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Charged particle motion and radiation in strong electromagnetic fields

A. Gonoskov, T. G. Blackburn, M. Marklund, and S. S. Bulanov
Rev. Mod. Phys. 94, 045001 – Published 7 October 2022
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  • Introduction
  • Theory of Strong Electromagnetic Fields
  • Numerical Methods
  • Charged Particle Dynamics
  • Experiments
  • Applications
  • Outlook
  • Conclusions
  • List of Symbols and Abbreviations
  • ACKNOWLEDGMENTS
    • References

    Abstract

    The dynamics of charged particles in electromagnetic fields is an essential component of understanding the most extreme environments in our Universe. In electromagnetic fields of sufficient magnitude, radiation emission dominates the particle motion and effects of quantum electrodynamics (QED) in strong fields are crucial, which triggers electron-positron pair cascades and counterintuitive particle-trapping phenomena. As a result of recent progress in laser technology, high-power lasers provide a platform to create and probe such fields in the laboratory. With new large-scale laser facilities on the horizon and the prospect of investigating these hitherto unexplored regimes, this review explores the basic physical processes of radiation reaction and QED in strong fields, how they are treated theoretically and in simulation, the new collective dynamics they unlock, recent experimental progress and plans, and possible applications for high-flux particle and radiation sources.

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    • Received 20 May 2021

    DOI:https://doi.org/10.1103/RevModPhys.94.045001

    © 2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    High intensity laser-plasma interactionsRadiation & particle generation in plasmasSchwinger effect
    Accelerators & BeamsPlasma Physics

    Authors & Affiliations

    A. Gonoskov, T. G. Blackburn, and M. Marklund

    • Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden

    S. S. Bulanov

    • Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

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    Vol. 94, Iss. 4 — October - December 2022

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    • Figure 1
      Figure 1

      Cube of theories. Its three axes correspond to relativistic (c), quantum (ℏ), and high-intensity effects (Ecr) and its vertices correspond to the theories: (0,0,0) is classical mechanics; (c,0,0) is special relativity; (0,ℏ,0) is quantum mechanics; (c,ℏ,0) is quantum field theory; (c,0,Ecr) is classical electrodynamics; (0,ℏ,Ecr) is atomic, molecular, and optical physics; and (c,ℏ,Ecr) is high-intensity particle physics. Here Ecr=m2c3/eℏ is the critical field of QED, where m is the electron mass and e is the elementary charge. Adapted from [84].

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    • Figure 2
      Figure 2

      Laser facilities on the map of pulse energy and pulse duration. Data were taken from [404], [127], and individual facilities; see Table 2. For illustration, we show the nominal peak intensity levels estimated, assuming ideal f/2 focusing of a linearly polarized pulse with Gaussian spatial and temporal profiles and a nominal wavelength of λ=1  μm. The physics in access is denoted by color and the following characteristic intensity scales (see Sec. 1c): 3.5×1016  W/cm2 [atomic field corresponding to a field strength of 1 a.u.; see 314], 1.37×1018  W/cm2 (relativistic electron corresponding to a0=1), 8×1022  W/cm2 [radiation-dominated dynamics corresponding to Ld=λ, assuming that γ=a0; see Eq. (13)], 3.5×1023  W/cm2 [avalanche-type cascades corresponding to Lp=λ, assuming that γ=a0; see Eq. (16)], and 4.65×1029  W/cm2 (corresponding to the Schwinger field strength). Inset: effective intensity boost that one would gain by splitting the laser power among the specified number of beams and colliding them so that the electric field is summed up coherently; see the Appendix of [212]. The boost is shown via the corresponding relative shift of location on the map for the cases using f/2 (left side) and f/1 (right side) focusing, and the dotted line shows the ultimate boost given by the dipole wave; see Sec. 5e3.

