Travelling waves and light-front approach in relativistic electrodynamics

TL;DR

This paper discusses a method using light-front coordinates to simplify the equations of motion for charged particles in combined electromagnetic fields, enabling easier analysis of extreme acceleration scenarios and plasma interactions.

Contribution

It introduces a light-front approach to reduce complex PDEs in relativistic electrodynamics to simpler ODE systems for specific field configurations.

Findings

Simplification of equations of motion in combined EM fields.

Decoupling of PDEs into ODEs in extreme acceleration cases.

Potential to analyze plasma wave phenomena and slingshot effects.

Abstract

We briefly report on a recent proposal (Fiore in J Phys A Math Theor 51:085203, 2018) for simplifying the equations of motion of charged particles in an electromagnetic (EM) field $F^{\mu\nu}$ that is the sum of a plane travelling wave $F_t^{\mu\nu}(ct\!-\!z)$ and a static part $F_s^{\mu\nu}(x,y,z)$; it adopts the light-like coordinate $\xi=ct\!-\!z$ instead of time $t$ as an independent variable. We illustrate it in a few cases of extreme acceleration, first of an isolated particle, then of electrons in a plasma in plane hydrodynamic conditions: the Lorentz-Maxwell \& continuity PDEs can be simplified or sometimes even completely reduced to a family of decoupled systems of ordinary ones; this occurs e.g. with the impact of the travelling wave on a vacuum-plasma interface (what may produce plasma waves or the slingshot effect).