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

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We simplify the nonlinear equations of motion of charged particles in an external electromagnetic field that is the sum of a plane travelling wave and a static part : by adopting the light-like coordinate instead of time t as an independent variable in the Action, Lagrangian and Hamiltonian, and deriving the new Euler–Lagrange and Hamilton equations accordingly, we make the unknown disappear from the argument of . We first study and solve the single particle equations in a few significant cases of extreme accelerations. In particular, we obtain a rigorous formulation of a Lawson–Woodward-type (no-final-acceleration) theorem and a compact derivation of cyclotron autoresonance, beside new solutions in the presence of uniform . We then extend our method to plasmas in hydrodynamic conditions, and apply it to plane problems: the system of (Lorentz–Maxwell + continuity) partial differential equations may be partially solved 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 the slingshot effect).Our method can be seen as an application of the light-front approach. Since Fourier analysis plays no role in our general framework, the method can be applied to all kinds of travelling waves, ranging from almost monochromatic to so-called ‘impulses’, which contain few, one or even no complete cycles.