Slide 1

Physics of a 10 GeV laser-plasma accelerator stageEric EsareyHBEB Workshop, Nov 16 -19, 2009

http://loasis.lbl.gov/C. Schroeder, C. Geddes, E. Cormier-Michel, W. LeemansLOASIS Program Lawrence Berkeley National Laboratory

1Regimes of laser-plasma acceleratorsQuasi-linear and highly nonlinear (blowout)Limits to single-stage energy gain in a LPADiffraction, dephasing, depletionScaling laws for single-stage energy gainAnalytic theory and fluid simulationsConceptual design of a laser-plasma collider at 1 TeVBased on 10 GeV stagesRequires tens of J laser pulses at tens of kHzPlasma and laser tailoring to improve performanceLongitudinal density tapering to eliminate dephasingHigher-order laser modes to control transverse fields

OutlineRef: Esarey, Schroeder, Leemans, Reviews of Modern Physics (2009)2Laser Wakefield Accelerator (LWFA)

B.A. Shadwick et al., IEEE PS. 2002Standard regime (LWFA): pulse duration matches plasma periodUltrahigh axial electric fields => Compact electron acceleratorsPlasma wakefields Ez > 10 GV/m, fast waves(Conventional RF accelerators Ez ~ 10 MV/m)Plasma channel: Guides laser pulse and supports plasma wave

Tajima, Dawson (79); Gorbunov, Kirsanov (87); Sprangle, Esarey et al. (88)3Conceptual LPA Collider

Leemans & Esarey, Physics Today, March 2009 Based on 10 GeV modules Quasi-linear wake: e- and e+ Driven by 40 J, 130 fs pulses 80 cm plasma channels (1017 cm-3) Staging & coupling modules Requires high rep-rate (10s kHz) Requires development of high average power lasers (100s kW)4

Basic design of a laser-plasma accelerator: single-stage limited by laser energylaserEz wakeLaser pulse length determined by plasma densitykp sz 1, sz ~ lp ~ n-1/2Wakefield regime determined by laser intensityLinear (a01) Determines bunch parameters via beam loading

Ex: a0 = 1 for I0 = 2x1018 W/cm2 and 0 = 0.8 mAccelerating field determined by density and laser intensityEz ~ (a02/4)(1+a02/2)-1/2 n1/2 ~ 10 GV/mEnergy gain determined by laser energy via depletion*Laser: Present CPA technology 10s J/pulse

*Shadwick, Schroeder, Esarey, Phys. Plasmas (2009) 5Linear & blowout regimes: e+/e- acceleration

run 405

Blowout regimehigh fieldvery asymmetricfocuses e-defocuses e+self-trapping

Quasilinearlinear: symmetric e+/e-high a0 desired for gradienttoo high enters bubblea0 ~1-2 good compromisedark current freee- accele- focuse+ focuse+ accela0=4

e- accele- focuse+ focuse+ accela0=1Axial fieldTransverse fieldPlasma density6note - gain in E is no longer as a^2 above a=1; closer to linear in a but need numerics. This reduces the advantage of the bubble

not dealing here with emittance, etc - later slide3D: Diffraction, Dephasing, DepletionDiffraction of laser pulseZR = p r02/l0 ~ 2 cm, ZR> 1: Ldeplete ~ Ldephase

DW = Ez . LLimits to acceleration length: depletion

Ezlaser

EzlaserSolution: staging

Rate of laser energy depositionDeveloped theory of nonlinear short-pulse laser evolution. Derived general energy evolution equation valid for any laser intensity and pulse shapeScale separation (laser frequency >> plasma frequency)Neglect backward going waves (Raman backscatter)Model plasma as cold fluid

Apply quasi-static approximation (laser slowly varying compared to plasma response):

Shadwick, Schroeder, Esarey, Physics of Plasmas (2009)

characteristic accelerating field:

Nonlinear plasma wave excitation by a Gaussian laser pulse

Peak plasma wave driven by Gaussian laser insensitive to pulse duration (broad resonance) over intensity regime of interestPump depletion length independent of intensity for ultra-intense pulses

