Classical and quantum dynamics of a charged scalar particle in a background of two counterpropagating plane waves

TL;DR

This paper analyzes the classical and quantum behavior of a charged scalar particle in a background of two counterpropagating plane waves, revealing limitations of high-energy approximations and identifying forbidden parameter regimes.

Contribution

It provides exact solutions and examines the validity of approximations for scalar particle dynamics in complex plane wave backgrounds, highlighting new phenomena.

Findings

High-energy approximation for the modified Volkov wavefunction is inaccurate at all energies.

The solution is unstable when photon emission is included.

Forbidden parameter regimes are identified in quantum and classical cases.

Abstract

We consider a scalar particle in a background formed by two counter-propagating plane waves. Two cases are studied: i) dynamics at a magnetic node and ii) zero initial transverse canonical momentum. The Lorentz and Klein-Gordon equations are solved for these cases and approximations analysed. For the magnetic node solution (homogeneous, time-dependent electric field), the modified Volkov wavefunction which arises from a high-energy approximation is found to be inaccurate for all energies and the solution itself unstable when photon emission (nonlinear Compton scattering) is included. For the zero initial transverse canonical momentum case, in both quantum and classical cases, forbidden parameter regimes, absent in the plane wave model, are identified.