Laser-Plasma Accelerators: Scaling Laws for Collider Applications Eric Esarey C. Schroeder, C. Benedetti, C. Geddes, W. Leemans BELLA Center LBNL FACET II Science Opportunities Workshop SLAC, 14 Oct 2015 Supported by the U.S. DOE under Contract No. DE-AC02-05CH11231 Office of Science

Laser-Plasma Accelerator Outline LPA Basics Scaling Laws Zeroth-order picture of LPA collider assuming idealized physics Real-world physics that further complicate LPA collider (Schroeder) Other possible LPA collider approaches Status and Required R&D for LPA collider (Leemans) Laser-Plasma Accelerator

Conceptual LPA Collider Based on 10 GeV modules Quasi-linear wake: e- and e+ Driven by 30 J, 60 fs pulses 80 cm plasma channels (1017 cm-3) Staging & coupling modules Requires high rep-rate (10’s kHz) Requires development of high average power lasers (100’s kW) Leemans & Esarey, Physics Today (2009); Esarey et al, Rev. Mod. Phys. (2009)

Laser-plasma accelerators (LPAs) Tajima & Dawson, Phys. Rev. Lett. (1979); Esarey, Schroeder, Leemans, Rev. Mod. Phys. (2009) Plasma wave: electron density perturbation Laser ponderomotive force (radiation pressure) λp = 2πc/ωp ~ np-1/2 ~ 30 μm short pulse, ultra-intense laser: I~1018 W/cm2 Laser pulse duration ~ λp/c ~ tens fs electron plasma density perturbation

Laser-plasma accelerators: >10 GV/m accelerating gradient plasma wave (wakefield) E ~100 GV/m (for n~1018 cm-3) >103 larger than conventional RF accelerators ⇒ “>km to <m” Accelerating bucket ~ plasma wavelength  ultrashort (fs) bunches (<λp /4) plasma density laser bunch beam charge (set by beam loading): ~100 pC (for n~1018 cm-3) beam duration (set by trapping physics): <10 fs  high peak current

*Shadwick, Schroeder, Esarey, Phys. Plasmas (2009) Basic design of a laser-plasma accelerator: single-stage limited by laser energy Laser pulse length determined by plasma density kp sz ≤ 1, sz ~ lp ~ n-1/2 Wakefield regime determined by laser intensity Linear (a0<1) or blowout (a0>1) Determines bunch parameters via beam loading Ex: a0 = 1 for I0 = 2x1018 W/cm2 and 0 = 0.8 m Accelerating field determined by density and laser intensity Ez ~ (a02/4)(1+a02/2)-1/2 n1/2 ~ 10 GV/m Energy gain determined by laser energy via depletion* Laser: Present CPA technology 10’s J/pulse laser Ez wake *Shadwick, Schroeder, Esarey, Phys. Plasmas (2009)

Wake structure depends on laser intensity Blowout regime a0 >> 1 very asymmetric focuses e- defocuses e+ self-trapping self-guiding Quasi-linear a0 ~ 1 symmetric e+/e- dark current free channel required tailor focusing forces via laser profile a0=4 a0=1 e+ note - 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 slide axial axial radial radial

Limits to acceleration length: diffraction DW = Ez . L Limits to acceleration length: diffraction “3D”: Diffraction, Dephasing, Depletion Diffraction of laser pulse ZR = p r02/l0 ~ 2 cm, ZR<< Ldephase < Ldeplete Solution: Density channels Parabolic channel guides gaussian modes Channel depth: Dn [cm-3] = 1020 / (r0[mm])2 ~ 2x1016 cm-3 W.P. Leemans et al, IEEE Trans. Plasmas Sci. (1996); Esarey et al., Phys. Fluids (1993)