Pump depletion length for near-resonant Gaussian laser pulse:Pump depletion length:

Characteristic length scale independent of intensity for relativistically-intense laser pulses

Single stage energy gain limited by laser energy depletionDiffraction limitation: mitigated by transverse plasma density tailoringDephasing limitation: mitigated by longitudinal plasma density tailoring

Depletion: necessitates multiple stagesMultiple-stages for controlled acceleration to high energy:

Depletion Length:

Energy gain (linear regime):

laser

+ channel Ex: Wstage = 10 GeV for I = 1018 W/cm2 and n = 1017 cm-3Accelerating field:

1516

Scaling laws: analytic theory16Laser pulse evolution

Laser energy evolution:Laser fieldplasma densityaccelerating fieldpt=500pt=1500pt=2500pt=3500Laser evolution interplay between laser intensity steepening, laser frequency red-shifting, energy depletion

Shadwick, Schroeder, Esarey, Physics of Plasmas (2009)

18Longitudinal e-bunch dynamics:energy spread minimum near dephasing

LaserWakePosition, kp(z-ct)Fluid plasma + e-bunch described by moments (includes beam loading)B.A. Shadwick et al.

Time, ptMomentumEnergy spreade-bunchEnergy spread Initial: / = 0.3% at = 100 Final: / = 0.01% at = 3000 18Scaling laws from fluid code: dephasing/depletion lengths & energy gain

Fraction of laser energy at dephasing lengthIndependent of k/kpFix laser parameters (a0, kpL0, kpr0), increase (k/kp) to increase energy Energy and dephasing length from 1D fluid simulations a0 =1: max = 0.7(k/kp)2 , kpLdp= 4(k/kp)2 a0 =1.5: max = 1.3(k/kp)2 , kpLdp= 3.5(k/kp)2 a0 =2: max = 2(k/kp)2 , kpLdp= 3(k/kp)2Quasi-linear: a0 ~ 1Dephasing ~ depletionGood efficiency

19Point designs: 10 and 100 GeVLaser power: P[GW] = 21.5(a0r0/)2 , Critical power: Pc[GW] = 17(k/kp)2, P/Pc = (a0kpr0)2 /32.All assume: kpL0 = 2, ma0P/PcP(PW)WLt0(fs)r0(m)p(m)n0(cm-3)Ldp We(GeV)22.20.3840 J9853801.7101738 cm101.51.10.3040 J13063991.1101779 cm1010.450.2240 J170821406.010162.4 m1022.23.81.3 kJ3101702501.7101612 m1001.51.13.01.3 kJ3902003101.1101625 m10010.452.21.3 kJ5502604306.0101578 m10020Parameter design for GeV and beyondP(PW)(fs)np (cm-3)w0 (m)L(m)a0nc/npQ(nC)E(GeV)0.0203011018140.0161.7660%0.180.990.040301.51018140.0112.5340%0.250.950.100302.01018150.0093.780%0.401.060.2001001.01017450.521.7660%0.579.92.01003.01017470.185.450%1.810.22.03101.0101614016.31.7660%1.899403304.010161464.27.60%81062010001.010154505001.7660%5.7999100010006.510154608212.10%401040Note: Channel guiding: 60% and 40%; Self-guiding: 0%; external injection: 60%; self-injection: 40% and 0%P/Pc=0.7 for 60% case, and 2 for 40% case W. Lu et al., Phys Rev STAB (2007)21Beam loading simulations predicts 300-500 pC for 10 GeV stages

Quasi-linear beam loadingmatches linear theory

density & kpL:kpr = 0.3 11.8kpL =2, a0=1 n0 = 1018 cm-3+*kpL =2, a0=1 n0 = 1019 cm-3+*+*+*kpL =1, a0=1.4n0 = 1019 cm-3++ 2D* 3D-- theory

VORPAL PIC simulations

500 pC at 1017 cm-3 for kpL=2, kpsr~ 210% of laser energy to electrons

Bunch length & profile alters field inside bunchflatten field across bunch reduces DEfocusing must be matched for emittance

