In a collisionless shock, there are no binary collisions to isotropize the flow. It is therefore reasonable to ask to which extent the magnetohydrodynamics (MHD) jump conditions apply. Following up on recent works which found a significant departure from MHD in the case of parallel collisionless shocks, we here present a model allowing to compute the density jump for collisionless shocks. Because the departure from MHD eventually stems from a sustained downstream anisotropy that the Vlasov equation alone cannot specify, we hypothesize a kinetic history for the plasma, as it crosses the shock front. For simplicity, we deal with non-relativistic pair plasmas. We treat the cases of parallel and perpendicular shocks. Non-MHD behavior is more pronounced for the parallel case where, according to MHD, the field should not affect the shock at all.

Collisionless shocks have been the subject on many studies in recent years, due to their ability to accelerate particles. In order to do so, a shock must fulfill three criteria. First, it must be strong enough to accelerate particles efficiently. Second, both the upstream and the downstream must be collisionless. Third, the shock front must be surrounded by electromagnetic turbulence capable of scattering particles back and forth. We here consider the encounter of two identical plasma shells with initial density, temperature, and velocity n0, T0, v0, respectively. We translate the three criteria to the corresponding requirements on these parameters. A non-trivial map of the allowed region for particle acceleration emerges in the (n0, T0, v0) phase space, especially at low velocities or high densities. We first assess the case of pair plasma shells, before we turn to electrons/protons.

In plasmas where the mean-free-path is much larger than the size of the system, shock waves can arise with a front much shorter than the mean-free-path. These so-called “collisionless shocks” are mediated by collective plasma interactions. Studies conducted so far on these shocks found that although binary collisions are absent, the distribution functions are thermalized downstream by scattering on the fields, so that magnetohydrodynamics prescriptions may apply. Here we show a clear departure from this pattern in the case of Weibel shocks forming over a flow-aligned magnetic field. A micro-physical analysis of the particle motion in the Weibel filaments shows how they become unable to trap the flow in the presence of too strong a field, inhibiting the mechanism of shock formation. Particle-in-cell simulations confirm these results.

Collisionless shocks are shocks in which the mean-free path is much larger than the shock front. They are ubiquitous in astrophysics and the object of much current attention as they are known to be excellent particle accelerators that could be the key to the cosmic rays enigma. While the scenario leading to the formation of a fluid shock is well known, less is known about the formation of a collisionless shock. We present theoretical and numerical results on the formation of such shocks when two relativistic and symmetric plasma shells (pair or electron/proton) collide. As the two shells start to interpenetrate, the overlapping region turns Weibel unstable. A key concept is the one of trapping time τp, which is the time when the turbulence in the central region has grown enough to trap the incoming flow. For the pair case, this time is simply the saturation time of the Weibel instability. For the electron/proton case, the filaments resulting from the growth of the electronic and protonic Weibel instabilities, need to grow further for the trapping time to be reached. In either case, the shock formation time is 2τp in two-dimensional (2D), and 3τp in 3D. Our results are successfully checked by particle-in-cell simulations and may help designing experiments aiming at producing such shocks in the laboratory.

Collisionless shocks are key processes in astrophysics where the energy dissipation at the shock front is provided by collective plasma effects rather than particle collisions. While numerous simulations and laser-plasma experiments have shown they can result from the encounter of two plasma shells, a first principle theory of the shock formation is still lacking. In this respect, a series of 2D Particle-In-Cells simulations have been performed of two identical cold colliding pair plasmas. The simplicity of this system allows for an accurate analytical tracking of the physics. To start with, the Weibel-filamentation instability is triggered in the overlapping region, which generates a turbulent region after a saturation time τs. The incoming flow then piles-up in this region, building-up the shock density region according to some nonlinear processes, which will be the subject of future works. By evaluating the seed field giving rise to the instability, we derive an analytical expression for τs in good agreement with simulations. In view of the importance of the filamentation instability, we show a static magnetic field can cancel it if and only if it is perfectly aligned with the flow.