Limits to Acceleration Length: dephasing DW = Ez . L Limits to Acceleration Length: dephasing Dephasing: e- outrun wake, Phase velocity: vp/c ≈ vg/c = 1- l02/2lp2 Ldephase (1-vg/c) = lp/2, Ldephase = lp3/l02 ~ n-3/2 ~ 1.6 m Solution: density tapering vp<c e- beam Ez laser vp<c e- beam Ez laser

Density Tapering: Phase Lock e- For a0 ~ 1, Ldephase may be < Ldeplete Phase velocity depends on density Phase position ~ lp ~ n-1/2 Taper density to tune wake velocity Depletion then limits e- energy gain n1 laser e- beam Ez n2>n1 e- beam laser Ez density Katsouleas, PRA (1986); Rittershofer et al, PP (2010)

Limits to acceleration length: depletion DW = Ez . L Limits to acceleration length: depletion Depletion: laser loses energy to wake Energy balance: EL2 sz = Ez2 Ldeplete Linear limit a02 << 1: Ldeplete = a0-2 Ldephase >> Ldephase Nonlinear limit a02 >> 1: Ldeplete ~ Ldephase laser laser Ez Ez Solution: staging

Depletion: necessitates multiple stages Single stage energy gain limited by laser energy depletion Diffraction limitation: mitigated by transverse plasma density tailoring Dephasing limitation: mitigated by longitudinal plasma density tailoring Depletion Length: Accelerating field: Energy gain (linear regime): Ex: Wstage = 10 GeV for I = 1018 W/cm2 and n = 1017 cm-3 Multiple-stages for controlled acceleration to high energy: laser

LPA Experiments (single stage) LPA plasma density scalings - staging required Laser-plasma interaction (depletion) length: Accelerating gradient: Energy gain: For high-energy applications, laser depletion (and reasonable gradient) necessitates staging Scalings verified with simulations LPA Examples (single stage): LPA Experiments (single stage) LBNL 2014 Texas 2013 LBNL 2006 e-beam energy gain (MeV) LLNL 2010 RAL 2009 MPQ 2010 U.Mich 2008 LOA 2006 APRI 2008 LOA 2004 LBNL 2004 RAL 2004 W ~ 10 GeV n ~ 1017 cm-3 Lacc ~ 1 m Ulaser ~ 40 J Plaser ~ 1 PW (BELLA Laser) W ~ 1 GeV n ~ 1018 cm-3 Lacc ~ 3 cm Ulaser ~ 1 J Plaser ~ 100 TW plasma density, np (cm-3)

LPA single-stage plasma density scalings E0 (GV/m) L (m) Single-stage length Accelerating gradient n (cm-3) n (cm-3) Single-stage energy gain Coefficients determined from simulations of resonant laser with a=1.5 W (GeV) n (cm-3)

Single-stage plasma density scalings verified with PIC simulations Vay, Geddes, et al., Phys. Plasmas (2011) Single-stage PIC simulations (using WARP code with boosted-frame technique) verifying plasma density scaling

Beam loading limits bunch charge: 300-500 pC for 10 GeV stages Beam loading theoretical limit e-bunch wake = laser wake Linear theory , kp sz < 1, kp sr ~ 1 Nb ~ 9x9 (n0 16 cm-3)-1/2 (Ez/E0) Nb ~ n0 -1/2 Ex.: Nb = 3x109 (0.5 nC) for n0 17 cm-3 and Ez/E0=1 plasma wake Figures are 66% loaded black: r = 0.085e-6 (kpr = 0.05) 3D equivalent charge = 3d charge/14 red: r = 0.085e-6 at n0 = 1018 cm-3 green: r = 0.085e-6 with kpLlaser=1 magenta: r = 1.68e-6 (kpr = 1) 3D equivalent charge = 3d charge/1.6 blue: r = 3.0e-6 (kpr = 1.8) 3D equivalent charge = 3d charge/1.2 (r=0.085 m) 3d eq charge 0.5pC bunch laser VORPAL PIC simulations 500 pC at 1017 cm-3 for kpL=2, kpsr~ 2 10% of laser energy to electrons * Cormier-Michel et al, Proc. AAC 2008, **Katsouleas PRA 1986

