When applied to compute the density jump of a shock, the standard magnetohydrodynamic (MHD) formalism assumes, 1) that all the upstream material passes downstream, together with the momentum and energy it carries, and 2) that pressures are isotropic. In a collisionless shock, shock accelerated particles going back and forth around the front can invalid the first assumption. In addition, an external magnetic field can sustain stable pressure anisotropies, invaliding the second assumption. It is therefore unclear whether the density jump of a collisionless shock fulfils the MHD jump or not.
Here we try to clarify this issue. A literature review is conducted on 68 articles dealing with Particle-In-Cell simulations of collisionless shocks. We analyze the factors triggering departure from the MHD density jump and quantify their influence on $Δ_{RH}$, the relative departure from the Rankine-Hugoniot jump. For small departures we propose $Δ_{RH} = + \mathcal{O}(10^{-1-3.7κ})t^κ- σ\mathcal{O}(1)$ where $t$ is the timescale of the simulation, $σ$ the magnetization parameter and $κ$ a constant of order unity. The first term stems from the energy leakage into accelerated particle. The second term stems from the downstream anisotropy triggered by the field (assuming an isotropic upstream). This relation allows to assess to which extent a collisionless shock fulfils the RH density jump.
In the strong field limit and for parallel shocks, the departure caused by the field saturates at a finite, negative, value. For perpendicular shocks, the departure goes to zero at small and high $σ$'s so that we find here a departure window. The results obtained have to be checked against full 3D simulations.
The research is aimed at the study of the properties of solutions for parallel MHD shock waves in collisionless plasma with heat fluxes, using 8-moment MHD approximation. Restrictions have been established on the upstream shock parameters preserving physical meaning of the downstream plasma parameters.
The properties of collisionless shocks, like the density jump, are usually derived from magnetohydrodynamics (MHD), where isotropic pressures are assumed. Yet, in a collisionless plasma, an external magnetic field can sustain a stable anisotropy. In \cite{BretJPP2018}, we devised a model for the kinetic history of the plasma through the shock front, allowing to self-consistently compute the downstream anisotropy, hence the density jump, in terms of the upstream parameters. This model dealt with the case of a parallel shock, where the magnetic field is normal to the front both in the upstream a…
Shockwaves in plasma are usually dealt with using Magnetohydrodynamics (MHD). Yet, MHD entails the assumption of a short mean free path, which is not fulfilled in a collisionless plasma. Recently, for pair plasmas, we devised a model allowing to account for kinetic effects within an MHD-like formalism. Its relies on an estimate of the anisotropy generated when crossing the front, with a subsequent assessment of the stability of this anisotropy in the downstream. We solved our model for parallel, perpendicular and switch-on shocks. Here we bridge between all these cases by treating the problem …
Statistical analysis of Faraday Rotation Measure (RM) maps of the intracluster medium (ICM) of galaxy clusters provides a unique tool to evaluate some spatial features of the magnetic fields there. Its combination with numerical simulations of magnetohydrodynamic (MHD) turbulence allows the diagnosis of the ICM turbulence. Being the ICM plasma weakly collisional, the thermal velocity distribution of the particles naturally develops anisotropies as a consequence of the large scale motions and the conservation of the magnetic moment of the charged particles. A previous study (Paper I) analyzed t…
The amplification and maintenance of the observed magnetic fields in the ICM are usually attributed to the turbulent dynamo action. This is generally derived employing a collisional MHD model. However, in the ICM the ion mean free path between collisions is of the order of the dynamical scales, thus requiring a collisionless MHD description. Unlike collisional MHD simulations, our study uses an anisotropic plasma pressure with respect to the direction of the local magnetic field, which brings the plasma within a parameter space where collisionless instabilities should take place. Within the ad…
The expansion of a dense plasma into a dilute plasma across an initially uniform perpendicular magnetic field is followed with a one-dimensional particle-in-cell (PIC) simulation over MHD time scales. The dense plasma expands in the form of a fast rarefaction wave. The accelerated dilute plasma becomes separated from the dense plasma by a tangential discontinuity at its back. A fast magnetosonic shock with the Mach number 1.5 forms at its front. Our simulation demonstrates how wave dispersion widens the shock transition layer into a train of nonlinear fast magnetosonic waves.
