arXiv subjects

Antoine Bret

Publications and source records attributed to Antoine Bret.

At least 37 records · Page 2Linked to original sources

arXiv2021

Bridging the gap between collisional and collisionless shock waves

While the front of a fluid shock is a few mean-free-paths thick, the front of a collisionless shock can be orders of magnitude thinner. By bridging between a collisional and a collisionless formalism, we assess the transition between these two regimes. We consider non-relativistic, un-magnetized, planar shocks in electron/ion plasmas. In addition, our treatment of the collisionless regime is restricted to high Mach number electrostatic shocks. We find that the transition can be parameterized by the upstream plasma parameter $Λ$ which measures the coupling of the upstream medium. For $Λ\lesssim 1.12$, the upstream is collisional, i.e. strongly coupled, and the strong shock front is about $\mathcal{M}_1 λ_{\mathrm{mfp},1}$ thick, where $λ_{\mathrm{mfp},1}$ and $\mathcal{M}_1 $ are the upstream mean-free-path and Mach number respectively. A transition occurs for $Λ\sim 1.12$ beyond which the front is $\sim \mathcal{M}_1λ_{\mathrm{mfp},1}\ln Λ/Λ$ thick for $Λ\gtrsim 1.12$. Considering $Λ$ can reach billions in astrophysical settings, this allows to understand how the front of a collisionless shock can be orders of magnitude smaller than the mean-free-path, and how physics transitions continuously between these 2 extremes.

physics.plasm-ph↗

arXiv2020

Can we trust MHD jump conditions for collisionless shocks?

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.

physics.plasm-ph↗

arXiv2019

Density jump as a function of magnetic field for collisionless shocks in pair plasmas: the perpendicular case

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 terms of the field strength for a parallel shock [J. Plasma Phys. (2018), vol. 84, 905840604]. Here, we extend the analysis to the case of a perpendicular shock. We still find that the field reduces the density jump, but the effect is less pronounced than in the parallel case.

physics.plasm-ph↗

arXiv2018

Density jump as a function of magnetic field strength for parallel collisionless shocks in pair plasmas

Collisionless shocks follow the Rankine-Hugoniot jump conditions to a good approximation. However, for a shock propagating parallel to a magnetic field, magnetohydrodynamics states that the shock properties are independent of the field strength, whereas recent Particle-in-Cell simulations reveal a significant departure from magnetohydrodynamics behavior for such shocks in the collisionless regime. This departure is found to be caused by a field-driven anisotropy in the downstream pressure, but the functional dependence of this anisotropy on the field strength is yet to be determined. Here, we present a non-relativistic model of the plasma evolution through the shock front, allowing for a derivation of the downstream anisotropy in terms of the field strength. Our scenario assumes double adiabatic evolution of a pair plasma through the shock front. As a result, the perpendicular temperature is conserved. If the resulting downstream is firehose stable, then the plasma remains in this state. If unstable, it migrates towards the firehose stability threshold. In both cases, the conservation equations, together with the relevant hypothesis made on the temperature, allows a full determination of the downstream anisotropy in terms of the field strength.

physics.plasm-ph↗

arXiv2018

On the Formation and Properties of Fluid Shocks and Collisionless Shock Waves in Astrophysical Plasmas

When two plasmas collide, their interaction can be mediated by collisionless plasma instabilities or binary collisions between particles of each shell. By comparing the maximum growth rate of the collisionless instabilities with the collision frequency between particles of the shells, we determine the critical density separating the collisionless formation from the collisional formation of the resulting shock waves. This critical density is also the density beyond which the shock downstream is field free, as plasma instabilities do not have time to develop electromagnetic patterns. We further determine the conditions on the shells initial density and velocity for the downstream to be collisional. If these quantities fulfill the determined conditions, the collisionality of the downstream also prevents the shock from accelerating particles or generating strong magnetic fields. We compare the speed of sound with the relative speed of collision between the two shells, thus determining the portion of the parameters space where strong shock formation is possible for both classical and degenerate plasmas. Finally, we discuss the observational consequences in several astrophysical settings.

physics.plasm-ph↗

arXiv2017

Hierarchy of instabilities for two counter-streaming magnetized pair beams: influence of field obliquity