Collider Requirements: Luminosity Rate of events: (luminosity) x (collision cross-section) Luminosity: cross-section  For fixed beam power, Pb=2f Nb(γmc2), transverse beam density must be increased Limitations: Achievable beam emittance Final focus optics to IP: adiabatic plasma lens Beam-beam interaction (beamstrahlung) Emittance growth in main linacs (beam scattering in plasma)

Collider scalings (for fixed luminosity): 1 TeV Collider Parameters: Plasma density and laser wavelength scalings Collider scalings (for fixed luminosity): Schroeder et al., Phys. Rev. ST AB (2010)

Collider scalings (for fixed luminosity): 1 TeV Collider Parameters: Plasma density and laser wavelength scalings Requires laser development 15 kHz 480 kW average power Collider scalings (for fixed luminosity): Schroeder et al., Phys. Rev. ST AB (2010)

Collider scalings (for fixed luminosity): 1 TeV Collider Parameters: Plasma density and laser wavelength scalings Present technology 32 J, 56 fs a0 = 1.5 Collider scalings (for fixed luminosity): Schroeder et al., Phys. Rev. ST AB (2010)

Collider scalings (for fixed luminosity): 1 TeV Collider Parameters: Plasma density and laser wavelength scalings Present technology 32 J, 56 fs a0 = 1.5 Collider scalings (for fixed luminosity): BELLA PW laser @ LBNL Explore physics of 10 GeV stage Schroeder et al., Phys. Rev. ST AB (2010)

Beamstrahlung-limited regime: modifies LPA collider scalings at low density Constraint of fixed beamstrahlung: fixed nγ (photons per electron) Collider wall-plug power beamstrahlung-limited regime beam-loading limited regime accelerating field: linac length: Ecm = 1 TeV L = 2x1034 s-2 cm-2 η = 6% σ2 = 100 nm2 laser energy/stage: multi-bunch operation Schroeder et al., PR ST-AB (2012)

LPA collider requires laser technology with high efficiency (~30%) fL [Hz] Laser average power requirements UL [J] Different operational plasma densities require different laser parameters (laser technologies) with varying efficiency n [cm-3] Laser duration (bandwidth) requirements TL [fs] n [cm-3]

Collider density scalings: total power required assuming fiber laser efficiency Laser to plasma wave efficiency: ~50% Plasma wave to beam efficiency: ~40% Independent of plasma density For fixed luminosity (e.g., 2x1034 s-1 cm-2 for Ecm = 1 TeV) and IP size, based on fiber laser technology J. Dawson: “30% at 50kHz”; ”10% at 2kHz”; “falls rapidly to 0% below kHz” wall-plug power P (MW) n (cm-3)

“International Coherent Amplification Network” Coherent laser combining: new laser technology provides a path for high average power Coherent combination of diode-pumped fiber lasers: path to high-peak power, high- average power, high-efficiency lasers: Fiber lasers: sub-ps pulses, ~mJ energy, ~10 kHz, ~10% wall-plug efficiency Coherent combination of fiber lasers is proposed to achieve high peak power (energy) Challenge: Requires combining (control of all laser phases, group velocity delays, dispersion) ~104 fiber lasers ICAN = “International Coherent Amplification Network” G. Mourou et al., Nature Photonics (2013)

Incoherent summation easier than coherent (requires no phase control) Wakefield excitation by incoherently combined lasers: path to high-average power Wakefield driven by time-integrated gradient of electromagnetic energy density: depends on the average properties of the radiation in the volume (~λp3) Wakefield excitation does not require coherence, only energy density Incoherent combination (of many low energy) lasers for wakefield excitation: Require only sufficient energy deposited in ~λp3 volume Benedetti et al., PoP (2014) Incoherent summation easier than coherent (requires no phase control)

