Elementary processes in the presence of super-intense laser fields; beyond perturbative QED

Transcription

1 Elementary processes in the presence of super- ; beyond perturbative QED University of Bucharest, Faculty of Physics madalina.boca@g.unibuc.ro 30 June 2016 CSSP 2016, June 26-July 09, Sinaia 1

2 Overview 1 2 Very radiation : classical vs quantum description 3 CSSP 2016, June 26-July 09, Sinaia 2

3 High intensity lasers facilities I Theoretical interest the progress in laser technology Existent/under construction high intensity laser facilities Central Laser Facility, Rutherford Appleton Laboratory Vulcan: (10 21 W/cm 2, 500 fs), Astra Gemini (10 21 W/cm 2, 30 fs) Michigan Center for Ultrafast Optical Science (CUOS) HERCULES laser ( W/cm 2 already reaches, expected W/cm 2, 30 fs) Berkeley Lab Laser Accelerator (BELLA) W/cm 2 ELI facility ELI-NP, Magurele, Romania: (2 beams up to W/cm MeV γ source) ELI-ALPS, Szeged, Hungary (Attosecond extreme-ultraviolet, soft and hard x-ray mj pulses with a 10 Hz khz repetition rate) ELI-Beamline, Prague, Czech Republic, the ELI-Beamlines short pulses up to W/cm 2 CSSP 2016, June 26-July 09, Sinaia 3

4 High intensity lasers facilities II High Power laser Energy Research facility (HIPER) (10 25 W/cm 2 ) CILEX/APOLLON Laser facility (France) I > W/cm 2 Petawatt Field Synthesizer (PFS) (Garching, Germany) I > W/cm 2 < 10 fs Exawatt Center for Extreme Light Studies (XCELS) (Nizhny Novgorod, Russia) I > W/cm 2 A new physics emerges CSSP 2016, June 26-July 09, Sinaia 4

5 Typical parameters I Atomic physics Atomic unit of intensity: I 0 = W/cm 2 I = I 0 perturbation theory validity limit : relativistic effects η = e A µa µ mc momentum acquired by a free electron in the laser field p max e E 0 = mcη ω η 1 relativistic effects are important at I = W/cm 2 (λ = 800 nm) η = 1 at I = W/cm 2 η 1000 CSSP 2016, June 26-July 09, Sinaia 5

6 Typical parameters II : non-linear effects η: the energy absorbed by the electron E = e E 0λ C in one Compton wavelength λ c = /(mc) in units of the incident laser photon energy ω; η = E ω if η > 1 the electron interacts with N eff > 1 photons simultaneously. for I = W/cm 2 (η 1000) N eff 1000 CSSP 2016, June 26-July 09, Sinaia 6

7 Typical parameters III : quantum effects electron recoil in radiation : a pure quantum effect define the relativistic invariant χ = e (F µνp ν F µα p α) (mc) 3 Equivalent form: χ = η ω ef N mc 2 eff ω ef : Effective photon energy seen mc 2 by the electron in its rest frame, in units of mc 2. if χ 1 electron recoil effects (quantum behavior) are important. CSSP 2016, June 26-July 09, Sinaia 7

8 Typical parameters IV : quantum effects (continuation) equivalent form of χ: χ = E ef E cr (the magnitude of the electric field amplitude in the electron rest frame measured in units of E cr = m2 c 3 ) e QED critical field E cr = V /m defined as: the intensity for which the energy absorbed over λ C is equal to the electron rest energy e E cr λ C = mc 2 the intensity corresponding to the critical field would be I cr = W/cm 2 (unattainable in the near future) : for electron energy E el = 500 MeV, ω L = 1 ev, η = 100 (I = W/cm 2 ) χ = 0.2 CSSP 2016, June 26-July 09, Sinaia 8

9 Typical parameters V References V.I. Ritus, Journal of Russian Laser Research 6, 5 (1985). Y. I. Salamin, S. Hu, K.Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 41 (2006). A. Di Piazza, C. Muller, K. Z. Hatsagortsyan, and C. H. Keitel, Rev. Mod. Phys. 84, 1177 (2012) CSSP 2016, June 26-July 09, Sinaia 9

10 : low intensity Thomson (elastic) Compton (inelastic) elastic in the electron rest frame ω 2 = ω 1 E 1 cn 1 p 1 E 1 cn 2 p 1 + (1 n 1 n 2) ω 1 ω 2 = ω 1 E 1 cn 1 p 1 E 1 cn 2 p 1 Head-on collision, forward, E 1 mc 2, ω 1 mc 2 ω max 2 4γ 2 ω 1 (inverse Compton ) CSSP 2016, June 26-July 09, Sinaia 10

11 Classical/quantum description CED formalism: the electron accelerated by the laser field emits radiation; Arbitrary laser field (monochromatic/plane-wave/focused) Electron equation of motion (w/wo radiation ) Lienard-Wiechert potentials Plane-wave, no RR: p i = p f Quantum description: single photon emission in the external field Dirac equation, semiclassical approximation (laser field: classical, emitted photon: quantized field) plane wave laser field ( ˆP eâl eâc mc)ψ = 0 Exact solutions of the Dirac equation for H e L (Volkov solutions); H c : first order perturbation theory A if 1 i dt ψ V (p 2 ) H C (k 2 ) ψ V (p 1 ) CSSP 2016, June 26-July 09, Sinaia 11

