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Sketch of the system considered. In 3D, the perpendicular magnetic field breaks the axial symmetry, and one has to investigate every possible orientations of the wave-vector.
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The shock formation process in electron–positron pair plasmas is investigated in the presence of an ambient perpendicular magnetic field. In initially unmagnetised plasmas, which are dominated by the Weibel or filamentation instability, the shock formation time is a multiple of the saturation time of the linear instability. While in weakly magnetis...
Citations
... Also, considering only two spatial dimensions necessary excludes waves and instabilities with a wavevector k oriented along the excluded spatial dimension. Indeed, theoretical explorations of the full unstable k-spectrum of some beam-plasma (or Weibel-like) instabilities, found it is truly 3D (Kalman et al. 1968;Dieckmann et al. 2008;Bret 2014;Novo et al. 2016). ...
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 invalidate the first assumption. In addition, an external magnetic field can sustain stable pressure anisotropies, invalidating the second assumption. It is therefore unclear whether or not the density jump of a collisionless shock fulfills the MHD jump. 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 ΔRH, the relative departure from the Rankine-Hugoniot (RH) jump. For small departures we propose ΔRH = + (10-1-3.7κ)tκ - σ(1), where t is the timescale of the simulation, σ is the magnetization parameter and κ is a constant of order unity. The first term stems from the energy leakage into the accelerated particle. The second term stems from the downstream anisotropy triggered by the field (assuming an isotropic upstream). This relation allows us to assess to what extent a collisionless shock fulfills 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. © 2020. The American Astronomical Society. All rights reserved..
... The difference is that we need to alleviate here some approximations that they adopted (ultra-relativistic or 3D ideal gas adiabatic index downstream) and derive the shock front speed and density compression ratio in a most general form. We note that a similar derivation to the one presented here was carried out recently by Stockem Novo et al. (2016). ...
Perpendicular relativistic ($\gamma_0=10$) shocks in magnetized pair plasmas are investigated using two dimensional Particle-in-Cell simulations. A systematic survey, from unmagnetized to strongly magnetized shocks, is presented accurately capturing the transition from Weibel-mediated to magnetic-reflection-shaped shocks. This transition is found to occur for upstream flow magnetizations $10^{-3}<\sigma<10^{-2}$ at which a strong perpendicular net current is observed in the precursor, driving the so-called current-filamentation instability. The global structure of the shock and shock formation time are discussed. The MHD shock jump conditions are found in good agreement with the numerical results, except for $10^{-4} < \sigma < 10^{-2}$ where a deviation up to 10\% is observed. The particle precursor length converges toward the Larmor radius of particles injected in the upstream magnetic field at intermediate magnetizations. For $\sigma>10^{-2}$, it leaves place to a purely electromagnetic precursor following from the strong emission of electromagnetic waves at the shock front. Particle acceleration is found to be efficient in weakly magnetized perpendicular shocks in agreement with previous works, and is fully suppressed for $\sigma > 10^{-2}$. Diffusive Shock Acceleration is observed only in weakly magnetized shocks, while a dominant contribution of Shock Drift Acceleration is evidenced at intermediate magnetizations. The spatial diffusion coefficients are extracted from the simulations allowing for a deeper insight into the self-consistent particle kinematics and scale with the square of the particle energy in weakly magnetized shocks. These results have implications for particle acceleration in the internal shocks of AGN jets and in the termination shocks of Pulsar Wind Nebulae.
... While the phase of the instability development has been analytically well characterized, a theoretical description of the shock formation stage is still lacking. Hence, an extensive numerical investigation has been performed in the last decades Spitkovsky, 2009, 2011a;Stockem et al., 2014;Caprioli and Spitkovsky, 2014a;Stockem-Novo et al., 2015;Bret et al., 2016;Novo et al., 2016;Ruyer et al., 2016;. These works have successfully described the physics behind shock formation and late stage of shock propagation in both electronion and pair plasma in unmagnetized and magnetized conditions, while the timing for shock formation is still an open discussion. ...
... (2. 5.16) in agreement with previous works (Gallant et al., 1992;Lemoine et al., 2016;Novo et al., 2016). Hence, we recover the classical result ∆n 3 for a perfect 2D gas in both the non-relativistic limit (γ d u 1 and T d mc 2 ) for which Γ ad = 2 and in the relativistic case (γ d u 1 and T d mc 2 ) for which Γ ad = 3/2. ...