Laser-plasma accelerator (LPA) based collider: challenges and solutions Laser diffraction guiding in plasma channel dephasing / depletion LPA staging positron focusing + acceleration quasi-linear regime / control focusing ion motion scattering in plasma near-hollow plasma channels high-beam quality shaped witness bunches beamstrahlung ultra-short beams / beam trains efficiency laser energy recovery laser average power laser beam combining

Future R&D to address challenges for laser-plasma-based HEP applications Plasma-based acceleration techniques: tremendous progress over the last decade Beam quality preservation: emittance and energy spread Plasma source devlopment Plasma channels: mitigate scattering; independent control of focusing/acceleration Plasma longitudinal shape: mitigate dephasing, control instabilities Particle beam injection techiniques Colliding laser pulses, ionization injection, down-ramp injection Shaped beam currents enables high efficiency without induced energy spread Charge limits imposed by beam loading, ion motion, instabilities, beamstrahlung, etc. Staging: coupling of drive (laser/particle) and witness beams: Compact transport with emittance preservation Compact coupling to perserve high average gradient, e.g., plasma mirrors LPA-based collider requires laser technology R&D (high average power, high efficiency) Fiber-based lasers; incoherent laser drivers Laser energy recovery Lasers and plasmas for other collider systems: Rapid methods for cooling electron/positron beams (replace damping rings?) Novel final focus concepts Size of plasma-based collider dominated by final focus/beam delivery (few km at TeV) Plasma lens (adiabatic) to overcome Oide limit As LPA R&D advances, collider concept and design will continue to evolve Realization of “low energy” applications are critical to validate and develop laser-plasma accelerator technology: many applications to most areas of Office of Science

Additional Information: Report for HEPAP Subcommittee R&D and facility investment needs towards a laser-plasma accelerator driven linear collider   Input for the HEPAP subcommittee on Accelerator R&D W. Leemans, E. Esarey, C. Schroeder, C. Geddes Lawrence Berkeley National Laboratory December 1, 2014 Introduction This document is in response to the request from the HEPAP subcommittee on accelerator R&D for the DOE-HEP office to provide input to the following questions in an email from Prof. James Rosenzweig, dated November 17th, 2014. For a 1 TeV collider with a luminosity of 10^34 and a 3 TeV collider with a luminosity of 10^35        1. What are the milestones to get there?        2. What R&D resources will be needed and when?        3. How does the roadmap depend on funding level and in particular how do the R&D costs change over the next five to ten years?  Please consider a constrained funding scenario with low levels as well as an “unconstrained” funding scenario that would allow technically limited progress.

Extras

Point designs: 10 and 100 GeV a0 P/Pc P(PW) WL t0(fs) r0(m) p(m) n0(cm-3) Ldp We (GeV) 2 2.2 0.38 40 J 98 53 80 1.71017 38 cm 10 1.5 1.1 0.30 130 63 99 1.11017 79 cm 1 0.45 0.22 170 82 140 6.01016 2.4 m 3.8 1.3 kJ 310 250 1.71016 12 m 100 3.0 390 200 1.11016 25 m 550 260 430 6.01015 78 m Laser power: P[GW] = 21.5(a0r0/)2 , Critical power: Pc[GW] = 17(k/kp)2, P/Pc = (a0kpr0)2 /32. All assume: kpL0 = 2, m

