Intense laser-matter interaction: Probing the QED vacuum

Transcription

1 Intense laser-matter interaction: Probing the QED vacuum Hartmut Ruhl Physics Department, LMU Munich, Germany ELI-NP, Bucharest March 11, 2011

2 Experimental configuration Two laser pulses (red) collide (yellow) and interact with an electron beam (blue). Energetic photons are generated (black). Under extreme conditions pairs can be produced.

3 Control parameter If we assume an electron interacting with a constant magnetic field B the peak of the emitted radiation spectrum versus its kinetic energy scales like ω 0 ɛ ( ɛ m ) 3 = B ɛ m E s, ω 0 = eb ɛ, E s = m2 e. This is equivalent to the quantum efficiency parameter χ χ = e (F µν p ν ) 2 = γ ( ) 2 E + v ( v E ) 2 B. m 3 c 4 E s c

4 Total transition rate The total transition rate for radiation is W rad α m2 c 4 χ 2 3. ɛ The larger χ is the more energetic photons become. Their emission will also be more likely as compared to classical Compton. The threshold for nonlinear photon emission scales as γ a a s > 1, a = ee m ω c, a s = ee s m ωc. Unlike photon generation via Compton scattering the emission can now be controled via the particle energy γ and the field stength a measured on the Schwinger scale a s.

5 W rad in a rotating electric field E(t) = (E 0 cos ωt, E 0 sin ωt) p(t) = e E(t), p(t 0 ) = 0 p x (t) = mca sin ωt p y (t) = mca (1 cos ωt) W rad (t) = ( a ω a mc 2 sin 4 ωt a αmc 2 sin 2 ωt 2 2 ) 2 3

6 W rad

7 Photon emission The energy distribution of the probability rate for photon emission by electron in electromagnetic field is given by (see: Fedotov, Ritus, Baier, Landau) dw rad (ε γ ) dε γ = αm2 c 4 ε 2 e x ( ) 2 Ai (ξ) dξ + x + χ γ x Ai (x) The parameter x is given by x = χ γ /χ e (χ e χ γ ) with 0 χ γ < χ e, Ai is the Airy function, ε γ, and ε e are the energies of the photon and electron, respectively. The quantum efficiency parameters χ e and χ γ are given by v χ e = e u t m 3 c 4 v χ γ = e u t m 3 c 4 ε 2 E + p H! ( p E) 2, c ε 2 E + k H! ( k E) 2. c

8 Cascading Starting from a seed electron in an intense laser field a cascade is triggered.

9 Pair creation The energy distribution of the probability rate for direct pair creation by photons is given by (see: Fedotov, Ritus, Baier, Landau) dw cr (ε e ) dε e = αm2 c 4 ε 2 γ y ( ) 2 Ai (ξ) dξ + y χ γ y Ai (y) The parameter y is given by y = χ γ /χ e (χ γ χ e ) with 0 χ e < χ γ. The quantum efficiency parameters χ e and χ γ are given on the previous slide.

10 Kinetic equations for e, e + and γ Each phase space volume element for electrons and positrons has gains and losses. The corresponding rate equations are t + v x + F p f ± ( x, p, t) Z = d 3 k dw E, B Z rad d 3 ( k, p + k) f ± ( x, p + k, t) f ± ( x, p, t) k Z + d 3 dw E, B pair k d 3 p ( k, p) f γ ( x, k, t). d 3 k dw E, B rad d 3 ( k, p) k Each phase space element for photons has gains and losses. The corresponding balance is t + c2 k ω x! Z f γ ( x, k, t) = d 3 p dw E, B rad d 3 ( k, p) ˆf +( x, p, t) + f ( x, p, t) k Z f γ ( x, k, t) d 3 p dw E, B pair d 3 p ( k, p).

11 Theoretical estimates (Fedotov, 2010) Cascading is a double chain process between electrons, positrons, and photons. The e + e -multiplicity of the cascade grows exponentially as N(t) e Γt, Γ 1 mc αµ 1/4 2 ω t em, µ = E αe s.

12 Cascading Electrons (red), positrons (blue), and photons (black). Trajectory of original seed (magenta).

13 Exponential growth of N e + e N(t) e Γt Γ 1/t em αµ 1/4 mc 2 ω/ The number of pairs N e + e as a function of time (results of three MC simulations for a 0 = , ω = 1 ev, Γ = 4.91 ± 0.75). Parametric study of the growth rate Γ(µ) for pairs in the range between a = (10 100) 10 4, for ω = 1 ev, and ω = 0.66 ev.

14 Primary electron dynamics Figure: χ e (t) of a primary electron in the laser field with a 0 = and ω = 1 ev as a function of time for three Monte-Carlo simulations. The analytical estimate in the absence of QED processes is plotted in purple. Right plot: Averaged electron quantum efficiency parameter < χ e > as a function of time found from the same simulations.

15 Scaling of energy and χ e ε mc 2 µ 3/4 mc 2 ω χ µ 3/2 Characteristic energy ε of electrons as a function of µ. Characteristic quantum efficiency parameter χ e of electrons as a function of µ.

16 Electrons injected into a focused laser beam Simulations for the field of two colliding Gaussian beams. The focal spot is R λ and the intensity is I W /cm 2. In addition, 600 MeV electrons are injected. The plot shows the electron and positrons trajectories created in the laser focus. The observed multiplicity is still 2.5 nonlinear QED.

17 Conclusions Preliminary simulations for focused counter-propagating circularly polarized laser beams predict the onset of nonlinear QED effects at a few times W /cm 2 and a few 600 MeV electrons. ELI-NP can probably be used for novel radiation sources (see talk of Nina Elkina).

18 In collaboration with Alexander Fedotov, MEPhi, Moscow; Nina Elkina, LMU, Munich; Constantin Klier, LMU, Munich; Dietrich Habs, LMU, Munich Y. Hadad, L. Labun, J. Rafelski, N. Elkina, C. Klier, and H. Ruhl, Effects of radiation reaction relativistic laser acceleration, Phy. Rev. D 82, (2010). E. N. Nerush, I. Yu. Kostyukov, A. M. Fedotov, N. B. Narozhny, N. Elkina, and H. Ruhl, Laser Field Absorption in Self-Generated Electron-Positron Pair Plasma, Phys. Rev. Lett. 106, (2011). N. V. Elkina, A. M. Fedotov, I. Yu. Kostyukov, M. V. Legov, N. B. Narozhny, E. N. Nerush, and H. Ruhl QED cascades induced by circularly polarized laser fields, arxiv: (2010).