On a `time' reparametrization in relativistic electrodynamics with travelling waves

TL;DR

This paper presents a method that simplifies the equations of motion for charged particles in electromagnetic fields with traveling waves by reparametrizing time and variables, enabling easier analysis of laser-induced accelerations.

Contribution

The authors introduce a novel reparametrization technique that reduces complex PDE systems to decoupled Hamiltonian systems, applicable to various traveling wave scenarios.

Findings

Method simplifies equations of motion for charged particles.

Applicable to a wide range of traveling wave types.

Reduces PDE systems to 1D Hamiltonian equations.

Abstract

We briefly report on our method [Fiore JPA 2017] of simplifying the equations of motion of charged particles in an electromagnetic field that is the sum of a plane travelling wave and a static part; it is based on changes of the dependent variables and the independent one (light-like coordinate instead of time t). We sketch its application to a few cases of extreme laser-induced accelerations, both in vacuum and in plane problems at the vacuum-plasma interface, where we are able to reduce the system of the (Lorentz-Maxwell and continuity) partial differential equations into a family of decoupled systems of Hamilton equations in 1 dimension. Since Fourier analysis plays no role, the method can be applied to all kind of travelling waves, ranging from almost monochromatic to socalled "impulse".