Novel approach to stochastic acceleration of electrons in colliding laser fields

Abstract

The mechanism of stochastic electron acceleration in colliding laser waves is investigated by employing proper canonical variables and effective time, such that the new Hamiltonian becomes time independent when the perturbative (weaker) laser wave is absent. The performed analytical analysis clearly reveals the physical picture of stochastic electron dynamics. It shows that when the amplitude of the perturbative laser field exceeds some critical value, stochastic electron acceleration occurs within some electron energy range. The conditions, at which the maximum electron energy gained under stochastic acceleration is greatly exceeding the ponderomotive energy scaling based on the amplitude of the dominant laser, are derived.

Electron dynamics in counter-propagating laser waves

“…This is because Py simply increases the effective electron mass. Then, following [30] by using the property of f (β) ≡ 4π 2 β 2 |Ai ′ (β)|, we find that the stochastic acceleration is only possible for a 1 > a sx , where…”

“…In this section, we will summarize the main idea of how to find the new Hamiltonian [30] and then examine the unperturbed electron trajectories in this new framework. To this purpose, in the following, the dimensionless variables will be used, where r and t are normalized, respectively, by the dominant laser wavenumber k and kc (c is the speed of light in vacuum).…”

“…Therefore, γ max can significantly exceed the ponderomotive scaling either for H min < H 0 (which corresponds to the electron moving along the dominant laser propagation direction and energy gain ratio is H 0 /H min ) or for H max > E p /H 0 (where the electron moves along the perturbative laser propagation direction and energy gain ratio is H max H 0 /E p ). The latter case requires k 1 ≫ a ≫ 1 [30], which is not considered in this paper.…”

“…The expressions for lower and upper boundaries of the stochastic region [30] remain unchanged with the presence of Py :…”

“…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. It demonstrated that the electron energy gained from a relativistic laser wave via the stochastic acceleration due to the presence of a perturbative counter-propagating laser wave can greatly exceed the ponderomotive energy scaling, where the essential role of the perturbation is to change the dephasing rate (new Hamiltonian) between the electron and dominant laser.…”