Beam loading simulations predicts 300-500 pC for 10 GeV stages Beam loading theoretical limit e-bunch wake = laser wake Linear theory , kp sz < 1, kp sr ~ 1 Nb ~ 9x9 (n0 16 cm-3)-1/2 (Ez/E0) Ex.: Nb = 3x109 (0.5 nC) for n0 17 cm-3 and Ez/E0=1 ~constant field inside bunch Quasi-linear beam loading matches linear theory + 2D * 3D -- theory VORPAL PIC simulations 500 pC at 1017 cm-3 for kpL=2, kpsr~ 2 10% of laser energy to electrons Bunch length & profile alters field inside bunch flatten field across bunch – reduces DE focusing must be matched for emittance Ongoing: precise control w/shaped bunches Figures are 66% loaded black: r = 0.085e-6 (kpr = 0.05) 3D equivalent charge = 3d charge/14 red: r = 0.085e-6 at n0 = 1018 cm-3 green: r = 0.085e-6 with kpLlaser=1 magenta: r = 1.68e-6 (kpr = 1) 3D equivalent charge = 3d charge/1.6 blue: r = 3.0e-6 (kpr = 1.8) 3D equivalent charge = 3d charge/1.2 (r=0.085 m) 3d eq charge 0.5pC density & kpL: kpr = 0.3 1 1.8 kpL =2, a0=1 n0 = 1018 cm-3 +* n0 = 1019 cm-3 kpL =1, a0=1.4 + * Cormier-Michel et al, Proc. AAC 2008, **Katsouleas PRA 1986

Transverse beam stability in hollow plasma channels Transverse wake fields can lead to beam break-up instabilities (growth or transverse displacement from channel axis) Higher-order channel modes and growth rates for the single-bunch transverse instability have been calculated Assuming weak/no focusing, growth rate: Moderate focusing suppresses instability: Sufficient focusing for electron beams can be provided in near-hollow plasma channel (with channel density << wall density) Higher-order mode detuning can be applied to suppress undesirable modes C. B. Schroeder et al., Phys. Rev. Lett. (1999) C. B. Schroeder et al., Phys. Plasmas (2013)

Length of staged-LPA linac [m] Staged LPAs: average gradient determined by driver in-coupling distance Number of stages: Compact laser in-coupling distance (enables high average gradient) Conventional optics: requires many Rayleigh ranges to reduce fluence on optic (avoid damage) Plasma mirror: relies on critical density plasma production (high laser intensity): coupling <1 m Length of 1 TeV staged-LPA linac Length of staged-LPA linac [m] coupling distance: 0.5 m 1 m 5 m 10 m Plasma density [cm-3]

Summary Physics considerations for a collider based on LPA: Laser depletion - staging required (with tapered plasma channels) Operation in quasi-linear regime (a~1) Allows positron acceleration Independent control of transverse (focusing) fields Plasma density scalings - determine required laser technology Beamstrahlung at IP and total power requirements - operation at 1016 <n<1018 Total linac length and collider power requirements independent of laser wavelength Estimates for a TeV-scale laser-plasma collider: 10 GeV stages (at n=1017 cm-3): requires laser pulse (at 1 micron) ~30 J, a~1, ~100 fs, ~15 kHz, ~30% efficiency for additional details on LPA-based collider design see Schroeder et al., PR ST-AB (2010) Schroeder et al., PR ST-AB (2012)

electron plasma density Focusing determined by background ion density in nonlinear regime: e+ focusing problematic Nonlinear (bubble/blow-out) regime: accelerating/focusing wakefields determined by background plasma density: Plasma electrons expelled (positron acceleration challenging) Strong focusing of beam suppresses scattering for e-beam Strong focusing results in electron dense beams: emittance growth from ion motion e+ focus e- focus electron plasma density a=4 ion cavity blow-out, expel electrons ion motion 0.1 um emittance 100 pC charge 1017/cc density kpLb=1 (positron focusing challenging) (emittance growth) Rosenzweig et al., PRL (2005) beam-driver, Rosenzweig et al., PRA (1991) laser-driver, Pukhov&Meyer-ter-Vehn, APB (2002)