The hierarchy of unstable modes when two counter-streaming pair plasmas interact over a flow-aligned magnetic field has been recently investigated [PoP \textbf{23}, 062122 (2016)]. The analysis is here extended to the case of an arbitrarily tilted magnetic field. The two plasma shells are initially cold and identical. For any angle $θ\in [0,π/2]$ between the field and the initial flow, the hierarchy of unstable modes is numerically determined in terms of the initial Lorentz factor of the shells $γ_0$, and the field strength as measured by a parameter denoted $σ$. For $θ=0$, four different kinds of mode are likely to lead the linear phase. The hierarchy simplifies for larger $θ$'s, partly because the Weibel instability can no longer be cancelled in this regime. For $θ>0.78$ (44$^\circ$) and in the relativistic regime, the Weibel instability always govern the interaction. In the non-relativistic regime, the hierarchy becomes $θ$-independent because the interaction turns to be field-independent. As a result, the two-stream instability becomes the dominant one, regardless of the field obliquity.

physics.plasm-ph↗

arXiv2017

Kinetic inhibition of MHD-shocks in the vicinity of a parallel magnetic field

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, isotropization is progressively suppressed, resulting in a strong influence of the field on the resulting structure. A micro-physics analysis allows to understand the mechanisms at work. Particle-in-cell simulations also support our conclusions and show that the results are not restricted to a strictly parallel field.

physics.plasm-ph↗

arXiv2017

Simulation study of the formation of a non-relativistic pair shock

We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed c/5 and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing upstream leptons. The interaction of the hot leptons, which leak back into the upstream region, with the inflowing cool upstream leptons continuously drives electrostatic waves that mediate the shock. These waves heat up the inflowing upstream leptons primarily along the shock normal, which results in an anisotropic velocity distribution in the post-shock region. This distribution gives rise to the Weibel instability. Our simulation shows that even if the shock is mediated by quasi-electrostatic waves, strong magnetowaves will still develop in its downstream region.

astro-ph.HE↗

arXiv2016

Simple model on collisionless thin-shell instability growth

The manuscript discusses a simple model on the Thin Shell Instability (TSI) growth phenomenon at early stage, by only imposing the fulfillment of conservation laws; and in particular just applying the laws of mass and linear momentum conservation, without taking into account the energy partitioning inside the thin shell.

physics.plasm-ph↗

arXiv2016

Particles trajectories in Weibel magnetic filaments with a flow-aligned magnetic field

For a Weibel shock to form, two plasma shells have to collide and trigger the Weibel instability. At saturation, this instability generates in the overlapping region magnetic filaments with peak field $B_f$. In the absence of an external guiding magnetic field, these filaments can block the incoming flow, initiating the shock formation, if their size is larger than the Larmor radius of the incoming particles in the peak field. Here we show that this results still holds in the presence of an external magnetic field $B_0$, provided it is not too high. Yet, for $B_0 \gtrsim B_f/2$, the filaments become unable to stop any particle, regardless of its initially velocity.

physics.plasm-ph↗

arXiv2016

Hierarchy of instabilities for two counter-streaming magnetized pair beams

The instabilities triggered when two counter-streaming pair beams collide are analyzed. A guiding magnetic field is accounting for, while both beams are considered identical and cold. The instability analysis is conducted over the full \textbf{k}-spectrum, allowing to derive the hierarchy map of the dominant unstable modes, in terms of the initial beams energy $γ_0$ and a magnetic field strength parameter $Ω_B$. Four different regions of the $(Ω_B,γ_0)$ phase space are identified, each one governed by a different kind of mode. The analysis also unravels the existence of a "triple point", where 3 different modes grow exactly the same rate. A number of analytical expressions can be derived, either for the modes growth-rates, or for the frontiers between the 4 regions.

physics.plasm-ph↗

arXiv2015

Particles trajectories in magnetic filaments

The motion of a particle in a spatially harmonic magnetic field is a basic problem involved, for example, in the mechanism of formation of a collisionless shock. In such settings, it is generally reasoned that particles entering a Weibel generated turbulence are trapped inside it, provided their Larmor radius in the peak field is smaller than the field coherence length. The goal of this work is to put this heuristic conclusion on firm ground by studying, both analytically and numerically, such motion. A toy model is analyzed, consisting of a relativistic particle entering a region of space occupied by a spatially harmonic field. The particle penetrates the magnetic structure in a direction aligned with the magnetic filaments. Although the conclusions are not trivial, the main result is confirmed.