12 spectrum I Calculation of { the photon } energy/angular ditribution dw dw dω 2, dω 2 d 2 W dω 2 dω 2 Monochromatic approximation: any fixed observation direction. ω (q) N d 2 W dω 2 dω 2 an infinite series of lines for = Nω E 1 cn 1 p 1 L [ ] mc E 1 cn 2 p 1 + (1 n 1 n 2) 2 η 2 + N ω 4(E 1 cn 1 p 1 ) L ω (cl) N = Nω E 1 cn 1 p 1 L E 1 cn 2 p 1 + (1 n 1 n 2) mc 2 η 2 4(E 1 cn 1 p 1 ) Finite pulse: continuum spectrum: for low intensity peaks at the same positions as he the previous lines CSSP 2016, June 26-July 09, Sinaia 12

13 spectrum II Spectrum characteristics η 0: Compton/Thomson formula for ω L Nω L (simultaneous absorption of N photons) ω (q) 1 = Nω L E 1 cn 1 p 1 E 1 cn 2 p 1 + (1 n 1 n 2)N ω L mc 2 η 2 4(E 1 cn 1 p 1 : nonlinearity effect electron dressing : ) p q = p + (mc)2 η 2 n, m 4(n m = m 1 p) 1 + η 2 /2 Classicality criterion: small electron recoil χ 1 Quantum cut-off ω (q) N < ω(cl) N ; frequency cut-off lim N ω(q) N = E 1 cn 1 p 1 1 n 1 n 2 = ω cut off Head-on collision For head-on collision, back, ultrarelativistic electron: ω cut off = E 1 (not always observed!) CSSP 2016, June 26-July 09, Sinaia 13

14 Blue shift/red shift γ 1 1 ω 2 ω l Blue shift: electron energy converted into the energy of the emitted photon η > 1 Red shift due to electron dressing Head-on collision, E 1 = 600 MeV, λ L = 532 nm (quasi-monochromatic); δθ = (p 1, k 2) CSSP 2016, June 26-July 09, Sinaia 14

15 Blue shift/red shift η 1 Onset of a different regime: the radiation distribution becomes quasi-continuous for well defined angles. CSSP 2016, June 26-July 09, Sinaia 15

16 Classical/quantum calculation χ ω 1γη mc 2 Classicality parameter Head-on collision, ω L = 0.043, E 1 = 5.1 GeV, η = 40 (quantum cutt-off reached) CSSP 2016, June 26-July 09, Sinaia 16

17 Angular distribution γ 1 η Head-on collision, γ 1 = 50, η = 100 Well defined shape of angular distribution, azimuthal symmetry lost CSSP 2016, June 26-July 09, Sinaia 17

18 Angular distribution γ η Shape of the distribution given by trajectory of β Possible field shape reconstruction from β Identical shape predicted by classical/quantum calculation CSSP 2016, June 26-July 09, Sinaia 18

19 Final electron distribution (γ η 1) the monochromatic case: a series of discrete lines for any electron direction finite pulse: discrete lines continuous spectrum λ 0 = 800 nm, η = 0.6, E 1 = 46 GeV, near head on collision (SLAC) monochromatic plane wave pulse CSSP 2016, June 26-July 09, Sinaia 19

20 Final electron distribution for large η λ 0 = 800 nm, E 1 = 5.1 GeV, head-on collision. η = 0.5 η = 5 λ 0 = 800 nm, η = 5 (I = W /cm 2 ), head-on collision; energy distribution of the final electron dp/de 2. CSSP 2016, June 26-July 09, Sinaia 20

21 Polarization effects: definitions Definition in classical electrodynamics E(t, r) = E 0Re {εe i(ωt k r)} One defines two unit vectors ɛ 1 and ɛ 2 such that ɛ 1 ɛ 2 = 0, ɛ 1 k = 0, ɛ 2 k = 0 ε = i ɛ i ɛ i ε i = ε ɛ i, i = 1, 2 Stokes parameters I ɛ intensity corresponding to the component of E along ɛ. ξ 1 [I ɛ1 I ɛ2 ] /I, [ ] ξ 2 I (ɛ1 +ɛ 2 )/ 2 I (ɛ 1 ɛ 2 )/ 2 /I [ ] ξ 3 I (ɛ1 +I ɛ 2 )/ 2 I (ɛ 1 I ɛ 2 )/ 2 /I CSSP 2016, June 26-July 09, Sinaia 21

22 Polarization effects: results I QED definition In QED: calculation of the Stokes parameters of an emitted photon dp = P(s 2, (...))dk 2 then the Stokes parameters are calculated according to ξ (f ) i = P(s(1) 2 P(s (1) 2, (...)) P(s(2) 2, (...)),, (...)) + P(s(2) 2, (...)) Calculation of observables work in the electron rest frame. calculate the degrees of linear/circular polarization of the emitted photon (relativistic invariants) p L = ξ ξ 2 2, p C = ξ 2 3 CSSP 2016, June 26-July 09, Sinaia 22