... However, since the Weibel instability is responsible for shock formation only in the weakly magnetized cases, we expect a marginal modification of the instability development with respect to the unmagnetized case, for which growth rate and saturation level are known. Therefore, Novo et al. (2016) suggests that shock formation in the weakly magnetized case should be reached at the same time than predicted by Bret et al. (2014) using Eq. (6. ...
The work presented in this thesis belongs to the general framework of Laboratory Astrophysics. We address various aspects of the physics of collisionless shocks developing in the presence of relativistic plasma flows, in configurations of interest for the astrophysical and the laser-plasma interaction (LPI) communities. The approach used throughout this thesis relied on both analytical modeling and high-performance kinetic simulations, a central tool to describe LPI processes as well as the non-linear physics behind shock formation. The PIC code SMILEI has been widely used and developed during this work. Three physical configurations are studied. First we consider the Weibel instability driven by two counter-streaming electron beams aligned with an external magnetic field. The linear and non-linear phases are explained using theoretical models confirmed by simulations.Then the generation of non-collisional shocks during the interaction of two relativistic plasma pairs is studied in the presence of a perpendicular magnetic field. We focus on the comparison of theoretical predictions for macroscopic variables with the simulation results, as well as on the definition and measurement of the shock formation time, all of which are of great importance for future experiments.Finally, we proposed a scheme to produce, in the laboratory, the ion-Weibel-instability with the use of an ultra-high-intensity laser. The produced flows are faster and denser than in current experiments, leading to a larger growth rate and stronger magnetic fields. These results are important for the LPI at very high intensity.
... The most general case would require considering an k y = 0 component for k. Nevertheless, previous 3D studies of the Weibel instability (k z = 0) found that the maximum growth-rates are to be found precisely for k y = 0 [9,10]. The present choice of the wave-vector orientation is therefore likely to render the largest growth-rates over the full 3D k-space. ...
... The computation unravels an extremely simple hierarchy map: it simply does not depend on σ. Previous works already found that the Weibel growth-rate becomes independent of σ for θ = π/2 because the instability has the charges moving sideways, that is, parallel to the field [10]. Other σ-dependent modes grow (not shown), but they do not outgrow the Weibel mode. ...
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 $\theta \in [0,\pi/2]$ 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 $\gamma_0$, and the field strength as measured by a parameter denoted $\sigma$. For $\theta=0$, four different kinds of mode are likely to lead the linear phase. The hierarchy simplifies for larger $\theta$'s, partly because the Weibel instability can no longer be cancelled in this regime. For $\theta>0.78$ (44$^\circ$) and in the relativistic regime, the Weibel instability always govern the interaction. In the non-relativistic regime, the hierarchy becomes $\theta$-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.
We report an experimental investigation of a laser-gas-converter approach for generating high-yield ultrashort MeV positrons. We observe that MeV electrons with a high charge of several tens of nC can be well generated by a ∼ 6 J , ∼ 40 f s laser interacting with a high-density gas jet. However, it is shown that the propagation of the highly charged electron beam is significantly inhibited because the electrons are reflected by the sheath potential in the density decreasing region of the gas target, thus leading to a low positron yield. Consequently, by using an integrated nozzle-converter design to eliminate the density falling ramp of the gas target such that the electron refluxing is inhibited, we observe a significant enhancement of positron yield (up to a factor of 15), finally reaching a positron yield of 5 × 10 8 s r − 1 . This high-yield ultrashort MeV positron may have great potential toward the simulation of astrophysical pair plasma.
When two collisionless plasma shells collide, they interpenetrate and the overlapping region may turn Weibel unstable for some values of the collision parameters. This instability grows magnetic filaments which, at saturation, have to block the incoming flow if a Weibel shock is to form. In a recent paper (Bret, J. Plasma Phys. , vol. 82, 2016 b , 905820403), it was found by implementing a toy model for the incoming particle trajectories in the filaments, that a strong enough external magnetic field $\unicode[STIX]{x1D63D}_{0}$ can prevent the filaments blocking the flow if it is aligned with them. Denoting by $B_{f}$ the peak value of the field in the magnetic filaments, all test particles stream through them if $\unicode[STIX]{x1D6FC}=B_{0}/B_{f}>1/2$ . Here, this result is extended to the case of an oblique external field $B_{0}$ making an angle $\unicode[STIX]{x1D703}$ with the flow. The result, numerically found, is simply $\unicode[STIX]{x1D6FC}>\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})/\cos \unicode[STIX]{x1D703}$ , where $\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})$ is of order unity. Noteworthily, test particles exhibit chaotic trajectories.
