Travelling waves and light-front approach in relativistic electrodynamics

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 field F_μν that is the sum of a plane travelling wave F_μνt(ct−z) and a static part F_μνs(x,y,z) ; it adopts the light-like coordinate ξ=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 and 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).