The formation of strong, high Mach number (2-3), electrostatic shocks by laser pulses incident on overdense plasma slabs is observed in one- and two-dimensional particle-in-cell simulations, for a wide range of intensities, pulse durations, target thicknesses, and densities. The shocks propagate undisturbed across the plasma, accelerating the ions (protons). For a dimensionless field strength parameter a(0)=16 (Ilambda(2) approximately 3 x 10(20) W cm(-2) microm(2), where I is the intensity and lambda the wavelength), and target thicknesses of a few microns, the shock is responsible for the highest energy protons. A plateau in the ion spectrum provides a direct signature for shock acceleration.

The kinetic theory of collisionless electrostatic shocks resulting from the collision of plasma slabs with different temperatures and densities is presented. The theoretical results are confirmed by selfconsistent particle-in-cell simulations, revealing the formation and stable propagation of electrostatic shocks with very high Mach numbers (M ≫ 10), well above the predictions of the classical theories for electrostatic shocks. The collision of clouds of plasma with different properties (temperature, density, composition etc.) is a scenario quite common in nature. For instance, during supernovae explosions, large quantities (10 solar masses) of high temperature plasma ( T ∼ 10 6−8 K) are ejected into the interstellar medium (n ∼ 1 cm −3 , T ∼ 10 2−4 K) [1,2], and plasma cloud collisions are at the core of the fireball model for gamma ray bursters [3]. Plasma cloud collisions also occur when the solar wind interacts with the Earth Magnetosphere, or when it encounters the interstellar medium in the heliosphere region [4]. In the laboratory, such scenarios appear during the laser induced compression of plasma foils in solid targets [5].The collision of plasma shells leads to the onset of plasma instabilities and to the development of nonlinear structures, such as solitons, shocks and double layers [6]. In the absence of an ambient magnetic field, the shock waves are electrostatic [7,8], and the dissipation is provided by the population of electrons trapped beyond the shock front [6,9] and, for stronger shocks, by the ion reflection from the shock front [10]. Whilst the properties of shocks induced by collision of identical plasma shells, or by compression of plasma clouds, have been extensively studied in the past [5,6,7,8,9,10,11,12,13,14], the properties of the electrostatic shock waves formed during the collision of diverse plasma slabs of arbitrary temperature and density are rather unexplored [15]. The theory for electrostatic shocks induced by impact of identical plasma shells predicts an absolute maximum Mach number M max ≃ 3 (or, when ion reflection and thermal effects are included, M * max ≃ 6). However, collisionless shock waves with Mach numbers ranging between 10 and 10 3 have been observed in many astrophysical scenarios [1], and very large Mach number cosmic shock waves are thought to play a crucial role in the evolution of the large scale structure of the Universe [16,17].In this Letter, we present a kinetic theory describing the properties of the very high Mach number (M ≫ 10) laminar shock waves arising from the collision of slabs of plasma with different properties (temperatures, densities), and in the absence of an ambient magnetic field. We demonstrate that the shock properties are strongly influenced by Θ, the ratio of the electron temperatures in the two slabs, and by Υ, the ratio of the electron densities in the two slabs. The analysis shows that when the electron temperature T e R of the downstream slab (R) is higher than the electron temperature T e L of the upstream slab (L), the shock wav...

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In particle-based algorithms, the effect of binary collisions is commonly described in a statistical way, using Monte Carlo techniques. It is shown that, in the relativistic regime, stringent constraints should be considered on the sampling of particle pairs for collision, which are critical to ensure physically meaningful results, and that nonrelativistic sampling criteria (e.g., uniform random pairing) yield qualitatively wrong results, including equilibrium distributions that differ from the theoretical Jüttner distribution. A general procedure for relativistically consistent algorithms is provided, and verified with three-dimensional Monte Carlo simulations, thus opening the way to the numerical exploration of the statistical properties of collisional relativistic systems.