Very High Mach-Number Electrostatic Shocks in Collisionless Plasmas

Abstract

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...

Experimental Observation of Thin-shell Instability in a Collisionless Plasma

“…The strength of the ambipolar electric field, and thus the angle at which the ion velocity is rotated by the double layer crossing, depends on the ratio between the collision speed and the ion-acoustic speed ), on how the density of the laser-generated blast shell compares to that of the ambient medium (Sorasio et al 2006), and on the ratio of the amplitude of the shell's oscillation to it wavelength. It is thus difficult to obtain identical conditions in the simulation and experiment, which may explain the different growth rates of the NTSI.…”

Electromagnetic Field Generation in the Downstream of Electrostatic Shocks Due to Electron Trapping

“…In our model, we assume only the initial conditions of the flows and that an electrostatic shock is formed [15,35]. The growth rate can be calculated theoretically from first principles.…”

“…Particles are trapped in the associated electrostatic potential, which steepens and eventually reaches a quasisteady-state collisionless electrostatic shock. Most of the theoretical work dates back to the 1970s [9-13] relying on the pseudo-Sagdeev potential [14] and progress has been mainly triggered by kinetic simulations [15][16][17][18].The short formation time scales and the one dimensionality of the problem make it easily accessible with theory and computer simulations. However, long time shock evolution was often one dimensional or electrostatic codes were used, and the role of electromagnetic modes was mostly neglected.…”

“…Particles are trapped in the associated electrostatic potential, which steepens and eventually reaches a quasisteady-state collisionless electrostatic shock. Most of the theoretical work dates back to the 1970s [9][10][11][12][13] relying on the pseudo-Sagdeev potential [14] and progress has been mainly triggered by kinetic simulations [15][16][17][18].…”

Particle-in-cell simulation study of a lower-hybrid shock

“…It is thus the only wave mode that can sustain an electrostatic shock [1][2][3][4][5][6][7][8] in a collisionless unmagnetized plasma unless the collision speed is high enough to yield a partially magnetic shock. 9,10 The density gradient at the electrostatic shock drives an ambipolar electric field, which puts the downstream region behind the shock on a higher positive potential than the upstream region ahead of it.…”