  We illustrate how our recent light-front approach simplifies relativistic
electrodynamics with an electromagnetic (EM) field $F^{\mu\nu}$ that is the sum
of a (even very intense) plane travelling wave $F_t^{\mu\nu}(ct\!-\!z)$ and a
static part $F_s^{\mu\nu}(x,y,z)$; it adopts the light-like coordinate
$\xi=ct\!-\!z$ instead of time $t$ as an independent variable. This can be
applied to several cases of extreme acceleration, both in vacuum and in a cold
diluted plasma hit by a very short and intense laser pulse (slingshot effect,
plasma wave-breaking and laser wake-field acceleration, etc.)