physics.plasm-ph↗

arXiv2015

Shock formation in electron-ion plasmas: mechanism and timing

We analyse the full shock formation process in electron-ion plasmas in theory and simulations. It is accepted that electromagnetic shocks in initially unmagnetised relativistic plasmas are triggered by the filamentation instability. However, the transition from the first unstable phase to the quasi-steady shock is still missing. We derive a theoretical model for the shock formation time, taking into account the filament merging in the non-linear phase of the filamentation instability. This process is much slower than in electron-positron pair shocks, so that the shock formation is longer by a factor proportional to sqrt(m_i/m_e) ln(m_i/m_e).

astro-ph.HE↗

arXiv2015

Collisional behaviors of astrophysical collisionless plasmas

In collisional fluids, a number of key processes rely on the frequency of binary collisions. Collisions seem necessary to generate a shock wave when two fluids collide fast enough, to fulfill the Rankine-Hugoniot relations, to establish an equation of state or a Maxwellian distribution. Yet, these seemingly collisional features are routinely either observed or assumed, in relation with collision\emph{less} astrophysical plasmas. This article will review our current answers to the following questions: How do colliding collisionless plasmas end-up generating a shock as if they were fluids? To which extent are the Rankine-Hugoniot relations fulfilled in this case? Do collisionless shocks propagate like fluid ones? Can we use an equation of state to describe collisionless plasmas, like MHD codes for astrophysics do? Why are Maxwellian distributions ubiquitous in Particle-In-Cell simulations of collisionless shocks? Time and length scales defining the border between the collisional and the collisionless behavior will be given when relevant. In general, when the time and length scales involved in the collisionless processes responsible for the fluid-like behavior may be neglected, the system may be treated like a fluid.

physics.plasm-ph↗

arXiv2014

Collisionless Weibel shocks: full formation mechanism and timing

Collisionless shocks in plasmas play an important role in space physics (Earth's bow shock) and astrophysics (supernova remnants, relativistic jets, gamma-ray bursts, high energy cosmic rays). While the formation of a fluid shock through the steepening of a large amplitude sound wave has been understood for long, there is currently no detailed picture of the mechanism responsible for the formation of a collisionless shock. We unravel the physical mechanism at work and show that an electromagnetic Weibel shock always forms when two relativistic collisionless, initially unmagnetized, plasma shells encounter. The predicted shock formation time is in good agreement with 2D and 3D particle-in-cell simulations of counterstreaming pair plasmas. By predicting the shock formation time, experimental setups aiming at producing such shocks can be optimised to favourable conditions.

physics.plasm-ph↗

arXiv2014

Influence of flavor oscillations on neutrino beam instabilities

We consider the collective neutrino plasma interactions, and study the electron plasma instabilities produced by a nearly mono-energetic neutrino beam in a plasma. We describe the mutual influence of neutrino flavor oscillations and electron plasma waves. We show that the neutrino flavor oscillations are not only perturbed by electron plasmas waves, but also contribute to the dispersion relation and the growth rates of neutrino beam instabilities.

physics.plasm-ph↗

arXiv2014

Robustness of the filamentation instability in arbitrarily oriented magnetic field: Full 3D calculation

The filamentation (Weibel) instability plays a key role in the formation of collisionless shocks which are thought to produce Gamma-Ray-Bursts and High-Energy-Cosmic-Rays in astrophysical environments. While it has been known for long that a flow-aligned magnetic field can completely quench the instability, it was recently proved in 2D that in the cold regime, such cancelation is possible if and only if the field is perfectly aligned. Here, this result is finally extended to a 3D geometry. Calculations are conducted for symmetric and asymmetric counter-streaming relativistic plasma shells. 2D results are retrieved in 3D: the instability can never be completely canceled for an oblique magnetic field. In addition, the maximum growth-rate is always larger for wave vectors lying in the plan defined by the flow and the oblique field. On the one hand, this bears consequences on the orientation of the generated filaments. On the other hand, it certifies 2D simulations of the problem can be performed without missing the most unstable filamentation modes.

physics.plasm-ph↗

arXiv2013

Robustness of the filamentation instability for asymmetric plasma shells collision in arbitrarily oriented magnetic field

The filamentation instability triggered when two counter streaming plasma shells overlap appears to be the main mechanism by which collisionless shocks are generated. It has been known for long that a flow aligned magnetic field can completely suppress this instability. In a recent paper [PHYSICS OF PLASMAS 18, 080706 (2011)], it was demonstrated in two dimensions that for the case of two cold, symmetric, relativistically colliding shells, such cancellation cannot occur if the field is not perfectly aligned. Here, this result is extended to the case of two asymmetric shells. The filamentation instability appears therefore as an increasingly robust mechanism to generate shocks.

astro-ph.HE↗