Synergistic Direct/Wakefield Acceleration In the Plasma Bubble Regime Using Tailored Laser Pulses Gennady Shvets, The University of Texas at Austin John Adams Institute for Accelerator Science, Oxford, UK, May 25, 2016
History of Accelerators: Higher Energies from Bright Ideas “ Fermi predicted that future accelerators would grow in power and size. They would not be built on the earth but around it, and physics laboratories would be in outer space… You may expect that at some future time accelerators will change the aspect of the earth and make it resemble the planet Saturn”, Laura Fermi, 1974. Prediction: 20 TeV CM energy by 1994 at a cost of $170B NB: SSC would have been 40 TeV CM if it was not cancelled in 1993 (!!) “What can we learn with High - Energy Accelerators”, Retiring Presidential Address of APS, Columbia, 1954
How big are today’s accelerators? *Tevatron: 1 TeV/6km proton/antiproton LHC: 7 TeV/27km proton-proton dE • Hadrons are made of quarks need high energy/proton 4 E huge radius for reasonable magnetic field strength 4 2 dz m R • Rings don’t work for high energy e -p need linacs *Bad picture: 3km Main Injector Ring Major problem: synchrotron radiation looks larger than the Tevatron!
Linacs are for Leptons: International Linear Collider (ILC), Next HEP Project (?) • SLC 2-mile linac: 50 Gev x 50 GeV collider with L = 10 30 cm -2 sec -1 • Conventional linacs are very long: 30km for 500 GeV • Accelerating gradient in SC cavities: 32 MV/m • High gradient acceleration enables miniaturization
High accelerating gradients high frequencies eE 1 trap E trap = 10 MeV/m x f [GHz] c m Use lasers whenever you can highest frequency Courtesy of Dave Whittum
The Basics of Laser Acceleration Linear in electric field acceleration in vacuum is impossible (Lawson-Woodward- Palmer’s theorem) ( 2 , 0 ) k p Cannot stop a photon photon in vacuum! Slow electron Fast electron p p Far-field accelerators: Near-field accelerators: electrons execute transverse motion possess non-radiative field in external DC fields (IFEL, inverse components due to boundaries CARM, inverse Ion Channel Laser) (inverse Smith Purcell, PBG, surface wave, plasma wakefield , …) ??
Plasma wave as a near-field accelerator Ultimate nonlinear wake: plasma bubble T. Tajima & J. M. Dawson, PRL‘79
Plasma bubble: the workhorse bubble plasma Particle advances inside bubble gains energy from low-frequency electric field energy gain is limited by dephasing 𝑰 𝑵𝑮 ≈ 𝒒 𝒚 𝟑 𝚬𝛀 𝟑 − 𝛀 → 𝚬𝐪 𝐲 = 𝟑𝜹 𝒄 𝟑𝜹 𝒄 Can we do better??
