1 / 40

Physics of a 10 GeV laser-plasma accelerator stage

Physics of a 10 GeV laser-plasma accelerator stage. Eric Esarey. C. Schroeder, C. Geddes, E. Cormier-Michel, W. Leemans LOASIS Program Lawrence Berkeley National Laboratory. http://loasis.lbl.gov/. HBEB Workshop, Nov 16 -19, 2009. Outline. Regimes of laser-plasma accelerators

neil
Download Presentation

Physics of a 10 GeV laser-plasma accelerator stage

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Physics of a 10 GeV laser-plasma accelerator stage Eric Esarey C. Schroeder, C. Geddes, E. Cormier-Michel, W. Leemans LOASIS Program Lawrence Berkeley National Laboratory http://loasis.lbl.gov/ HBEB Workshop, Nov 16 -19, 2009

  2. Outline • Regimes of laser-plasma accelerators • Quasi-linear and highly nonlinear (blowout) • Limits to single-stage energy gain in a LPA • Diffraction, dephasing, depletion • Scaling laws for single-stage energy gain • Analytic theory and fluid simulations • Conceptual design of a laser-plasma collider at 1 TeV • Based on 10 GeV stages • Requires tens of J laser pulses at tens of kHz • Plasma and laser tailoring to improve performance • Longitudinal density tapering to eliminate dephasing • Higher-order laser modes to control transverse fields Ref: Esarey, Schroeder,Leemans, Reviews of Modern Physics (2009)

  3. B.A. Shadwick et al., IEEE PS. 2002 Laser Wakefield Accelerator (LWFA) Standard regime (LWFA): pulse duration matches plasma period Ultrahigh axial electric fields => Compact electron accelerators Plasma 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)

  4. Conceptual LPA Collider • 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 (10’s kHz) • Requires development of high average power lasers (100’s kW) Leemans & Esarey, Physics Today, March 2009

  5. Basic design of a laser-plasma accelerator: single-stage limited by laser energy • Laser pulse length determined by plasma density • kpsz ≤ 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)-1/2n1/2 ~ 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)

  6. Linear & blowout regimes: e+/e- acceleration • Blowout regime • high field • very asymmetric • focuses e- • defocuses e+ • self-trapping • Quasilinear • linear: symmetric e+/e- • high a0 desired for gradient • too high enters bubble • a0 ~1-2 good compromise • dark current free a0=1 a0=4 Axial field e- accel e+ accel e- accel e+ accel run 405 Plasma density e+ focus Transverse field e- focus e+ focus e- focus

  7. 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)

  8. 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

  9. 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 laser e- beam Ez density Katsouleas, PRA (1986); Sprangle et al, PRE (2001)

  10. Alternative tapering options:Step density transition (2) (1) (3) (1) (2) • Maintains near-resonance of plasma response with laser • Experimental realization: staged accelerator sections (3) C. Schroeder et al.

  11. DW = Ez . L Limits to acceleration length: depletion • Depletion: laser loses energy to wake • Energy balance: EL2sz = Ez2 Ldeplete • Linear limit a02 << 1: Ldeplete = a0-2 Ldephase >> Ldephase • Nonlinear limit a02 >> 1: Ldeplete ~ Ldephase laser laser Ez Ez Solution: staging

  12. Rate of laser energy deposition • Developed theory of nonlinear short-pulse laser evolution. • Derived general energy evolution equation valid for any laser intensity and pulse shape • Scale 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): characteristic accelerating field: Shadwick, Schroeder, Esarey, Physics of Plasmas (2009)

  13. 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 interest

  14. Pump depletion length independent of intensity for ultra-intense pulses Pump depletion length: Pump depletion length for near-resonant Gaussian laser pulse: • Characteristic length scale independent of intensity for relativistically-intense laser pulses

  15. laser 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: + channel …

  16. Scaling laws: analytic theory

  17. Laser pulse evolution ωpt=500 plasma density Laser field Laser energy evolution: accelerating field ωpt=1500 ωpt=2500 ωpt=3500 • Laser evolution interplay between laser intensity steepening, laser frequency red-shifting, energy depletion Shadwick, Schroeder, Esarey, Physics of Plasmas (2009)

  18. Longitudinal e-bunch dynamics: energy spread minimum near dephasing Fluid plasma + e-bunch described by moments (includes beam loading) Laser Wake Momentum e-bunch Energy spread Position, kp(z-ct) Energy spread Initial: / = 0.3% at = 100 Final: / = 0.01% at = 3000 Time, pt B.A. Shadwick et al.

