We discuss the physical processes, which take place in a multi-component plasma set in expansion by a minority of energetic electrons. The expansion is in the form of a collisionless rarefaction wave associated with three types of electrostatic shocks. Each shock manifests itself in a potential jump and in the spatial separation of plasma species. The shock front associated with the proton-electron separation sets the maximum proton velocity. Two other shocks are due to the hot-cold electron separation and the light-heavy ion separation. They result in the light ion acceleration and their accumulation in the phase space. These structures open possibilities for control of the number and the energy spectrum of accelerated ions. Simple analytical models are confirmed in numerical simulations where the ions are described kinetically, and the electrons assume the Boltzmann distribution.

The acceleration of light and heavy ions in an expanding plasma slab with hot electrons produced by an intense and short laser pulse is studied by using the hybrid Boltzmann–Vlasov–Poisson model. Spatial profiles, energy distributions, and maximum energies of accelerated ions are analyzed in function of the plasma and hot electron parameters. The crucial parameter for ion acceleration is found to be the ratio of the foil thickness to the hot electron Debye length. Special attention is paid to characterization of protons accelerated from a thin hydrogenated layer at the target surface. The evolution of the proton spectrum is studied for the cases of isothermal and cooling hot electron distributions. The obtained dependencies of the ion energy on the pulse duration and the target characteristics allow one to define the optimal conditions for the ion acceleration with lasers.

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Collisionless shocks generated by colliding relativistic plasmas are studied using particle-in-cell (PIC) simulations. The shock is produced due to the Weibel instabilities that generate current and density filaments and small-scale magnetic fields that are amplified from initial fluctuations. Localized regions of the strong magnetic field in the form of magnetic dipole vortices upstream of the shock are observed in the simulation developed during the nonlinear evolution of the electron and ion filaments. The vortices developing from the merger and subsequent pinching of the small-scale filaments are shown to be moving in the direction opposite to that of the shock. We also found an analytical estimate of the drift velocity of the vortices that are confirmed by the PIC simulations.