The properties of collisionless shocks are frequently assessed in the magnetohydrodynamics (MHD) model. Yet, in a collisionless plasma, an ambient magnetic field can sustain a stable anisotropy in the upstream or the downstream, resulting in a departure from the MHD predicted behavior. We present a model allowing to derive the downstream anisotropy, hence the shock density jump, in terms of the upstream quantities. For simplicity, the case of a parallel shock in pair plasma is considered. Contrary to previous works where the upstream was assumed isotropic, here the upstream anisotropy $A=T_\pe…
Shocks waves are a ubiquitous feature of many astrophysical plasma systems, and an important process for energy dissipation and transfer. The physics of these shock waves are frequently treated/modeled as a collisional, fluid MHD discontinuity, despite the fact that many shocks occur in the collisionless regime. In light of this, using fully kinetic, 3D simulations of non-relativistic, parallel propagating collisionless shocks comprised of electron-positron plasma, we detail the deviation of collisionless shocks form MHD predictions for varying magnetization/Alfvénic Mach numbers, with particu…
In the absence of frequent binary collisions to isotropize the plasma, the fulfillment of the magnetohydrodynamic (MHD) Rankine-Hugoniot jump conditions by collisionless shocks is not trivial. In particular, the presence of an external magnetic field can allow for stable anisotropies, implying some departures from the isotropic MHD jumps. The functional dependence of such anisotropies in terms of the field is yet to be determined. By hypothesizing a kinetic history of the plasma through the shock front, we recently devised a theory of the downstream anisotropy, hence of the density jump, in te…
Within the context of Magnetohydrodynamics (MHD), the properties of a parallel shock do not depend on the field strength, as the field and the fluid are disconnected for such a geometry. However, in the collisionless case, the field can sustain a stable anisotropy in the downstream, triggering a departure from the expected MHD behavior. In a recent work [A. Bret and R. Narayan, J. Plasma Phys. \textbf{84}, 905840604 (2018)], a theoretical model was presented allowing to derive the density ratio of a non-relativistic parallel collisionless shock in an electron/positron plasma, as a function of …
It has recently been proposed (Loureiro & Boldyrev 2017; Mallet et al. 2017) that the inertial interval in magnetohydrodynamic (MHD) turbulence is terminated at small scales not by a Kolmogorov-like dissipation region, but rather by a new sub-inertial interval mediated by tearing instability. However, many astrophysical plasmas are nearly collisionless so that the MHD approximation is not applicable to turbulence at small scales. In this Letter, we propose the extension of the theory of reconnection-mediated turbulence to plasmas which are so weakly collisional that the reconnection occurring …
The linear MHD Kelvin-Helmholtz instability (KHI) in an anisotropic plasma concerning the direction of an external magnetic field is examined in detail. For this purpose, the MHD equations are used to describe the motion of plasma as a fluid, which is derived from 16 moments of Boltzmann-Vlasov kinetic equations for collisionless plasma. In addition, the heat flux along the magnetic field is taken into account. The growing rates of KHI are calculated as functions of the anisotropic plasma properties for a shear flow along the magnetic field at supersonic velocities. On the other hand, the quas…
A comprehensive study of a reduced version of Lust's equations, the extended magnetohydrodynamic (XMHD) model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality, is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way energy conservation along with four families of Casimir invariants are naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their con…
The first complete estimation of the compressible energy cascade rate $|\varepsilon_\text{C}|$ at magnetohydrodynamic (MHD) and sub-ion scales is obtained in the Earth's magnetosheath using Magnetospheric MultiScale (MMS) spacecraft data and an exact law derived recently for {\it compressible} Hall MHD turbulence. A multi-spacecraft technique is used to compute the velocity and magnetic gradients, and then all the correlation functions involved in the exact relation. It is shown that when the density fluctuations are relatively small, $|\varepsilon_\text{C}|$ identifies well with its incompres…
In weakly collisional astrophysical plasmas, such as the intracluster medium of galaxy clusters, the amplification of cosmic magnetic fields by chaotic fluid motions is hampered by the adiabatic production of magnetic-field-aligned pressure anisotropy. This anisotropy drives a viscous stress parallel to the field that inhibits the plasma's ability to stretch magnetic-field lines. I demonstrate through the use of kinetic simulations that in high-$β$ plasmas, kinetic ion-Larmor scale instabilities sever the adiabatic link between the thermal and magnetic pressures, reducing this viscous stress a…
