Travelling waves and light-front approach in relativistic electrodynamics

Abstract

We briefly report on a recent proposal [1] for simplifying the equations of motion of charged particles in an electromagnetic (EM) field F µν that is the sum of a plane travelling wave F µν t (ct − z) and a static part F µν s (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 & 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).

Light-front approach to relativistic electrodynamics

“…collisions among (sufficiently close) Z-electron layers with Z < Z d , occur only at sufficiently large times, due to the nontrivial Z-dependence of (39) in the regions where n 0 (Z) is non-homogenous (in particular near the vacuum-plasma interface Z ∼ 0). There our hydrodynamic description is globally self-consistent for t < t c (t c stands for the time of the first wave-breaking) and allows to determine [24] t c and where wave-breakings occur; the use of kinetic theory (a statistical description of the plasma in phase space that takes collisions into account) is necessary after the first wave-breaking. As known, a moderate wave-breaking is actually welcome as a possible injection mechanism in the plasma wave of a bunch of electrons fast enough and in phase to be accelerated 'surfing' the wave, according to the LWFA mechanism [5]; a phase of the right sign arises where n 0 (Z) decreases.…”

“…All Eulerian fields are found to depend on t, z only through ct−z, e.g. u(t, z) = û(ct−z),...: a plasma travelling-wave with spacial period Ξ H (n 0 ) and phase velocity c trails the pulse for z ≥ Z d [24]. On the other hand, plasma wave breakings [25], i.e.…”

Hydrodynamic impacts of short laser pulses on plasmas

“…Since at the impact time t = 0 the plasma is made of two static fluids, by continuity such a hydrodynamical description (HD) is justified and one can neglect the depletion of the pulse at least for small t > 0; the specific time lapse is determined a posteriori, by self-consistency. This allows us to reduce (see [28,29], or [30,31,32,33] for shorter presentations) the system of Lorentz-Maxwell and continuity partial differential equations (PDEs) into ordinary ones, more precisely into the following continuous family of decoupled Hamilton equations for systems with one degree of freedom. Each system determines the complete Lagrangian (in the sense of non-Eulerian) description of the motion of the electrons having a same initial longitudinal coordinate Z > 0 (the Z-electrons, for brevity), and reads…”

Energy cutoff, effective theories, noncommutativity, fuzzyness: the case of $O(D)$-covariant fuzzy spheres

“…All of them admit (in general, non-equivalent) generalizations; see e.g. [37,38,39,40,41,42], also for an overview on applications in elementary particle, nuclear, atomic, condensed matter, plasma physics. The canonical SCS fulfills the following properties: a) Strong continuity of φ z as a function of z ∈ Ω;…”