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We simplify the nonlinear equations of motion of charged particles in anexternal electromagnetic field that is the sum of a plane travelling waveF_t(ct-z) and a static part F_s(x,y,z): by adopting the light-like coordinatect-z instead of time t as an independent variable in the Action, Lagrangian andHamiltonian, and deriving the new Euler-Lagrange and Hamilton equationsaccordingly, we make the unknown z(t) disappear from the argument of F_t. Westudy and solve first the single particle equations in few significant cases ofextreme accelerations. In particular we obtain a rigorous formulation of aLawson-Woodward-type (no-final-acceleration) theorem and a compact derivationof cyclotron autoresonance, beside new solutions in the presence of uniformF_s. We then extend our method to plasmas in hydrodynamic conditions and applyit to plane problems: the system of partial differential equations may bepartially solved and sometimes even completely reduced to a family of decoupledsystems of ordinary ones; this occurs e.g. with the impact of the travellingwave on a vacuum-plasma interface (what may produce the slingshot effect).Since Fourier analysis plays no role in our general framework, the method canbe applied to all kind of travelling waves, ranging from almost monochromaticto socalled "impulses", which contain few, one or even no complete cycle.

Travelling waves and a fruitful `time' reparametrization in relativistic electrodynamics