On plane waves in diluted relativistic cold plasmas

We briefly report on some exact results [G. Fiore, J. Phys. A: Math. Theor. 47 (2014) 225501] regarding plane waves in a relativistic cold plasma. If the plasma, initially at rest, is reached by a transverse plane electromagnetic travelling-wave, then its motion has a very simple dependence on this wave in the limit of zero density, otherwise can be determined by an iterative procedure whose accuracy decreases with time or the plasma density. Thus one can describe in particular the impact of a very intense and short laser pulse onto a plasma and determine conditions for the "slingshot effect" [G. Fiore, R. Fedele, U. De Angelis, "The slingshot effect: a possible new laser-driven high energy acceleration mechanism for electrons", arXiv:1309.1400] to occur. The motion in vacuum of a charged test particle subject to a wave of the same kind is also determined, for any initial velocity.