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    • Figure 3
      Figure 3

      Interaction regimes in the space of the normalized field amplitude a0 and the quantum nonlinearity parameter χ. We identify the importance of different processes by comparing key space scales with a characteristic laser wavelength λ=1  μm. The decreasing depletion length Ld [Eq. (13)] denotes the transition from weak to strong radiation losses (Ld>103λ in white, Ld<λ in dark gray). A quantization length Lq [Eq. (14)] comparable to λ indicates that the discrete nature of radiation emission is important (Lq>λ, checkered area). As the pair-creation length Lp [Eq. (16)] becomes smaller than λ, electron-positron pair creation by photons in strong fields becomes prolific (Lp<λ in light blue). The field amplitude necessary for the onset of vacuum pair creation by the Schwinger mechanism, shown in violet, assumes a nonzero F=a0(ℏω0/mc2). Key limits on theoretical treatments are as follows: the field cannot be assumed to be constant if the formation length Lf<λ [Eq. (15)] (yellow line), perturbation theory in SFQED is expected to break down when αχ2/3≳1 (blue line), and a general electromagnetic field cannot be approximated as crossed if χ2<F,G. We also outline the prospects for laser experiments in interactions with a stationary plasma target (γ≲a0, red dashed line) or ultrarelativistic electron beams (green lines). Numbered green points indicate experiments that have probed the strong-field regime (in order of publication): (1) [75] and [97], (2) [575], (3) [119], and (4) [425].

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    • Figure 4
      Figure 4

      Interaction regimes as a function of the amplitude a0 and the wavelength λ of the electromagnetic wave driving an electron, using the same key as in Fig. 3. The importance of RR effects is parametrized by Ld [Eq. (13)] and Lq [Eq. (14)], which are both wavelength dependent.

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    • Figure 5
      Figure 5

      The Lorentz factor γ of an electron in a rotating electric field of normalized amplitude a0, as predicted by the LAD and Landau-Lifshitz equations, Eqs. (18) and (19), respectively: linear (left panel) and log scaled (right panel). The vertical lines indicate, from left to right, onset of classical radiation-reaction effects, Eq. (73) (red line); a quantum parameter of unity, Eq. (74) (orange line); and the QED-critical field strength, Eq. (1) (black line). Here ϵrad=1.47×10−8, which is equivalent to a wavelength of 0.8  μm. Adapted from [89].

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    • Figure 6
      Figure 6

      Radiation at unphysically large frequencies is predicted by classical theory if χe≳1: classical power spectra (dashed lines) and quantum-corrected power spectra (solid lines) at χe=0.1 (blue lines, left), 1 (green lines, center), and 10 (orange lines, right), using Eqs. (22) and (23), respectively.

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    • Figure 7
      Figure 7

      Nonperturbativity in strong-field quantum electrodynamics arises in two ways: from the coupling between the charge and the background (external) field (lower set of wavy lines, in red) and the coupling between the charge and the radiation (quantized) field (upper set of wavy lines, in orange). For a0>1, the former interaction must be taken into account exactly, i.e., to all orders in a0, as indicated by the double fermion lines in a diagrammatic representation. For fields with a sufficient magnitude or duration, higher-order contributions to the coupling with the radiation field can dominate lower-order terms.

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    • Figure 8
      Figure 8

      Evolution of a Volkov wave packet (in a time t and a coordinate z) in a laser pulse with a normalized amplitude a0=2 and duration Δϕ=20 (color or gray scale density indicates the wave function). The wave packet begins with a Gaussian distribution of light-front momentum (mean mc and standard deviation 0.05mc) and zero transverse momentum. The centroid closely follows the equivalent classical trajectory, which is indicated as a solid black line. The laser pulse propagates between the two dashed lines. From [477].

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    • Figure 9
      Figure 9

      Feynman diagrams of the Compton (e→eγ) and Breit-Wheeler (γ→ee) processes. Double fermion lines indicate that the process occurs in an external field.

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    • Figure 10
      Figure 10

      Classically, the photon formation length Lf can be related to the emission angle θγ and the instantaneous radius of curvature rc of the electron trajectory. From [61].

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    • Figure 11
      Figure 11

      One-loop mass operator, polarization operator, and vertex correction displayed from left to right.

