On a ‘time’ reparametrization in relativistic electrodynamics with travelling waves

Abstract

Abstract. We briefly report on our method [23] of simplifying the equations of motion of charged particles in an electromagnetic (EM) 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 ξ 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 "impulses".

Travelling waves and a fruitful ‘time’ reparametrization in relativistic electrodynamics

“…We acknowledge partial support by GNFM (Gruppo Nazionale di Fisica Matematica) of INdAM. Note added in proof: A short summary about the present results can be found in [47].…”

“…(49) Note that this reduces to (46) in the limit κ → 0, and again ∂v/∂ξ =v . In the case of initial conditions x(0) = 0 = u(0) then (49) becomes (46)(47).…”

“…We also recall how to tune B s = B z k so that the acceleration by the pulse becomes resonant, and the quantitative features of this mechanism (cyclotron autoresonance). We emphasize that instead our solution (47) is exact for all pumps ⊥ , and with it one can also determine the deviations from autoresonance due to an arbitrary modulation (21)(22) of the monochromatic pulse.…”

Travelling waves and light-front approach in relativistic electrodynamics

“…the backward acceleration and expulsion from the plasma of some surface electrons (those with smallest Z and closest to the z-axis) with remarkable energy. For reviews see also [29,30,31].…”

“…When v = 0 then(31) implies ∆ = −M ∆/ŝ 3 . In the nonrelativistic regime ŝ 1, ξ(t) ct, cd/dξ d/dt, and this becomes the nonrelativistic harmonic equation ∆ = −ω 2 p ∆.…”