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Electrons Trapping in the Plasma Wakefield Accelerator

Electrons Trapping in the Plasma Wakefield Accelerator. Patric Muggli University of Southern California muggli@usc.edu Erdem Oz, Neil Kirby. Work supported by US Department of Energy. Introduction to particle trapping. Trapped particles characteristics.

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Electrons Trapping in the Plasma Wakefield Accelerator

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  1. Electrons Trapping in the Plasma Wakefield Accelerator Patric Muggli University of Southern California muggli@usc.edu Erdem Oz, Neil Kirby Work supported by US Department of Energy

  2. Introduction to particle trapping Trapped particles characteristics Trapping in the SLAC PWFA experiment Conclusions OUTLINE

  3. Ultra-high energy cosmic rays: plasma shock waves and frozen magnetic field Plasma accelerators: PARTICLE TRAPPING Supernova SN 1006. The images reveal high energy synchrotron radiation from the rims of the supernova remnant. This suggests that electrons are accelerated in the shock waves at the boundary of the remnant. http://www.tp1.ruhr-uni-bochum.de/~hs/forschung/shockaccel.html + Injection mechanism for LWFA, PWFA - Limit plasma wave amplitude: wavebreaking

  4. Laboratory Frame “Wave” Frame Laboratory Frame vf vf vf=0 No turn around v’<0 v=v+vf v’=v- vf V=gh m m v v’=0 Turn around v’>0 Turn around if: need injection mechanism e- born at rest (lab frame) Energy, and phase condition for trapping PARTICLE TRAPPING Small amplitude plasma wave: Trapped Accel. gmax Esarey, IEEE TPS 24,2 (1996) gmin Injection/trapping

  5. Non Relativistic Relativistic Dawson, Phys. Rev. 113, 2 (1959) Akhiezer, Polovin, JETP 3, 5 (1956) Cold Warm Coffey, PoF 14, 7 (1971) Katsouleas, Mori, PRL 61, 1 (1988) Plasma frequency Wave phase velocity and relativistic factor Thermal energy to wave kinetic energy ratio WAVE AMPLITUDE LIMIT WAVEBREAKING Rosenzweig, PRA 38, 7, 3634 (1988) Mori, Katsouleas, Phys. Scripta T30, 127 (1990)

  6. Akhiezer Polovin Katsouleas Mori Coffey Dawson Relativistic effects increase Emax Thermal effects decrease Emax WAVE AMPLITUDE LIMIT Katsouleas, Mori, PRL 61, 1 (1988) Mori, Katsouleas, Phys. Scripta T30, 127 (1990)

  7. Wave-particles dephasing Wave breaking Injection and trapping Harmonics of wp, sine to “sawtooth” wave WAVE BREAKING - TRAPPING Katsouleas, Nature 431,515 (2004).

  8. Gordon, PRL 80(10), 1998 … but well described by simulations! SM-LWFA: self-injection, no control, large energy spread … Wavebreaking = injection mechanism for (SM-)LWFA LWFAINJECTION MECHANISM

  9. Katsouleas, Nature 431,515 (2004). y Self-injection ∆E/E<<1 Transverse injection, Umstadter, PRL 76, 2073 (1996). Co-linear injection, Esarey, PRL 79, 2682 (1997). INJECTION LOA, this workshop Extract Inject Geddes,C.G.R.et al.Nature 431, 538 (2004). Mangles,S.P.D.et al.Nature 431, 535 (2004). Faure,J.et al.Nature 431, 541 (2004).

  10. Courtesy of M. Thompson

  11. Focusing (Er) Defocusing Decelerating (Ez) Accelerating Akhiezer, Polovin, JETP 3, 5 (1956) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + - - - - - - - - - + - - + + + + + - + + + + + - + + + + + + + - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + + + + + + + + + + + + + + + - - - - - - - + + + + + + + + - - - Relativistic electron bunch - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - gf=gb ? No trapping? PLASMAWAKEFIELD ACCELERTAOR (e-) PWFA = beam-driven plasma accelerator • Focusing + acceleration = large energy gain • Single bunch => particles at all phases => ∆E/E≈200% • Wavebreaking limit: cold-relativistic SLAC PWFA: gp=55686 (28.5 GeV) N=1.8´1010 sz=30 µm ne=2.6 ´1017 cm-3 kpsz≈√2, kpsr<<1 1.7 TV/m >> 39 GV/m