According to magnetohydrodynamics (MHD), the encounter of two collisional magnetized plasmas at high velocity gives rise to shock waves. Investigations conducted so far have found that the same conclusion still holds in the case of collisionless plasmas. For the case of a flow-aligned field, MHD stipulates that the field and the fluid are disconnected, so that the shock produced is independent of the field. We present a violation of this MHD prediction when considering the encounter of two cold pair plasmas along a flow-aligned magnetic field. As the guiding magnetic field grows, isotropizatio…
Results from a numerical study of fluctuation dynamo in a collisionless, weakly magnetized plasma are presented. The key difference between this dynamo and its magnetohydrodynamic (MHD) counterpart is the adiabatic production of magnetic-field-aligned pressure anisotropy by the amplification of a weak seed field. This in turn drives kinetic instabilities on the ion-Larmor scale---namely, firehose and mirror---which sever the adiabatic link between the thermal and magnetic pressures, thereby allowing the dynamo to proceed. After an initial phase of rapid growth driven by these instabilities, th…
A prediction of the steady-state reconnection electric field in asymmetric reconnection is obtained by maximizing the reconnection rate as a function of the opening angle made by the upstream magnetic field on the weak magnetic field (magnetosheath) side. The prediction is within a factor of two of the widely examined asymmetric reconnection model [Cassak and Shay, Phys. Plasmas 14, 102114, 2007] in the collisionless limit, and they scale the same over a wide parameter regime. The previous model had the effective aspect ratio of the diffusion region as a free parameter, which simulations and o…
The magnetorotational instability (MRI) is a fundamental mechanism determining the macroscopic dynamics of astrophysical accretion disks. In collisionless accretion flows around supermassive black holes, MRI-driven plasma turbulence cascading to microscopic (i.e. kinetic) scales can result in enhanced angular-momentum transport and redistribution, nonthermal particle acceleration, and a two-temperature state where electrons and ions are heated unequally. However, this microscopic physics cannot be captured with standard magnetohydrodynamic (MHD) approaches typically employed to study the MRI. …
The paper examines the prospects of using laser plasmas for studying novel regimes of the magnetic field line reconnection and charged particle acceleration. Basic features of plasma dynamics in the three-dimensional configurations relevant to the formation of current sheets in a plasma are addressed by analyzing exact self-similar solutions of the magneto-hydrodynamics and electron magneto-hydrodynamics equations. Then the magnetic field annihilation in the ultrarelativistic limit is considered, when the opposite polarity magnetic field is generated in collisionless plasma by multiple laser p…
In the past years we have experienced an increasing interest in understanding of the physical properties of collisionless plasmas, mostly because of the large number of astrophysical environments, e.g. the intracluster medium (ICM), containing magnetic fields which are strong enough to be coupled with the ionized gas and characterized by densities sufficiently low to prevent the pressure isotropization with respect to the magnetic line direction. Under these conditions a new class of kinetic instabilities arises, such as firehose and mirror ones, which were extensively studied in the literatur…
Collisionless, magnetized turbulence offers a promising framework for the generation of non-thermal high-energy particles in various astrophysical sites. Yet, the detailed mechanism that governs particle acceleration has remained subject to debate. By means of 2D and 3D PIC, as well as 3D (incompressible) magnetohydrodynamic (MHD) simulations, we test here a recent model of non-resonant particle acceleration in strongly magnetized turbulence~\cite{2021PhRvD.104f3020L}, which ascribes the energization of particles to their continuous interaction with the random velocity flow of the turbulence, …
We report analysis of sub-Alfvénic magnetohydrodynamic (MHD) perturbations in the low-\b{eta} radial-field solar wind using the Parker Solar Probe spacecraft data from 31 October to 12 November 2018. We calculate wave vectors using the singular value decomposition method and separate the MHD perturbations into three types of linear eigenmodes (Alfvén, fast, and slow modes) to explore the properties of the sub-Alfvénic perturbations and the role of compressible perturbations in solar wind heating. The MHD perturbations there show a high degree of Alfvénicity in the radial-field solar wind, with…