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    • Figure 12
      Figure 12

      Dressed loop expansion of the polarization operator P (top row) and mass operator M (bottom row). According to the Ritus-Narozhny conjecture, these diagrams represent the dominant contribution at n loops, and αχ2/3 is the true expansion parameter of SFQED in the regime χ≫1. From [581].

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    • Figure 13
      Figure 13

      Examples of higher-order SFQED processes. Trident pair creation, double nonlinear Compton scattering, phototrident pair creation, and photon splitting are displayed from left to right.

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    • Figure 14
      Figure 14

      G(χe) is the factor by which quantum effects reduce the radiation power from its classically predicted value: the full expression (blue solid line) and limiting values at small and large χe (black dashed line on the left and red dashed line on the right, respectively) from Eqs. (62) and (63), respectively.

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    • Figure 15
      Figure 15

      Overview of the ways that spin influences, and is influenced by, particle degrees of freedom (top and right blue panels) and radiation (left yellow panel). Individual couplings are denoted by arrows, with those introduced in Sec. 2d given in black. Adapted from [526].

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    • Figure 16
      Figure 16

      Spin-resolved photon-emission rates dNs,s′/dτ, normalized to the spin-averaged rate dN/dτ, for electrons orbiting in a rotating electric field of normalized amplitude a0. Here s and s′ are the projections of the electron initial and final spin on the axis of rotation. From [131].

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    • Figure 17
      Figure 17

      Schematic representation of the energy spectrum of the electromagnetic field in a high-intensity laser-matter interaction. The frequencies shown (from left to right) are characteristic of the target (ωt=c/L, with target size L), the laser (ωL), the plasma density (ωp), the upper limit of coherent emission processes (ωcoh), and incoherent synchrotron emission (ωc). From [213].

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    • Figure 18
      Figure 18

      Particle merging in a simulation of a laser-driven QED cascade indicating energy conservation and growth in the number of particles over the course of the simulation. Adapted from [551].

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    • Figure 19
      Figure 19

      Principal experimental schemes aimed at the study of nonlinear QED. Upper panel: laser–electron-beam interactions (all-optical setup). Lower panel: colliding laser pulses. Adapted from [86].

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    • Figure 20
      Figure 20

      Radiation-free direction nRFD+, as a function of the end point of the electric-field vector E, given a fixed magnetic-field vector B (blue arrow). Arrows denote the projection of nRFD+ onto the plane spanned by E and B, and the color scale shows the projection on B×E: values are negative (positive) in the upper (lower) half. From [215].

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    • Figure 21
      Figure 21

      Radiation-reaction trapping in simulations of laser-wakefield acceleration. Shown are the densities of (a),(d) the electrons, (b),(e) the protons, and (g) the γ photons, as well as (c),(f) the transverse component of the electric field obtained using 3D PIC simulations with (right column) and without (left column) radiation reaction. From [274].

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    • Figure 22
      Figure 22

      Electron number density as a function of the wave amplitude (here called a=a0) in a linearly polarized, standing electromagnetic wave. As a increases, the ponderomotive, normal, and anomalous radiative trapping regimes are accessed. The curves in the lower region indicate the ponderomotive potential (thick gray line), as well as the electric (thin red line) and magnetic (dot-dashed blue line) field amplitudes, in arbitrary units. From [212].

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    • Figure 23
      Figure 23

      Explanation of ART through the net migration of electrons toward electric-field maxima. The particle trajectory (black curve, axis to the left), its gamma factor (red dashed curve, axis to the right), and asymptotic trajectories (thin green curves) are shown together with the regions of electric-field (red) and magnetic-field (blue) dominance (see details in the text). From [212].

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    • Figure 24
      Figure 24

      Poincaré sections showing particle coordinates in the space of position x and momentum px at time intervals equal to the period of the driving field. (a) a0=617, ϵrad=1.2×10−8. (b) a0=778, ϵrad=6×10−9. (c) a0=1996, ϵrad=1.2×10−9 From [92].