Far-field Accelerators Far-field accelerators (no boundaries, plasmas, etc): • Inverse free-electron laser (IFEL): 𝜕 𝑀 − 𝑙 𝑀 𝑤 𝑦 = 𝑙 𝑥 𝑤 𝑦 • Cyclotron resonance laser accelerator: 𝜕 𝑀 − 𝑙 𝑀 𝑤 𝑦 = Ω 𝑑 /𝛿 • Inverse ion-channel laser (a.k.a. DLA): 𝝏 𝑴 − 𝒍 𝑴 𝒘 𝒚 = 𝝏 𝜸 Drawbacks: (a) accelerating gradient reduces with 𝜹 , (b) large transverse undulating motion, (c) difficult to maintain resonance condition 𝒆𝜹/𝒆𝒜 ∝ 𝟐/𝜹 IFEL curse
DLA History: From Plasma Channels… Dave Whittum, Andy Sessler, and John Dawson invent an ion channel laser D. H. Whittum et. al., PRL’90; Phys. Plasmas ‘92 The MPQ team proposes and realizes the inverse ion channel laser A. Pukhov et. al., PoP’99; C. Gahn et. al ., PRL’99
Electrons motion inside the bubble and Direct Laser Acceleration laser pulse ( 𝝏 𝑴 , 𝒍 𝑴 ) Electrons execute betatron motion with frequency 𝝏 𝜸 Transverse energy 𝝑 ⊥ is reduced due to the conservation of the action 𝑱 ⊥ = 𝝑 ⊥ /𝝏 𝜸 Betatron motion Betatron frequency Break the adiabatic invariant 2𝛿 1/2 𝜕 𝛾 = 𝜕 𝑞 by introducing an additional resonant laser pulse DLA 𝜕 𝑀 − 𝑙 𝑀 𝑤 = (2𝑜 + 1) 𝜕 𝑞 Transverse energy 𝟑 /𝟑𝜹𝒏 𝒇 + 𝝏 𝒒 𝟑 𝒏 𝒇 𝟑 𝒜 𝟑 /𝟓 𝝑 ⊥ ≡ 𝒒 ⊥ 2𝛿 Δ𝛿 = Δ𝜗 ⊥ /𝑛𝑑 2 1 − 𝑑/𝑤 𝑞ℎ
Earlier indications? Dino Jaroszynski produces MeV Gamma rays, possibly via DLA mechanism inside a bubble!! S. Cipiccia et. al., Nature Physics’2011 “In fact, this observation of high harmonic generation could provide the first (albeit somewhat indirect) experimental evidence of DLA, which has so far been elusive.” G. Shvets, Nature Physics’2011 A great deal of theoretical work: Nemeth, et al., PRL’07 , PRL; Phuoc, et al., PoP’08 , J. L. Shaw et. a l., PPCF’14 Big questions: (a) monochromatic beam? (b) best laser pulse format? (c) best injection approach? (d) major paradigm shift of LPAs in the making??
Outline of the Talk • How LWFA and DLA can work together, delay dephasing, and bifurcate the phase space • How to inject electrons into the plasma bubble and have them experience synergistic DLA/LWFA • Constant gradient DLA in the decelerating phase of the wake • Mix-and-match: combining multiple lasers for DLA + LWFA
Can LWFA and DLA work together? • DLA’s resonance condition can be undone by rapid wakefield LWFA is acceleration: 𝝏 𝑴 𝟐 − 𝒘 𝒚 /𝒘 𝒒𝒊 = 𝝏 𝒒 / 𝟑𝜹 bad for • DLA requires large 𝒘 ⊥ because 𝑩 𝑴 ∝ 𝒘 ⊥ ⋅ 𝑩 𝑴 , but the conservation DLA of 𝑱 ⊥ reduces |𝒘 ⊥ | during acceleration! • DLA laser pulse can distort the bubble and impede LWF DLA is acceleration or electron injection into the bubble bad for • Large amplitude of betatron oscillations may reduce the LWFA accelerating gradient experienced inside the bubble But the benefits of combining the two could be substantial! X. Zhang, V. Khudik, and GS, PRL 114, 184801 (2015) X. Zhang, V. Khudik, A. Pukhov, and GS, PPCF 58, 034011 (2016)
