9

40 J 10 GeV300pC

Px [GeV at 1017]

kpL=1 stage: 300pC scaled to 1017

Px [MeV at 1019]

12

Scalable design for HEP, GeV stagesEfficient collider stages with 40 J/PW

ne (1/cm^3) 1.0E+17a0 1.4lambda_p(um) 108kp*L_laser 1tau (fs) 57w0 (µm) 90kp*w0 5.3P(TW) 563P/Pc 1.8

0.5 J 0.4 GeV

50pC

0 120

Quasilinear designs*

NOTE : Nonlinear** stages accessible with same laser

•40 J laser focused to 41µm3 (a0=2) at ne = 1.3e17 -> 10 GeV, 200pC

•range of regimes can be explored

0 12

kpL=1 stage: 300pC scaled to 1017

** Lu et al, PRL 96, 0165002 (2006).

* Cormier-Michel et al, AAC2008, Geddes et al PAC 2009.

BELLA 40 J PW Laser – Components for aLaser Plasma Collider + Radiation Sources

BELLAPW laser

40 J / 40 fs

10 GeV stages Injection + Staging

Positron acceleration + PWFA expt.’s

Energy spread & Emittance preservation

Radiation sources

Efficient collider module stages are accessible for e+ e- Combination of models is required Wake load & shaping for high efficiency (Cormier- Michel) Low emittance injectors – (Cormier-Michel) Low noise fluid simulations for low emittance structures (Bruhwiler) Full scale stages & evolution- Envelope (Cowan), Lorentz (Vay, Mori)

SciDAC plans for BELLA project and a laser – plasma collider

Low emittance injector Downramp (Envelope,Explicit) Colliding pulse (Explicit)

Model collider emittances Accurate momentum advance, error accumulation

(weighting, mesh refinement, high order models) Noise control (fluids, EM dispersion, Cerenkov) Scattering & radiation, bench BD codes

10 GeV m-scale (PW laser)+staging Stage design for efficiency, emittance Scaling & speed- 1000x problem size

Reduced models(Envelope,QS,Lorentz) Laser vgroup (EM dispersion) Hydro sim. of capillaries, jets

Key model development Explicit PIC, Fluid, hybrid Long stage scaling, EM

dispersion, Momentum accuracy Laser Envelope model, Quasistatic Resolve depletion/wavelength

shift, Small bunch Optimal Lorentz Frame Diagnostics (simultaneity),

Noise control, Backward waves

Accurately model experiments – interpret & guide (Bruhwiler, Cormier-Michel)

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