Emission and its back-reaction accompanying electron motion in relativistically strong and QED-strong pulsed laser fields

The emission from an electron in the field of a relativistically strong laser pulse is analyzed. At pulse intensities of $J\ge 2\times {10}^{22}\text{W}/{\text{cm}}^2$ the emission from counterpropagating electrons is modified by the effects of quantum electrodynamics (QED), as long as the electron energy is sufficiently high: $\mathcal{E}\ge 1\text{GeV}$. The radiation force experienced by an electron is for the first time derived from the QED principles and its applicability range is extended toward the QED-strong fields.

Figure 1

The volume over which to integrate the matrix element while finding the emission probability: in the standard scheme for the dipole emission (in dashed lines) and in the TST (in solid lines). Arrows show the direction, along which the Heisenberg operator advances the wave functions.

Figure 2

Emission spectra for various values of $\chi$.

Figure 3

Emitted radiation power in the QED approach vs classical (solid); an interpolation formula $I_{\text{QED}}=I_{\text{cl}}/{\left(1+1.04\sqrt{I_{\text{cl}}/I_C}\right)}^{4/3}$ (dashed).

Figure 4

The emission spectrum for 600 MeV electrons interacting with 30 fs laser pulses of intensity $2\times {10}^{22}\text{W}/{\text{cm}}^2$: with (solid) or without (dashed) accounting for the QED effects. Here $\hslash {\omega }_{c0}\approx 1.1\text{MeV}$ for $\lambda =0.8\mu \text{m}$.

Figure 5

Expectation of the emitted photon energy. In dimensional units $\Delta \mathcal{E}=\hslash {\omega }^{\prime }$ and $\mathcal{E}$ is the dimensional energy of an electron prior to emission.