  19. Scaling laws from fluid code: dephasing/depletion lengths & energy gain Fraction of laser energy at dephasing length • Quasi-linear: a0 ~ 1 • Dephasing ~ depletion • Good efficiency Independent of k/kp • Fix 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)2

  20. Point designs: 10 and 100 GeV • 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

  21. Parameter design for GeV and beyond W. Lu et al., Phys Rev STAB (2007) Note: 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

  22. Beam loading simulations predicts 300-500 pC for 10 GeV stages • Beam loading theoretical limit • e-bunch wake = laser wake • Linear theory , kpsz < 1, kpsr ~ 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 controlw/shaped bunches * Cormier-Michel et al, Proc. AAC 2008, **Katsouleas PRA 1986

  23. Beam loading: tailored bunches for high efficiency • Linear theory • Symmetric bunches • Energy spread ~ N/Nmax • Efficiency ~ N/Nmax (2 - N/Nmax) • Ex: Spread100%, Effic100% as NNmax • Triangle bunches (high density in front) • Load wake with constant Ez inside bunch • Can minimize energy spread with high efficiency (at reduced Ez) • Requires density tapering to phase lock bunches T. Katsouleas et al., Part. Accel. 22, 81 (1987) Blowout regime: M. Tzoufras, et al., PRL (2008)

  24. Adjusting length flattens field for minimum energy spread Beam loading versus bunch length • Gaussian bunch • Length adjusts wake loading within bunch • Bunch & laser wakefield nearly balanced even for symmetric bunches • Flattens field across bunch – reduces DE • Shaped bunch can further reduce DE no charge L = 0.085 m L = 0.85 m L = 0.51 m kpr = 0.3 scaled charge 60pC

  25. Axial 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 matching initial kpL=1 results : 50% depletion, 10 GeV gain for 300 pC, 2.5%FWHM Spectra at dephasing __e- --e+ no taper Taper 0 #/GeV/c [A.U.] 1 0 Gain [GeV/c at 1019/cc] 0.12 0 Scale Gain [GeV/c at 1017/cc] 12 • gain in stages with kpL=2 at 1019 cm-3 • 50% beam loaded -kpr = 1, kpL = 0.5 • 3D charge: 22.5pC • 225pC, 9 GeV gain, 4% FWHM, at 1017 cm-3

  26. Matched electron beam spot size is small • Matched beam spot size • linear regime • bubble regime • matched beam < 1 mm (<< lp ~ 100 mm) for g = 20,000 (10 GeV), n0 = 1017 cm-3, en = 1 mm mrad • Limits electron beam charge and quality • Increase sy for higher charge, with nbpeak small • In linear regime kb2 ∝ E⊥∝ ∇⊥a2 •  Reduce transverse field gradient to increase matched beam radius

  27. Higher order laser mode to tailor transverse wakefield • Linear regime : E⊥/E0 ~ ∇⊥a2/2 • Add first order Hermite-Gaussian mode in 2D a2 = a02 HG02 + a12 HG12 a2 a1/a0 HG0 HG1 0.7 0.5 0.4 0 y/r0 gaussian y/r0 Ey/E0 first order hermite-gaussian mode exact solutions of the paraxial wave equation analytic calculation (low a) no channel y/r0

  28. Higher order mode propagation in plasma channel Low intensity propagation in matched plasma channel integrated transverse intensity profile • Hermite-Gaussian modes exact solution of the linear paraxial wave eq • Guiding in plasma channel is the same for all modes • Dn = Dnc = 1/prer02 • Phase / group velocity different for each mode • Intensity modulation when modes co-propagate HG02 (HG0 + HG1)2 kpy (HG02 + HG12) HG12 kpy a0=0.1 a0=0.1 a1=0.1 a1=0.5a0 • Solution • Use cross-polarization • Use different frequencies kbeat= m/ZR kbeat>> kp

  29. Transverse field tailoring in the quasi linear regime • Wakefield driven by higher order modes in the quasi linear regime a0=1 • Transverse field flattened by flat top laser profile • Mode propagation to depletion • short pulse kpL = 1 minimizes pulse variations • shallower plasma channel compensates for self-focusing 30 30 30 laser envelope Ey Ex 0.3 0.03 high order mode reduces Ey, @ y = -1 mm (y/w0 ~ 0.1) ___ Ex/E0 ---- Ey/E0 higher order mode ….. Ey/E0 gaussian Y(µm) Y(µm) Y(µm) -30 -30 -30 -0.03 -0.3 X(µm) X(µm) X(µm) 200 240 200 X(µm) 200 225 200 225 225 30 30 30 30 Ey Ex laser envelope integrated laser intensity profile Y(µm) Y(µm) Y(µm) Y(µm) -30 -30 -30 -30 X(µm) X(µm) X(µm) 1935 1980 0 X(mm) 1935 1965 1935 1965 4