Quasi-linear regime: e+ focusing and independent control of acceleration/focusing e+ accel. e- accel. Operate in “quasi-linear” regime: Quiver momentum weakly-relativistic a ~ 1 (Intensity ~ 1018 W/cm2) Region of acceleration/focusing for both electrons and positrons Stable laser propagation in plasma channel Accelerating field e- accel+focus Transverse position Plasma density e+ accel+focus e+ focus e- focus Quasi-linear regime: control of focusing force by laser driver shape (transverse intensity profile) Shape driver profile to control focusing forces: Provide weak focusing to prevent blow-out enables positron acceleration increases scattering Cormier-Michel et al., PRST-AB (2011) Focusing field Longitudinal position

Shaping the transverse profile of plasma channel: independent control of accelerating and focusing Schroeder et al., PoP (2013) plasma density radius Near-hollow plasma channels: Laser guided in channel (set by channel depth, not on-axis density) Accelerating field (set by wall density): Focusing field (set by channel density): accelerating wakefield distance behind driver kw (laser spot) =2.3 kw (rms length) = 1 a0 = 1 channel size: kw rc = 1.5 radial position matched beam: focusing wakefield PIC simulation (INF&RNO)

Near-hollow plasma channels: ultra-low emittance preservation Independent control over accelerating and focusing forces: Acceleration uniform in radial position Focusing uniform in longitudinal position (no head-to-tail variation in focusing) and linear in radial position Near-hollow plasma channel geometry provides emittance preservation: Mitigates Coulomb scattering (reduce plasma density near bunch): Control of focusing force and beam density: prevents ion motion for relevant (1 TeV) parameters: Ion motion in channel negligible if ratio of beam density to wall density less than ion-electron mass ratio: Schroeder et al., PoP (2013)

Beam loading in near-hollow plasma channels: shaped bunches eliminate energy spread Energy spread minimized using shaped beams Katsouleas et al., PA (1987) Ramped triangular current distribution : normalized field amplitude normalized distance behind driver, kw (z-ct) constant acceleration Example: Trade-off between gradient and efficiency (for no induced energy spread) fraction of peak accel. field wake to beam efficiency beam charge: lower plasma density, higher beam charge

Positron beams accelerated in linear regime in hollow plasma channel In quasi-linear regime, acceleration of positrons is symmetric to electrons normalized field amplitude normalized distance behind driver, kw (z-ct) Focusing for positrons may be provided from external magnets

Ultra-short beams can be accelerated without energy spread growth Ultra-short beams are desirable, e.g., beamstrahlung suppression in colliders. beamstrahlung photons/electron: Trapezoidal current distribution: normalized field amplitude normalized distance behind driver, kw (z-ct) Improved efficiency achieved using bunch trains

Bunch trains allows ultra-short bunches with high efficiency, gradient, and no energy spread Example: with 1 bunches: with 6 bunches: normalized field amplitude normalized distance behind driver, kw (z-ct) Improved efficiency achieved using bunch trains: Each bunch has same charge Experiences same (constant across bunch) accelerating gradient Efficiency increased by number of bunches in train Trade-off between gradient and efficiency, with no energy spread growth Transverse bunch stability requires analysis

Improved efficiency using additional laser pulses to absorb remaining plasma wave energy Drive laser depositing energy into wave (frequency red-shifting) “Energy-recovery” laser absorbing wave energy (frequency blue-shifting) Additional laser pulse allows for no energy to remain in coherent plasma oscillations after energy transferred to particle beam η(plasma to beam)= 0.75 gradient = 0.5(peak field) laser bunch laser normalized field amplitude plasma wave normalized distance behind driver, kw(z-ct)

(fraction of laser energy to plasma wave) Energy recovery: Improved efficiency (>50%) using additional laser pulses Lasers η(plasma to beam)= 0.75 η(energy recovery) = 0.9 plasma with 2nd “energy-recovery” laser beam single (pump) laser laser energy recovery Efficiency of energy transfer: laser to beam Re-use in another LPA stage Sent to photovoltaic (energy back to grid) without energy recovery total efficiency (driver to beam): beam energy gain Pump laser depletion (fraction of laser energy to plasma wave) input laser energy recovered laser energy