Benefits of Synergistic Laser Wakefield & Direct Laser Acceleration • Cumulative energy gain from LWFA and DLA • Potentially higher energy gain from LWFA due to delayed dephasing • Large transverse momentum 𝑳 = 𝒒 ⊥ /𝒏𝒅 efficient source of X-rays and 𝜹 − rays up to 𝑳 𝟒 harmonic of 𝝏 𝑴 • Combining multiple laser pulses (mid-IR + near-IR) accel decel 𝟑 /𝒏 𝒇 𝟑 𝒅 𝟑 𝒆𝜼 𝟐 𝟑 − 𝟐 + 𝒒 ⊥ 𝒆(𝒅𝒖) ≈ 𝜹 𝟑 𝟑𝜹 𝒄 X. Zhang et. al., PRL 114, 184801 (2015); PPCF 58, 034011 (2016) 𝜼 = 𝒚 − 𝒘 𝒄 𝒖
Synergistic DLA/LWFA: single-particle simulations of a particle swarm Resonance DLA electron condition: 𝝏 𝒆 ≈ 𝝏 𝜸 𝝏 𝒆 (𝒚) non-DLA electron 𝝏 𝜸 (𝒚) 2 𝑛 2 𝑑 2 1 + 𝑞 𝑨 1 Swarm of initial 𝜕 𝑒 = 𝜕 𝑀 + conditions ( 𝒒 ⊥ , 𝒔 ⊥ ) 2𝛿 2 2 2𝛿 𝑞ℎ Necessary ingredients of DLA/LWFA synergy: (a) electron injection with large transverse energy (b) strong overlap between electrons and the laser (c) betatron resonance between electrons and the laser
Can DLA happen in a plasma bubble? Pump pulse creates a bubble Density bump “shakes” the Density bubble side-injection with ramp large 𝒒 ⊥ facilitates DLA injection scenario Self-injected electrons interact with the weaker laser pulse delayed by Dt =80fs n 0 =1.8×10 18 cm -3; n 1 =5.4×10 18 cm -3 I 0 =6×10 19 w/cm 2; I 1 =6×10 18 w/cm 2 𝝁 = 𝟏. 𝟗𝝂𝒏 delay:80fs X. Zhang et. al. PRL 114, L 2 =1.6mm, L 3 = L 4 = L 5 ≈ 𝟐𝟏𝟏𝝂𝒏 184801 (2015)
DLA inside a plasma bubble after 1cm propagation Electrons separated into two groups DLA electrons with large 𝒒 ⊥ gain more energy and fall behind the non-DLA ones Pump: 𝒃 𝑴 = 𝟔. 𝟒, 𝝊 𝑴 = 𝟖𝟏𝒈𝒕 , 𝒙 𝟏 = 𝟑𝟏𝝂𝒏 DLA : 𝒃 𝑴 = 𝟐. 𝟖 , 𝝊 𝑴 = 𝟒𝟔𝒈𝒕, 𝒙 𝟏 = 𝟑𝟏𝝂𝒏 non-DLA Phase space bifurcation with DLA pulse DLA Two-peak spectrum separated by 400 MeV Bifurcation is absent DLA without DLA pulse w/o DLA pulse X. Zhang et. al. PRL 114, 184801 (2015)
Phase Space Correlations: Key to Synergy DLA electrons strong correlation between total energy 𝛿𝑛𝑑 2 and DLA transverse energy 𝟑 𝒜 𝟑 𝟑 𝒏𝝏 𝒒 𝒒 𝒜 𝝑 ⊥ = 𝟑𝜹𝒏 + 𝟓 non-DLA 𝟑 /𝒏 𝒇 𝟑 𝒅 𝟑 𝒆𝜼 𝟐 𝟑 − 𝟐 + 𝒒 ⊥ 𝒆(𝒅𝒖) ≈ Strong bifurcation in (𝝑 ⊥ , 𝜹) phase space 𝜹 𝟑 𝟑𝜹 𝒄 Synergy between DLA and LWFA higher energy DLA electrons gain extra 200 MeV gain from the wake for the DLA population from the wake and extra 400MeV from the laser (DLA) delayed dephasing!
DLA is compatible with ionization injection! Electrons after 3mm 𝑜 0 = 4 × 10 18 𝑑𝑛 −3 𝐽 pump = 2.3 × 10 19 𝑋/𝑑𝑛 2 𝐽 DLA = 𝐽 pump /2 𝑄 pump = 96 𝑈𝑋 𝑉 ion = 870𝑓𝑊 from 𝑃 7+ to 𝑃 8+ Off-axis or off-peak phase ionization produces DLA electrons!
Off- peak phase ionization and “ricochet” DLA electrons: real atoms meet meta-atoms Off-peak ionization phase: 𝑭 ⊥ electrons leave the laser pulse with finite transverse momentum 𝒒 ⊥ + 𝒇𝑩 ⊥ /𝒅 = 𝒇𝑩 ⊥ 𝒖 𝒋 /𝒅 𝑩 ⊥ Phase Ricochet electron starts out with large 𝒒 ⊥ , interacts with the DLA pulse gains even larger 𝒒 ⊥ and more energy
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