  30. Summary • Design considerations for a laser-plasma collider module • Diffraction, Dephasing, Depletion: necessitates staging • Conceptual design of laser-plasma collider at 1 TeV • Quasi-linear wake (a0 ~ 1), electrons and positrons • 10 GeV modules: Laser pulse 40 J, 130 fs, 10 kHz • Requires development of 100’s kW average power (10 kHz) lasers • Requires research on LWFA physics and staging technology • Demonstrate low emittance, high charge, short e-bunches • Plasma and laser tailoring to improve performance • Longitudinal density tapering to eliminate dephasing • Higher-order laser modes to control transverse fields • BELLA will give us the capabilities to study 10 GeV stages

  31. Additional information

  32. Proper choice of plasma density and staging minimizes main linac length • Linac length will be determined by staging technology • Number of stages: Laser LPA Lc Lacc Lstage • Conventional optics (~10 m) • Plasma mirror (~10 cm)

  33. 0.5 TeV γ-γ Collider Example Plasma density scalings: Stage density scalings: Collider density scalings (for fixed luminosity):

  34. 10 GeV gain with efficient loading accessible on BELLA 40 J 10 GeV ~300pC 0.5 J 0.4 GeV ~50pC • 300 pC 10 GeV stage with taper@kpL=1 • Demonstrated control by shaping laser, plasma, ebunch • Initial efforts reduced DE10%2.5% • shaped bunches & taper in progress • matching bunch emittance, shape to structure

  35. Emittance matched bunch radius << lp for Gaussian-laser linear, nonlinear regimes • can reduce loading efficiency and/or cause ion motion • Linear regime: Fields shaped via laser mode to compensate emittance* • demonstrated propagation, channel compensation Laser mode controls transverse field, controls bunch emittance matching Laser Envelope Scale 1 Propagation to depletion Ex@ 5.1018 scale 60GV/m Ey @ 5.1018 scale 20GV/m 30 30 30 10 Y(µm) Y(µm) Y(µm) --kpx --10 -30 -30 -30 1110 1070 0 ct(ZR) 5 1070 1095 1070 1095 X(µm) X(µm) X(µm) • Ongoing: compensation of beam loaded fields * Cormier-Michel et al, in prep.

  36. 2D PIC simulations demonstrate a factor 3 in matched electron beam radius • With higher order mode and delay beam radius can be increased x3  charge x9 • Beam radius limited by linear region of focusing field • Can increase flat top region by using higher order modes 0.3 • simulation at n0 = 5x1018 cm-3 • matched emittance 0.014 mm mrad varies < 1% • scaled parameters at 1017 cm-3 • sy = 2 mm • en = 0.1 mm mrad 0.2 sy (mm) 0.1 0.0 2 3 0 1 ct (mm) —·— gaussian + hermite gaussian with delay —— gaussian + hermite gaussian ______gaussian pulse …….. gaussian pulse (unmatched)

  37. Energy depletion: Analytic result in good agreement with numerical solution Analytic result (- - - - - -) :

  38. Fluid simulations: verify and quantify scaling laws Axial wakefield GeV-class example: • 1D fluid code (B.A. Shadwick) • Standard LWFA regime • a0 = 1.5, k0/kp = 40, kp L =2 • Laser: 0.8 mm, 5x1018 W/cm2, 30 fs • Plasma: 1018 cm-3, 3 cm Energy gain Laser pulse 1 GeV =z-ct E. Esarey et al., AAC Proc 2004

  39. Fluid simulation of scaled BELLA point design n monemtum Ez energy spread bunch distance • Scaled point design example: 1D fluid code (B.A. Shadwick) • Quasi-linear LWFA regime • a0 = 1.0, k0/kp = 40, kp L =2 • Laser: 0.8 mm, 2x1018 W/cm2, 40 fs • Plasma: 1018 cm-3, • Bunch: kpsz = 0.5, Dg/g = 0.9% (initial), 0.05% (final@ 0.5 GeV)

  40. Reducing energy spread and emittance requires controlled injection Transverse motion • Self-injection experiments have been in bubble regime: • Cannot tune injection and acceleration separately • Emittance degraded due to off-axis injection and high transverse fields. • Energy spread degraded due to lack of control over trapping 5 Y[µm] -5 800 X[µm] 2000 ⇒ Use injector based on controlled trapping at lower wake amplitude and separately tunable acceleration stage to reduce emittance and energy spread

More Related