  12. Number e- (´1010) Light Counts (a.u.) Peak Decellerating Field (GV/m) Excess charge/light appear at ≈18 GV/m Excess charge of the order of incoming charge, 1.6-1.8´1010 e- Excess visible light >> excess charge Excess visible light<< (excess charge)2 EVIDENCE FOR TRAPPED PARTICLES Incoming N≈1.6´1010 e- Li I Atomic Lines <18 GV/m >18 GV/m “Coherent” Cherenkov Continuum Partially Coherent

  13. Energy Spectrum c W Mask +FCT y Li Plasma ne≈0-3x1017 cm-3 L≈10,20,30 cm x Cherenkov Cell 1 atm He e- z FCT N=1.81010 z=20-40µm E=28.5 GeV Cherenkov Radiator CTR Energy Plasma Light Dump Cherenkov/ TR Light Magnetic Spectrometer Transition radiation (TR) and Cherenkov light Magnetic spectrometer gives high energy trapped particles spectrum Cherenkov cell gives low energy trapped particles spectrum TRAPPED PARTICLES DIAGNOSTICS

  14. Plasma Light Diagnostic Heaters Wick n0=0.5-3.51017 cm-3 T=700-1050°C L=13-22-31-90 cm PHe≈1-40 T e- Be Window “PLASMA SOURCE” Cooling Jackets Boundary Layers Pressure He He Li 20 Li Vapor 10 L r/sr Plasma 0 -10 -20 -2 -1 0 1 2 z/sz •Lithium vapor in a heat-pipe oven P. Muggli et al., IEEE TPS (1999) •Field-ionization (ADK theory): - Lithium: low Z, low IP (5.4 eV) - Ultra-short bunch Er field > 6GV/m - ne=no, Li -Plasma very “reproducible”

  15. He e- born in the He-Li transition region, inside the wake ORIGIN OF TRAPPED e- Measured Li Density Profile: 10 cm FWHM 1) Bunch does not ionize He I (24.5874 eV), but does ionize Li I (5.392 eV) 2) Bunch is focused by the wake in the Li I plasma 3) Bunch ionizes He I (24.5874 eV), but not Li II (75 eV)

  16. Li e- support the wake (not trapped) He e- born on-axis inside the wake and trapped ORIGIN OF TRAPPED PARTICLES OSIRIS Simulation: Real Space (r-z) of Li & He e-: ne=1.6´1017 cm-3 Li at z=11.3 cm 3sz Multiple trapped e- bunches ~2-3 m sz He at z=11.3 cm N=0.05x1010 0.3x1010 0.25x1010

  17. TRAPPING IN IONIZING WAKE Ultra-relativistic blow-out regime W. Lu, PRL, 96 2006 Longitudinal Wake Amplitude x Trapping threshold for field-ionized e- 3-D Potential Y=F-Az -Vp E. Oz to be submitted to PRL x e- : Pre-ionized (Li) e- : Ionized inside the wake (He) -Vp Vp: Plasma Wake Phase Velocity

  18. Short Oven Profile Li e- beam He Recover Dawson’s EWB for field ionized (He) e- ! Simulations verification TRAPPING IN IONIZING WAKE + • Short simulation • Increase wake by increasing Nbeam • “Measure”, count Ntrapped • “Measure” k • Compare Ntrapped threshold with Emax(k)

  19. Beam charge is varied from 0.4 to 1 times 1.8´1010 e-/bunch Excellent “analytical model” - simulations agreement! THRESHOLDS COMPARISON k’: calculated from linear fits to Ez from simulations Peak field: calculated from simulations Threshold at ~28 GeV/m: Peak Field >Emax and Ntrapped >>1

  20. Experiment Number e- (´1010) 16 GV/m Peak Decellerating Field (GV/m) Beam charge is varied from 0.4 to 1 times 1.8´1010 e-/bunch Excellent “analytical model” - simulations - experiment agreement!!! THRESHOLDS COMPARISON Analytical - Simulations 18 GV/m Edecell=Edecell./1.8 28 GeV

  21. Dz l (nm) -10 0 10 20 30 40 50 60 Z (µm) 16 x 10 6 4 2 Dl 0 0.5 1 1.5 2 2.5 l (nm) 4 x 10 l (nm) Trapped particles are emitted in multiple, ultra-short bunches (≈µm), spaced by ∆z=“lp” TRAPPED e-CHARCTERISTICS Spectrum of trapped e- TR or Cherenkov visible light: Spectral interferences ß Coherent, +103-105 times more light *

