Collisionless shocks are ubiquitous in astrophysics and in the lab. Recent numerical simulations and experiments have shown how they can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step towards a microscopic understanding of the process, we analyze here in detail the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two symmetric initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes govern the linear phase. We derive an expression for the duration of the linear phase in good agreement with the simulations. This saturation time constitutes indeed a lower-bound for the shock formation time.

Next generation of ultra-intense laser facilities will lead to novel physical conditions ruled by collective and quantum electrodynamics effects, such as synchrotron-like emission of high-energy photons and e + e − pair generation. In view of the future experiments performed in this regime, the latter processes have been implemented into the particle-in-cell code calder.

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We present a predictive model of the nonlinear phase of the Weibel instability induced by two symmetric, counter-streaming ion beams in the non-relativistic regime. This self-consistent model combines the quasilinear kinetic theory of Davidson et al. [Phys. Fluids 15, 317 (1972)] with a simple description of current filament coalescence. It allows us to follow the evolution of the ion parameters up to a stage close to complete isotropization, and is thus of prime interest to understand the dynamics of collisionless shock formation. Its predictions are supported by 2-D and 3-D particlein-cell simulations of the ion Weibel instability. The derived approximate analytical solutions reveal the various dependencies of the ion relaxation to isotropy. In particular, it is found that the influence of the electron screening can affect the results of simulations using an unphysical electron mass. PACS numbers:First-principles kinetic simulations of plasma collisions governed by electromagnetic effects are now made possible using massively parallel particle-in-cell (PIC) codes, hence paving the way to quantitative modeling of a number of high-energy astrophysical scenarios [1,2]. The turbulent shocks possibly arising from plasma instabilities in these systems are believed to be responsible for the generation of nonthermal particles and radiation [3][4][5]. In this context, many simulation studies have demonstrated the ability of the Weibel-filamentation instability [6][7][8][9][10][11] to provide the electromagnetic turbulence required for efficient dissipation of the flow energy and Fermi-type acceleration processes [2,12,13]. These numerical advances go along with experimental progress towards the laserdriven generation of collisionless turbulent shocks in the laboratory [14][15][16][17].Collisionless shocks developing in electron-ion plasmas may be of laminar or turbulent nature depending on the type (electrostatic or electromagnetic) of the dominant underlying instability [18]. In this work, we concentrate on initially unmagnetized electron-ion systems whose collective dynamics is eventually ruled by the electromagnetic ion Weibel instability, which may evolve into a turbulent shock. While this problem has inspired a number of numerical studies [1,2,13,[16][17][18][19], there is as yet no analytical model of the nonlinear evolution of the ion Weibel instability leading to shock formation. Our goal is to provide such a description within the simplifying assumption of homogeneous and infinite colliding plasmas of equal densities and temperatures. Our paper is organized as follows. In Sec. I, we first analyze the results of a reference PIC simulation, pointing out the transition from the early-time electron-driven phase, associated with various fast-growing modes, to the ion-driven phase ruled by the ion Weibel instability. In Sec. II, * Electronic address: charles.ruyer@polytechnique.edu † Electronic address: laurent.gremillet@cea.fr we present a set of quasilinear equations describing the evolution of the ion parameters ...

We report on the first self-consistent numerical study of the feasibility of laser-driven relativistic pair shocks of prime interest for high-energy astrophysics. Using a QED-particle-in-cell code, we simulate the collective interaction between two counterstreaming electron-positron jets driven from solid foils by short-pulse (~60 fs), high-energy (~100 kJ) lasers. We show that the dissipation caused by self-induced, ultrastrong (>10^{6} T) electromagnetic fluctuations is amplified by intense synchrotron emission, which enhances the magnetic confinement and compression of the colliding jets.

We present a particle-in-cell simulation of the generation of a collisionless turbulent shock in a dense plasma driven by an ultra-high-intensity laser pulse. From the linear analysis, we highlight the crucial role of the laser-heated and return-current electrons in triggering a strong Weibel-like instability, giving rise to a magnetic turbulence able to isotropize the target ions.PACS numbers:

The formation of collisionless shocks mediated by the ion Weibel instability is addressed theoretically and numerically in the nonrelativistic limit. First, the model developed in C. Ruyer et al., Phys. Plasmas 22, 032102 (2015) for the weakly nonlinear ion Weibel instability in a symmetric two-stream system is shown to be consistent with recent experimental and simulation results. Large-scale kinetic simulations are then performed to clarify the spatiotemporal evolution of the magnetic-field and plasma properties in the subsequent strongly nonlinear phase leading to shock formation. A simple analytical model is proposed which captures the simulation results up to a point close to ion isotropization. Electron screening effects are found important in the instability dynamics, so that numerical simulations using a nonphysical electron mass should be considered with caution.

We study the stability of current filaments produced by the Weibel, or current filamentation, instability in weakly magnetized counterstreaming plasmas. It is shown that a resonance exists between the current-carrying ions and a longitudinal drift-kink mode that strongly deforms and eventually breaks the current filaments. Analytical estimates of the wavelength, growth rate, and saturation level of the resonant mode are derived and validated by three-dimensional particle-in-cell simulations. Furthermore, self-consistent simulations of counterstreaming plasmas indicate that this drift-kink mode is dominant in the slow down of the flows and in the isotropization of the magnetic field, playing an important role in the formation of collisionless shocks.