On the impact of short laser pulses on cold diluted plasmas

Abstract

We analytically study the impact of a (possibly, very intense) short laser pulse onto an inhomogeneous cold diluted plasma at rest, in particular: the duration of the hydrodynamic regime; the formation and the features of plasma waves (PWs); their wave-breakings (WBs); the motion of test electrons injected in the PWs.If the pulse is a plane wave travelling in the z-direction, and the initial plasma density (IPD) depends only on z, then suitable matched bounds on the maximum and relative variations of the IPD, as well as the intensity and duration of the pulse, ensure a strictly hydrodynamic evolution of the electron fluid during its whole interaction with the pulse, while ions can be regarded as immobile. This evolution is ruled by a family (parametrized by Z≥0) of decoupled systems of non-autonomous Hamilton equations with 1 degree of freedom, which determine how electrons initially located in the layer Z≤z<Z+dZ move; ξ=ct−z replaces time t as the independent variable. This family of ODEs is obtained by reduction from the Lorentz–Maxwell and continuity PDEs for the electrons’ fluid within the spacetime region where the change of the pulse is negligible. After the laser–plasma interaction the Jacobian of the map from Lagrangian to Eulerian coordinates is linear-quasi-periodic in ξ. We determine spacetime locations and features of the first wave-breakings of the wakefield PWs, the motion of test electrons (self-)injected in the PWs. The energy of those trapped in a single PW trough grows linearly with the distance gone, where the IPD is constant.If the pulse has cylindrical symmetry and a not too small radius, the same conclusions hold for the part of the plasma enclosed within the causal cone swept by it.This computationally light approach may help in a preliminary study of extreme acceleration mechanisms of electrons (LWFA, etc.), before 2D or 3D PIC simulations.