Stochastic electron heating in the laser and quasi-static electric and magnetic fields

Abstract

The dynamics of relativistic electrons in the intense laser radiation and quasi-static electromagnetic fields both along and across to the laser propagating direction are studied in the 3/2 dimensional Hamiltonian framework. It is shown that the unperturbed oscillations of the relativistic electron in these electric fields could exhibit a long tail of harmonics which makes an onset of stochastic electron motion be a primary candidate for electron heating. The Poincaré mappings describing the electron motions in the laser and electric fields only are derived from which the criterions for instability are obtained. It follows that for both transverse and longitudinal electric fields, there exist upper limits of the stochastic electron energy depending on the laser intensity and electric field strength. Specifically, these maximum stochastic energies are enhanced by a strong laser intensity but weak electric field. Such stochastic heating would be reduced by the superluminal phase velocity in both cases. The impacts of the magnetic fields on the electron dynamics are different for these two cases and discussed qualitatively. These analytic results are confirmed by the numerical simulations of solving the 3/2D Hamiltonian equations directly.

Novel approach to stochastic acceleration of electrons in colliding laser fields

“…Noticing that the Hamiltonian in Eq. ( 5) has similar structure to that for electron in the laser and quasi-static electric fields considered in [16], we find that, for relativistic case a > 1, unperturbed (or weakly perturbed) electron trajectories have characteristics of zigzag time dependence of canonical coordinate χ (e.g., see the upper panel of Fig. 1).…”

Electron dynamics in laser and quasi-static transverse electric and longitudinal magnetic fields

“…However, from Eq. (3) we have zz P C U(y) ( 1)P         , which indicates that whereas static electric field could enhance the electron-laser interaction when U approaches C  , the superluminal phase velocity of laser radiation, 1  , would reduce it [19]. For simplicity, in the rest of this paper, we consider the luminal case, 1  , and assume that x P0  .…”

“…where j  is the "time" of previous "collision". In [19] it was shown that the transverse electric filed itself leads to stochastic electron heating, depending on laser polarization, up to the energies…”

“…Recently, it was shown that the electron dynamics in an arbitrarily polarized laser radiation and transverse or longitudinal quasi-static electric fields as well as transverse magnetic field can be described by the 3/2 dimensional (3/2D) Hamiltonian approach [17,18], which greatly simplifies the analysis of electron interactions with laser and quasi-static electromagnetic fields. It was demonstrated [19] that, the acceleration of electron is attributed to an onset of stochasticity [20,21].…”

Electron dynamics in counter-propagating laser waves

“…Recently, it was shown that, by employing the integrals of motion for electrons in laser and quasi-static electromagnetic fields, the electron dynamics can be described by the 3/2 dimensional (3/2D) Hamiltonian approach [25,26], which has greatly simplified the analysis of electron dynamics [27,28] and the boundary of electron energy due to the stochastic motion was obtained by finding the Chirikov-like mapping [29]. Such method has been extended to the case of electrons in the colliding laser waves [30] by employing proper canonical variables and effective time, such that the new Hamiltonian becomes time independent when the perturbative laser wave is absent, where the electron dynamics for luminal planar laser waves, which are linearly polarized in the same direction, and transverse canonical momentum be-ing zero was exhaustively examined.…”