We illustrate how our recent light-front approach simplifies relativistic electrodynamics with an electromagnetic (EM) field $F^{mu u}$ that is the sum of a (even very intense) plane travelling wave $F_t^{mu u}(ct!-!z)$ and a static part $F_s^{mu u}(x,y,z)$; 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.)
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