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    • Figure 25
      Figure 25

      Electron trajectories in the standing wave formed by two colliding circularly (upper frame) and linearly (lower frame) polarized laser pulses propagating along the x axis with I=1.37×1024  W/cm2, λ=1  μm, duration 33 fs, and focal spot 3  μm. Modeled with semiclassical radiation reaction [Eq. (64)]. From [179].

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    • Figure 26
      Figure 26

      Electron trajectories in the standing wave formed by two colliding circularly (upper frame) and linearly (lower frame) polarized laser pulses propagating along the x axis with I=1.11×1024  W/cm2, λ=1  μm, duration 30 fs, and focal spot 3  μm. Modeled with quantum stochastic radiation reaction. From [276].

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    • Figure 27
      Figure 27

      Feedback between SFQED processes and classical relativistic plasma dynamics in a QED plasma.

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    • Figure 28
      Figure 28

      Experimental configurations envisaged for (top panel) laser-electron and (bottom panel) laser-γ collisions at LUXE. From [3].

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    • Figure 29
      Figure 29

      All-optical realization of a laser–electron-beam collision experiment. One laser pulse is focused using a short-focal-length optic with a hole in it to allow for counterpropagation of an electron beam that is accelerated by a laser wakefield in a gas jet. Electrons, and the radiation they emit, are transmitted through this hole before being diagnosed. The collision is timed so that it occurs close to the edge of the gas jet, where the electron beam is smallest, to maximize overlap with the laser pulse. From [119].

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    • Figure 30
      Figure 30

      Experimental evidence of radiation reaction in the correlation between the energy of the electron beam after the collision and the critical energy of the γ-ray spectrum as measured in four successful collisions (points), which are compared to simulations of the interaction that include various models of radiation reaction and fluctuations in the electron energy and laser intensity. Colored (shaded) regions from left to right: classical RR (blue), stochastic RR (orange), and no RR (green). From [119].

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    • Figure 31
      Figure 31

      Experimental evidence of radiation reaction and quantum corrections: electron energy spectra as measured at best overlap, without the scattering laser (black line) and with it (red line), and from simulations without (a) radiation reaction, (b) classical (Landau-Lifshitz) radiation reaction, (c) a quantum-corrected Landau-Lifshitz model, and (d) stochastic radiation reaction (PIC and single-particle codes in green and blue, respectively), all including experimental uncertainties in the initial electron spectrum, the magnetic spectrometer, and the laser intensity. Adapted from [425].

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    • Figure 32
      Figure 32

      Interaction regimes in the collision of an electron beam of energy ϵ0 with a dipole wave generated by MCLPs with total power P. Number of high-energy (ℏω>ϵ0/2) photons per incident electron, red-orange color scale, solid contours; number of electron-positron pairs per incident electron, blue-green color scale, dashed contours; final electron-beam energy, percent of initial value, gray color scale, dotted contours. From [361].

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    • Figure 33
      Figure 33

      Brightness of radiation emitted in high-intensity laser interactions with electron beams (empty circles) or plasma targets (filled circles), as well as in nonlaser strong-field environments, as (1 and 2) measured in recent experiments and (3–10) predicted using simulations.

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    • Figure 34
      Figure 34

      Efficiency of γ-ray generation in plasmas driven by single (filled circles), dual (double circles), and multiple (diamonds) lasers as predicted by simulations.

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    • Figure 35
      Figure 35

      Number of positrons produced in high-intensity laser-plasma interactions. For laser–electron-beam interactions (empty circles), the energy of the electron beam is noted in brackets. Points marked with asterisks indicate experimental results from LWFA electron-beam interactions with high-Z foils; in these cases the laser power is not indicated.

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    • Figure 36
      Figure 36

      Dedicated SFQED facility housing multiple petawatt-class lasers. The facility can operate in several modes, including (i) an e+e− collider, with all lasers used to drive the staged acceleration of electron and positron beams; (ii) a laser–electron-beam collider where half of the lasers drive the staged acceleration of the electron beam and the remaining half provides the high-field region via the multiple colliding pulses configuration; and (iii) all the laser pulses are brought to the interaction point to generate the highest intensity possible. From [592].

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