23 Polarization effects: results II Two pulse shapes used in numerical calculations Linear laser polarization Investigate the effect of the intensity and pulse duration quasimonochromatic laser pulse very short laser pulse CSSP 2016, June 26-July 09, Sinaia 23

24 Polarization: intensity effects I η = 5, quasimonochromatic pulse, fixed detection direction θ 2 = 0.1π, φ 2 = π/4 The normalized photon probability distribution P(ω 2) The degrees of linear (p L )/circular (p C ) polarization It is natural to represent the scaled quantities P L,C (ω 2) = p L,C (ω 2)P(ω 2) CSSP 2016, June 26-July 09, Sinaia 24

25 Polarization: intensity effects II In the zero intensity limit the observable value of p C is in fact 0 (in agreement with LC calculations) CSSP 2016, June 26-July 09, Sinaia 25

26 Polarization: intensity effects III The scaled (observable) degrees of linear (p L )/circular (p C ) polarization for moderate intensity (η = 20) The scaled (observable) degrees of linear (p L )/circular (p C ) polarization for high intensity (η = 50) CSSP 2016, June 26-July 09, Sinaia 26

27 Results: Pulse length effects I In the case of a very short laser pulse the picture is different The (scaled) vector potential for a very short Gaussian pulse The photon probability density for η = 1 CSSP 2016, June 26-July 09, Sinaia 27

28 Results: Pulse length effects II The degrees of linear (p L )/circular (p C ) polarization The scaled degrees of linear (p L )/circular (p C ) polarization CSSP 2016, June 26-July 09, Sinaia 28

29 Results: Pulse length effects III The scaled degrees of linear (p L )/circular (p C ) polarization The scaled degrees of linear (p L )/circular (p C ) polarization For a very short laser pulse circularly polarized photons should be observable even a very low intensity CSSP 2016, June 26-July 09, Sinaia 29

30 Charged particle in laser field I The classical equation of motion dp µ ds = e m F µν (x)p ν, with F µν = µa ν νa µ Analytic solution for a plane wave field A A(φ) e r = p0 0 p 0 r = φ φ 0 φ φ 0 [ A (χ) A 0 p 0 e [ e 2 A 2 (χ) dχ (p0 0 p 0) + p ] 0 2 p0 0 p. 0 ] dχ A 2 (φ) = (A(φ) A 0) 2 + 2mv 0 e (A (φ) A 0 ) Here quantities with 0 index: initial values, and relative to the field propagation direction, v = βc, u = γv CSSP 2016, June 26-July 09, Sinaia 30

31 Charged particle in laser field II (RR) Lorentz-Abraham-Dirac (LAD) equation: dp µ dτ = e m F µν p ν + 2 [ ( e0 2 d 2 p µ 3 c 2 (mc) dτ + pµ dp ν 2 (mc) 2 dτ )] dp ν dτ [Landau, L. D. and Lifshitz, E. M.: The Classical Theory of Fields, Elsevier, Oxford (1975)] runaway solutions, i.e., of solutions that show an exponential increase of the electron acceleration even in the absence of external fields Landau-Lifshitz (LL) equation: perturbative; in RHS use dp µ dτ = e m F µν p ν analytic solution for a plane-wave field [DiPiazza, Lett. Math. Phys. 83, 105 (2008)] CSSP 2016, June 26-July 09, Sinaia 31

32 Charged particle in laser field III RR effect: the particle slows down in a plane wave-field numerical simulations for a particle with γ i = 50 in head-on collision with a plane-wave laser pulse without RR p i = p f with RR p i p f p depends on: laser intensity, frequency, duration Not included in the quantum formalism as presented before λ = 1000 nm, η = 100 (I = W/cm 2 ) CSSP 2016, June 26-July 09, Sinaia 32

33 RR effects in radiation I Classical description electron slowing down: the very bright line finite band whose width increases with the pulse lenght Quantum description of RR Incoherent multiple one-photon emission by the electron [DiPiazza et al, Phys. Rev. Lett. 105, (2010)] CSSP 2016, June 26-July 09, Sinaia 33

34 RR effects in radiation II Future experimental detection of RR not detected at the moment numerical simulations indicating the possibility to observe RR effects in radiation : [A. Di Piazza, K. Z. Hatsagortsyan, and C. H. Keitel, Phys Rev Lett 102, (2009); Phys Rev Lett 105, (2010)] in laser-plasma acceleration [Igor V. Sokolov et al, Physics of Plasma, 16, (2209), Phys. Rev. E (2010)], [R. Capdessus and P. McKenna, Phys. Rev. E 91, (2015)] (LAD equations in PIC codes) [O Har-Shemesh, A. Di Piazza, Opt. Lett. Vol. 37, 1352 (2012)] Measurment of the laser peak intensity exploiting the directionality of the radiation emitted by ultrarelativistic electrons via nonlinear Thomson. RR must be included into the simulations for I W/cm 2. CSSP 2016, June 26-July 09, Sinaia 34