The current filamentation instability, which generically arises in the counterstreaming of supersonic plasma flows, is known for its ability to convert the free energy associated with anisotropic momentum distributions into kinetic-scale magnetic fields. The saturation of this instability has been extensively studied in symmetric configurations where the interpenetrating plasmas share the same properties (velocity, density, temperature). In many physical settings, however, the most common configuration is that of asymmetric plasma flows. For instance, the precursor of relativistic collisionless shock waves involves a hot, dilute beam of accelerated particles reflected at the shock front and a cold, dense inflowing background plasma. To determine the appropriate criterion for saturation in this case, we have performed large-scale 2D particle-in-cell simulations of counterstreaming electron-positron pair and electron-ion plasmas. We show that, in interpenetrating pair plasmas, the relevant criterion is that of magnetic trapping as applied to the component (beam or plasma) that carries the larger inertia of the two; namely, the instability growth suddenly slows down once the quiver frequency of those particles equals or exceeds the instability growth rate. We present theoretical approximations for the saturation level. These findings remain valid for electron-ion plasmas provided that electrons and ions are close to equipartition in the plasma flow of larger inertia. Our results can be directly applied to the physics of relativistic, weakly magnetized shock waves, but they can also be generalized to other cases of study.
The saturation of the electron beam filamentation instability by the self-generated magnetic field and magnetic pressure gradient-driven electric field
Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations
We present the first 2X2V continuum Vlasov-Maxwell simulations of interpenetrating, unmagnetized plasmas to study the competition between two-stream, Oblique, and filamentation modes in the weakly relativistic regime. We find that after nonlinear saturation of the fastest-growing two-stream and Oblique modes, the effective temperature anisotropy, which drives current filament formation via the secular Weibel instability, has a strong dependence on the internal temperature of the counter-streaming plasmas. The effective temperature anisotropy is significantly more reduced in colder than in hott…
Ab initio simulations of the propagation in a plasma of a soon to be available relativistic electron-positron beam or fireball beam provide an effective mean for the study of microphysics relevant to astrophysical scenarios. We show that the current filamentation instability associated with some of these scenarios reaches saturation after only 10 cm of propagation in a typical laboratory plasma with a density 10^17/cc. The different regimes of the instability, from the purely transverse to the mixed mode filamentation, can be accessed by varying the background plasma density. The instability g…
In this second paper of a series, we discuss the dynamics of a plasma entering the precursor of an unmagnetized, relativistic collisionless pair shock. We discuss how this background plasma is decelerated and heated through its interaction with a microturbulence that results from the growth of a current filamentation instability (CFI) in the shock precursor. We make use, in particular, of the reference frame $\mathcal R_{\rm w}$ in which the turbulence is mostly magnetic. This frame moves at relativistic velocities towards the shock front at rest, decelerating gradually from the far to the nea…
Plasma streaming instabilities play an important role in magnetic field amplification and particle acceleration in relativistic shocks and their environments. However, in the far shock precursor region where accelerated particles constitute a highly relativistic and dilute beam, streaming instabilities typically become inefficient and operate at very small scales when compared to the gyroradii of the beam particles. We report on a plasma cavitation instability that is driven by dilute relativistic beams and can increase both the magnetic field strength and coherence scale by orders of magnitud…
Perpendicular relativistic ($γ_0=10$) 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 $10^{-3}<σ<10^{-2}$ 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 …
We study the stability of current filaments produced by the Weibel, or current filamentation, instability in weakly magnetized counter-streaming 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 counter-streaming plasmas indicate that this drift-kink mod…
In this first paper of a series dedicated to the microphysics of unmagnetized, relativistic collisionless pair shocks, we discuss the physics of the Weibel-type transverse current filamentation instability (CFI) that develops in the shock precursor, through the interaction of an ultrarelativistic suprathermal particle beam with the background plasma. We introduce in particular the notion of "Weibel frame", or scattering center frame, in which the microturbulence is of mostly magnetic nature. We calculate the properties of this frame, using first a kinetic formulation of the linear phase of the…
Multidimensional simulations of magnetic field amplification and electron acceleration to near-energy equipartition with ions by a mildly relativistic quasi-parallel plasma collision
