On the impact of short laser pulses on cold diluted plasmas

Abstract

We analytically study the impact of a 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 $Z\ge 0$) of decoupled systems of non-autonomous Hamilton equations with 1 degree of freedom, which determine how electrons initially located in the layer $Z\le z<Z+dZ$ move; $\xi =ct-z$ 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 $\xi$. 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.

Latex2e file, 46 pages, 10 figures. Final version accepted in Physica D: nonlinear phenomena

References in corpus (4)

• The REsonant Multi-Pulse Ionization injection
• On plane waves in diluted relativistic cold plasmas
• Hydrodynamic impacts of short laser pulses on plasmas
• On a `time' reparametrization in relativistic electrodynamics with travelling waves

Cited by in corpus (6)

• Hydrodynamic impacts of short laser pulses on plasmas
• On a `time' reparametrization in relativistic electrodynamics with travelling waves
• The time-dependent harmonic oscillator revisited
• An analytical optimization of plasma density profiles for downramp injection in laser wake-field acceleration
• Hydrodynamic regime and cold plasmas hit by short laser pulses
• A preliminary analysis for efficient laser wakefield acceleration