# Electron dynamics in counter-propagating laser waves

## TL;DR

This paper introduces a new Hamiltonian approach to analyze electron dynamics in counter-propagating laser waves, revealing stochastic acceleration mechanisms and the effects of superluminal phase velocity through analytical and numerical methods.

## Contribution

A novel Hamiltonian framework is developed to study stochastic electron acceleration in counter-propagating laser fields, including threshold conditions and phase velocity effects.

## Key findings

- Threshold laser amplitude for stochastic acceleration is derived.
- Superluminal phase velocity reduces maximum electron energy.
- Analytical results are validated by numerical simulations.

## Abstract

The electron dynamics in counter-propagating laser waves is investigated by employing a novel approach, where the new Hamiltonian is time-independent when the perturbative laser wave is absent. The physical picture of stochastic electron dynamics is clearly revealed and the threshold values of the amplitude of the perturbative laser field for triggering stochastic electron acceleration are derived for different laser polarization directions and initial electron momentum. It demonstrates that the dephasing rate (new Hamiltonian) between the electron and the dominant laser can be randomly reduced if the amplitude of the perturbative laser is above the threshold such that the electron could be accelerated by the dominant laser well beyond the ponderomotive energy scaling. The impact of a superluminal phase velocity is examined, which slightly changes the stochastic region in Hamiltonian space if the superluminal phase velocity is under a threshold value but significantly decreases the maximum electron kinetic energy. All the analytic considerations are confirmed by the numerical simulations.