  22. Li e- do not get trapped (low oscillation energy) Multiple short bunches He e-, gain up to 2 GeV in <10 cm TRAPPED PARTICLES CHARCTERISTICS OSIRIS Simulation, ne=1.6´1017 cm-3 Li e- at z=11.3 cm Ez(r=0) He e- at z=14.6 cm

  23. Cherenkov Rings Trapped e- energy scales with plasma length Trapped e- energy up to 18 GeV over 90 cm Trapped e- with ∆E/E<1, and may have very low e TRAPPED e-ENERGY ne=2.7x1017 cm-3 Lp=90 cm raw raw Energy (GeV)

  24. Particle trapping plays a very important role in plasma accelerators He e- ionized inside the PWFA wake follow Dawson’s trapping condition Observed trapped e- in a PWFA at Trapping value agree: experiments-simulation-”analytical” model Ionization trapping is a “new” injection mechanism Akhiezer-Polovin SUMMARY & CONCLUSIONS

  25. More diagnostics are needed for the trapped particles (time structure, emittance, …) Investigate trapping of positrons in e+-driven PWFA Trapped e- have very interesting properties: • Multiple bunches • Multi-GeV energies, ∆E/E<1? • Short features (<600 nm or 2 fs??) • Low emittance? SUMMARY & CONCLUSIONS Applications? (FEL, …) Rosenzweig, PRA 38, 7, 3634 (1988)

  26. THANK YOU to my colleagues of the E-167 Collaboration: I. Blumenfeld, F.-J. Decker, P. Emma, M. J. Hogan, R. Iverson, R. Ischebeck, N.A. Kirby, P. Krejcik, R.H. Siemann, D. Walz Stanford Linear Accelerator Center D. Auerbach, C. E. Clayton, C. Huang, C. Joshi, K. A. Marsh, W. B. Mori, W. Lu, M. Zhou University of California, Los Angeles T. Katsouleas, E. Oz, P. Muggli University of Southern California and of the E-157/162/164/164X Collaborations THANK YOU to DoE THANK YOU to SLAC

  27. Most of the excess charge is at < 20 MeV Trapped charge originate from 2nd Li/He boundary TRAPPED PARTICLES ENERGY

  28. ENERGY GAIN VS. BUNCH LENGTH ne=2.6´1017cm-3 Number of e- Energy gain increases bunch peak current or z-1 Loading of the wake by the trapped e-?

  29. y x z Coherent Transition Radiation and Interferometer y x y,E x EXPERIMENTAL SET UP (GENERIC) IP2: IP0: Energy Spectrum “X-ray” Li Plasma ne≈0-3x1017 cm-3 L≈10-20 cm X-Ray Diagnostic, e-/e+ Production ∫Cdt Cherenkov Gas Cell Plasma light e- N=1.81010 z=20-12µm E=28.5 GeV Imaging Spectrometer Cherenkov Radiator Optical Transition Radiators (OTR) Dump 25m • OTR • Cherenkov (aerogel) • X-ray Chicane • Coherent Transition Radiation (CTR) - CTR Energy≈Ipeak≈1/z E - Spatial resolution ≈100 µm • Spatial • resolution ≈9 µm - Energy resolution≈30 MeV • Energy • resolution≈60 MeV

  30. High current drive beam drive lp = 52 microns

  31. 1.6e17 hpc simulation lower current driver beam lp = 97 microns

  32. Parameters of OSIRIS Simulation For The Full E-164X PWFA Experiment

  33. Analytical Model of Trapping Constant of motion for arbitrary wave potentials of the form, A= A(zct), F=F(z −ct) For Particles Born at Rest on Axis at a phase Y0~Ymin The trapping condition for these particles:

  34. Making Use of The Linear Region of Wake Over the linear region

  35. Plasma Density Transition Trapping Plasma Density Transition Trapping is a self-trapping scenario that uses the rapid change in the wake field wavelength at a steep drop in the plasma density to dephase plasma elections into an accelerating phase of the wake. • Automatic injection of substantial charge into the accelerating phase. • Operates in the PWFA “Blow Out” regime where nbeam > nplasma or in strongly driven LWFAs. • The length of the plasma density transition must be shorter than the plasma skin depthkp-1= c/ωpfor significant trapping to occur. • Brightness of the trapped beam scales linearly with plasma density and surpasses state-of-the-art photoinjectors at densities higher than about 1017 cm-3. Major Transition Trapping Papers: Concept Proposed - H. Suk, et al., Phys. Rev. Lett. 86, 1011 (2001) Analysis of Trapped Beam Brightness and Scaling - M.C. Thompson, et al., Phys. Rev. STAB 7, 011301 (2004) Demonstration of sub-skin depth plasma density transitions - M.C. Thompson, et al., Rev. Sci. Instrum. 76, 013303 (2005).