Ongoing: precise control w/shaped bunches

~constant field inside bunch* Cormier-Michel et al, Proc. AAC 2008, **Katsouleas PRA 1986Beam loading theoretical limite-bunch wake = laser wakeLinear theory , kp sz < 1, kp sr ~ 1Nb ~ 9x9 (n0 16 cm-3)-1/2 (Ez/E0)Ex.: Nb = 3x109 (0.5 nC) for n0 17 cm-3 and Ez/E0=1

Figures are 66% loaded

black: r = 0.085e-6 (kpr = 0.05)3D equivalent charge = 3d charge/14red: r = 0.085e-6 at n0 = 1018 cm-3green: r = 0.085e-6 with kpLlaser=1magenta: r = 1.68e-6 (kpr = 1)3D equivalent charge = 3d charge/1.6blue: r = 3.0e-6 (kpr = 1.8)3D equivalent charge = 3d charge/1.2

(r=0.085 m)3d eq charge 0.5pC

Linear theorySymmetric bunchesEnergy spread ~ N/Nmax Efficiency ~ N/Nmax (2 - N/Nmax)Ex: Spread100%, Effic100% as NNmaxTriangle bunches (high density in front)Load wake with constant Ez inside bunchCan minimize energy spread with high efficiency (at reduced Ez)Requires density tapering to phase lock bunches

Beam loading: tailored bunches for high efficiencyT. Katsouleas et al., Part. Accel. 22, 81 (1987)

Blowout regime:M. Tzoufras, et al., PRL (2008)23Adjusting length flattens field for minimum energy spreadGaussian bunch Length adjusts wake loading within bunchBunch & laser wakefield nearly balanced even for symmetric bunchesFlattens field across bunch reduces DE

Shaped bunch can further reduce DE

Beam loading versusbunch lengthno chargeL = 0.085 mL = 0.85 mL = 0.51 mkpr = 0.3 scaled charge 60pC

matched emittance, kp sigma_r=0.3 (sigmar=0.5e-6) 0.1mm mrad --> 60pC (~50% beam loaded)

521 sigma r=0.5umkp sigma_r = 0.33d eq charge 6pcscaled charge at 10^17 60 pC

(r=0.085 m)3d eq charge 0.5pC

24Axial density taper locks bunch phase:improves gain and reduces DE for e+,e-Compensate dephasing by changing lp ~ n1/2

Linear taper at kpL=2 produces 4x gain

Positron acceleration ~symmetric

Ongoing:optimize taper, emittance matchinginitial kpL=1 results : 50% depletion, 10 GeV gain for 300 pC, 2.5%FWHM

Spectra at dephasing

gain in stages with kpL=2 at 1019 cm-3 50% beam loaded -kp r = 1, kp L = 0.53D charge: 22.5pC 225pC, 9 GeV gain, 4% FWHM, at 1017 cm-3

Taper

no taper0 Gain [GeV/c at 1019/cc] 0.120 Scale Gain [GeV/c at 1017/cc] 120 #/GeV/c [A.U.] 1

__e---e+25Linear taper at kpL=260% Dne over dephasing4x gain, 30% depletion, few % DEPositron acceleration ~symmetric80% of e- gain mildly nonlinear

matched emittance 1.25 mm mrad (kp sigma_r=1) Using kpsr~1: approximately 240pC at 1017, 10% DE/E

taper electrons:density from 1019cm-3 to 1.66 x 1019 cm-3 in 0.5mmdephasing without taper ~ 0.5mm , with taper ~ 0.7mm

463 30% initial charge in peak, 94 MeV 0.06% energy spread 1mm propagation laser 30% depleted72% in 1% rms (+-2.8)

443 no taper: 45% charge in peak 27 MeV 0.2% energy spread 63% in 1% rms (+- 0.9)

