1 1 Office of Science Multiple Colliding EM pulses: Depletion of intense fields S. S. Bulanov 1, D. Seipt 2, T. Heinzl 3, M. Marklund 4 1 Lawrence Berkeley National Laboratory, Berkeley, CA 2 Helmholtz-Institut Jena, Germany 3 Plymouth University, Plymouth, UK 4 Chalmers University of Technology, Gothenburg, Sweden We acknowledge support from the Office of Science of the US DOE under Contract No. DE-AC02- 05CH Advanced Accelerator Concepts Workshop (AAC 2016), July 31 – August 5, National Harbor, MD

2 2 Office of Science 4-wave mixing (Lundström et al, 2006) Mulitphoton Compton and Breit- Wheeler processes A. I. Nikishov, V. I. Ritus (1964); Bula et al (1996); Burke et al (1997) High Intensity Particle Physics High order harmonic generation through quantum vacuum interaction (Di Piazza, Hatsagortsyan, C. H. Keitel, 2005 Fedotov & Narozhny, 2006) Birefringent e.m. vacuum (Rozanov, 1993) Electron positron pair production from vacuum (Schwinger, 1951) Photon-photon scattering via relativistic mirrors (Koga et al (2012)) - Electromagnetic avalanches - Electromagnetic cascades High Intensity Particle Physics

3 3 Office of Science Ultra-high intensities for Particle Physics studies SLAC experiments (1996) C. Bula et al., Phys. Rev. Lett. 76, 3116 (1996) D. Burke et al., Phys. Rev. Lett. 79, 1626 (1997) C. Bamber et al., Phys. Rev. D 60, (1999) ELI Femtosecond pulse of 10 KJ the intensity above W/cm 2 High Field Science, Particle Acceleration Laboratory Astrophysics & Hadron Therapy 30 fs pulse 40 J Energy W/cm 2 Intensity Particle Acceleration, Future collider studies, High Field Science

4 4 Office of Science Unanswered Questions of High Intensity Particle Physics Theory -Beyond the plane wave approximation -Finite size effects -Beyond the external field approximation -Electromagnetic Cascades and Avalanches Ultimate limit for attainable laser intensity -Physics beyond the Standard Model Experiment -Uncharted region in the parameter space of the Standard Model -Electromagnetic Cascades and Avalanches -Test bed for future detector techniques -Test bed for interactions at future colliders Backreaction???

5 5 Office of Science Parameters of High Intensity Particle Physics Critical QED field can create an electron-positron pair at Compton length, electron bunch Relativistic regime of interaction Electron energy gain over laser wavelength in units of mc 2 Classical nonlinearity parameter Quantum Effects counter-propagating laser and electron/photon photon

6 6 Office of Science Interaction of a laser pulse with an ultra relativistic electron beam: thresholds of different regimes 1.Radiation effects become dominant 2.QED effects become dominant 3.QED cascade γ e+e+ e-e- Laser pulse electron bunch LWFA Gas jet Wake wave Colliding laser pulse and an electron beam G. Breit and J. A. Wheeler (1934) H. R. Reiss (1962) L. S. Brown and T. W. B. Kibble (1964) A. I. Nikishov and V. I. Ritus (1964) C. Harvey, T. Heinzl, and A. Ilderton (2009) A. Di Piazza, K. Z. Hatsagortsyan, and C. H. Keitel (2010) I. V. Sokolov, J. Nees, V. P. Yanovsky, N. M. Naumova, and G. Mourou (2010) F. Mackenroth and A. Di Piazza (2011) A. I. Titov, H. Takabe, B. Kampfer, and H. Hosaka (2012) K. Krajewska and J. Z. Kaminski (2012) S. S. Bulanov, C. B. Schroeder, E. Esarey, W. P. Leemans (2013) M. Vranic, et al., (2014); T. Grismayer, et al. (2016)

7 7 Office of Science e+e+ e-e- e+e+ e-e- e-e- electron bunch When interacting with intense laser pulse electrons, positrons, and photons undergo a cascade-type process involving multiple emissions of photons W/cm W/cm W/cm 2 1) 3x10 26 W/cm 2 2) 3x10 24 W/cm 2 3) 3x10 22 W/cm 2 4) 3x10 20 W/cm 2 5) 3x10 18 W/cm 2 Multiphoton Compton effect Multiphoton Breit-Wheeler effect Spectrum of emitted photons Spectrum of created electrons/positrons GeV GeV in a.u.

8 8 Office of Science Depletion of intense fields: significant absorption of laser photons by electrons during Thompson/Compton processes External field approximation is valid if The number of photons absorbed (ΔN A ) << The number of photons in the pulse (N L ) Natural criterion for depletion ΔN A =N L N T is the number of electrons in the bunch is the energy loss upon radiating P rad per laser period T In the reference frame where the electron is on average at rest is laser frequency in this frame

9 9 Office of Science Classical estimate places the depletion threshold well into the quantum regime for the electron to emit one high frequency photon, it needs to absorb For an electron bunch containing a charge of 1 nC, a laser with a 0 ~10 3 is needed significant radiation reaction with ensuing changes of the particle trajectories E. Sarachik, G. Schappert, PRD (1970) E. Esarey, et al., PRE (1993)

10 Office of Science Quantum estimate reveals weak dependence of the depletion threshold on electron energy L C is the radiation length of the electron in a strong EM field For an electron bunch containing a charge of 1 nC, a laser with a 0 ~10 3 is needed The thresholds of depletion for N T =10 9 (magenta), (red), and (blue). Dashed lines represent the asymptotic estimate when

11 Office of Science Taking into account the dependence of the emission probability on the number of absorbed photons The average amount of energy, drawn from the laser field in a single photon emission or pair production, is then

12 Office of Science How many laser photons are needed for an electron to emit a high-energy photon? At t=1/2has a sharp maximum Thus, when a Compton photon with a certain value of χ γ is emitted, the number of laser photons drawn from the laser field approximately equals s(χ γ )

13 Office of Science The angle of emission is determined by the most probable number of absorbed photons

14 Office of Science The emission angle and the change of electron momentum can be important inputs for PIC-QED codes Scattering angle: The photon is emitted along the instantaneous direction of electron momentum

15 Office of Science Conclusions We considered the depletion of strong EM fields due to photon absorption in multi-photon Compton and Breit- Wheeler processes We found that the depletion threshold is rather high: a 0 ~10 3 for electron beams carrying tens of nC These numbers are typical for EM avalanches as shown by previous studies by different groups We found that the most probable number of absorbed photons determine the emission angle

16 Office of Science Thank you!

17 Office of Science Parameters of High Intensity Particle Physics Critical QED field can create an electron-positron pair at Compton length, electron bunch Relativistic regime of interaction Electron energy gain over laser wavelength in units of mc 2 Classical nonlinearity parameter Quantum Effects counter-propagating laser and electron/photon photon

18 Office of Science Probabilities of multiphoton Compton and Breit-Wheeler effects BELLA(10 GeV) SLAC E144 ELI(10 GeV) ELI(100 GeV)

19 Office of Science High Intensity Particle Physics - Nonperturbative Quantum Field Theory - Matter in extreme conditions - Next generation lasers: day-to-day operation new laser-matter interaction applications - Future lepton colliders - Future γγ colliders - Various astrophysical phenomena - Electromagnetic Avalanches - Electromagnetic Cascades - Ultimate Laser Intensity Limit High Intensity Particle Photon Interactions Workshop on "Nonlinear QED Phenomena with Ultra-Intense PW-class Lasers" Berkeley Cube