  36. LWFA “bubble” regime Breaking of plasma waves: “Injector” for LWFA Controlled injection/trapping in LWFA S.P.D. Mangles et al., Nature 431, 535 (2004) C. Geddes et al., Nature 431, 538 (2004) J. Faure et al., Nature 431, 541 (2004) C. Coverdale et al., Phys. Rev. Lett. 74, 4659 (1995) A. Modena et al., Narture 337, 606 (1995) D. Umstadter, J. Kim, and E. Dodd, Phys. Rev. Lett. 76, 2073 (1996) E. Esarey et al., Phys. Rev. Lett. 79, 2682 (1997)

  37. Li e- do not get trapped (low oscillation energy) He e- gain up to 2.5 GeV in 10 cm TRAPPED PARTICLES CHARCTERISTICS OSIRIS Simulation, ne=1.6´1017 cm-3 Li e- at z=5600 c/wp Ez(r=0) He e- at z=11000 c/wp

  38. Short Oven Profile Li e- beam He “ANALYTICAL”THRESHOLD EXPRESSION Short simulations to test trapping theory Recover Dawson’s value?? Simulation Parameters: the same as the full e164X run except spot size is 2.4 m to mock focusing of the beam and beam is propagated only a short portion of the buffer region

  39. Transverse injection Umstadter, PRL 76, 2073 (1996). Co-linear injection, Esarey, PRL 79, 2682 (1997). PBWA, LWFA, PWFA CONTROLLED INJECTION “all optical” w1= w0 w2= w0-∆w lp=100 l0 External injection Requires: Short bunches (sz<<lp) Temporal synchronization (∆t<<2π/wp)

  40. Self-injection ∆E/E<<1 SELF-INJECTION Geddes,C.G.R.et al.Nature 431,538 (2004). Mangles,S.P.D.et al.Nature 431,535 (2004). Faure,J.et al.Nature 431,541 (2004). Katsouleas, Nature 431,515 (2004).

  41. Katsouleas, Nature 431,515 (2004). y Self-injection ∆E/E<<1 Transverse injection, Umstadter, PRL 76, 2073 (1996). Co-linear injection, Esarey, PRL 79, 2682 (1997). External injection:PBWA, LWFA, PWFA INJECTION LOA, this workshop Extract Inject Geddes,C.G.R.et al.Nature 431, 538 (2004). Mangles,S.P.D.et al.Nature 431, 535 (2004). Faure,J.et al.Nature 431, 541 (2004). Requires: Short bunches (sz<<lp), temporal synchronization (∆t<<2π/wp)

  42. Vplasma electrons≈c, vf≈c Vthermal≈vf Injection and trapping WAVE BREAKING Rosenzweig, PRA 38, 7, 3634 (1988) Dawson, Phys. Rev. 113, 2 (1959)

  43. Focusing (Er) Defocusing Decelerating (Ez) Accelerating Akhiezer, Polovin, JETP 3, 5 (1956) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + - - - - - - - - - + - - + + + + + - + + + + + - + + + + + + + - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + + + + + + + + + + + + + + + - - - - - - - + + + + + + + + - - - Relativistic electron bunch - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - No trapping? PLASMAWAKEFIELD ACCELERTAOR (e-) PWFA = beam-driven plasma accelerator • Focusing + acceleration = large energy gain • Single bunch => particles at all phases => ∆E/E≈200% • Wavebreaking limit: cold-relativistic gf=gb ? SLAC: N=1.8´1010 g=55686 (28.5 GeV) sz=30 µm ne=2.6 ´1010 cm-3 1.7 TeV/m >> 39 GeV/m

  44. Wave-particles dephasing Wave breaking Injection and trapping Harmonics of wp, sine to “sawtooth” wave WAVE BREAKING - TRAPPING Dawson, Phys. Rev. 113, 2 (1959)

  45. Number e- (´1010) Peak Decellerating Field (GV/m) Excess charge appear with threshold at ≈18 GV/m Excess charge of the order of incoming charge, 1.6-1.8´1010 e- EVIDENCE FOR TRAPPED PARTICLES <18 GV/m >18 GV/m Incoming N≈1.6´1010 e-

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