UPDATEchoose one. same run, 2 different time steps

Matched electron beam spot size is smallMatched beam spot size linear regimebubble regime matched beam < 1 mm (> kp a0=0.1a0=0.1a1=0.1 a1=0.5a028Transverse field tailoring in the quasi linear regimeWakefield driven by higher order modes in the quasi linear regime a0=1Transverse field flattened by flat top laser profileMode propagation to depletionshort pulse kpL = 1 minimizes pulse variationsshallower plasma channel compensates for self-focusing200X(m)225Y(m)30X(m)-30Y(m)30200X(m)240-30Y(m)30X(m)-0.30.3-0.030.03-30200225200225@ y = -1 mm(y/w0 ~ 0.1)___ Ex/E0---- Ey/E0 higher order mode.. Ey/E0 gaussian1935X(m)1965Y(m)30X(m)-30Y(m)301935X(m)1980-30Y(m)30-3019351965

-30Y(m)30X(mm)04integrated laser intensity profile

laser envelope

Ey

Ex

high order mode reduces Ey,

laser envelope

Ex

Ey# 1106_spot varies by ~4%~ 10% depleted at 2mm / 25% depleted at 4mm

scale laser 1scale ey -0.093 0.093 (20 GV/m @ 5.10^18)scale ex @200 microns 0.28 (60GV/m) @2mm 0.55 (120 GV/m)

29Design considerations for a laser-plasma collider moduleDiffraction, Dephasing, Depletion: necessitates stagingConceptual design of laser-plasma collider at 1 TeVQuasi-linear wake (a0 ~ 1), electrons and positrons10 GeV modules: Laser pulse 40 J, 130 fs, 10 kHzRequires development of 100s kW average power (10 kHz) lasersRequires research on LWFA physics and staging technologyDemonstrate low emittance, high charge, short e-bunchesPlasma and laser tailoring to improve performanceLongitudinal density tapering to eliminate dephasingHigher-order laser modes to control transverse fieldsBELLA will give us the capabilities to study 10 GeV stages

SummaryAdditional informationLinac length will be determined by staging technologyLstageLPALaserLaccLc

Conventional optics (~10 m)Plasma mirror (~10 cm)

Number of stages:Proper choice of plasma density and staging minimizes main linac length0.5 TeV - Collider Example

Plasma density scalings:Stage density scalings:

Collider density scalings (for fixed luminosity):

33ne (1/cm^3)2.0e18a01lambda_p(um)24kp*L_laser2tau (fs)25w0 (m)20kp*w05.3P(TW)14P/Pc0.940 J 10 GeV~300pC10 GeV gain with efficient loading accessible on BELLAne (1/cm^3)1.0E+17a01.4lambda_p(um)108kp*L_laser1tau (fs)57w0 (m)90kp*w05.3P(TW)563P/Pc1.80.5 J 0.4 GeV~50pC

300 pC 10 GeV stage with taper@kpL=1

Demonstrated control by shaping laser, plasma, ebunchInitial efforts reduced DE10%2.5%shaped bunches & taper in progressmatching bunch emittance, shape to structure

30% depletion#run 528 (black)kpLlaser=2kp sigma_r=1kp sigma_L=0.506Initial charge 15pC equivalent 3D charge --> x 1.5 for kp sigma_r = 1 ~ 23 pC --> 230pC equivalent 10^17~45% beam loadedtaper is the same as other runs ( \propto 1320*x)~ 0.7 mm propagation distance45% of charge in peak94MeV 1.8% energy spread RMS (when taking +- 3 sigma of gaussian that fits the peak) emittance of particles in peak 0.74 mm mrad (not sure how seriously to take this number ...)#run 536 (magenta)kpLlaser=1kp sigma_r=1kp sigma_L=0.7Initial charge 32pC equivalent 3D charge --> x 1.5 for kp sigma_r = 1 ~ 50 pC --> 500pC equivalent 10^1760% beam loadedtaper is the same as other runs~ 0.6 mm propagation distance45% charge in peak76 MeV, 2.8% energy spread rmsnormalized emittance calculated only with particles in peak: 0.75 mm mrad (0.1 MeV PX and PY spread initially)34Laser mode controls transverse field, controls bunch emittance matchingEy @ 5.1018scale 20GV/m1070X(m)1095-30Y(m)30Ex@ 5.1018scale 60GV/m1070X(m)1095-30Y(m)30Laser EnvelopeScale 11070X(m)1110-30Y(m)30

* Cormier-Michel et al, in prep.

Emittance matched bunch radius