Transverse electron-scale instability in relativistic shear flows

Abstract

Electron-scale surface waves are shown to be unstable in the transverse plane of a sheared flow in an initially unmagnetized collisionless plasma, not captured by (magneto)hydrodynamics. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroomlike electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. This transverse electron-scale instability may play an important role in relativistic and supersonic sheared flow scenarios, which are stable at the (magneto)hydrodynamic level. Macroscopic ( c/ω pe ) fields are shown to be generated by this microscopic shear instability, which are relevant for particle acceleration, radiation emission, and to seed magnetohydrodynamic processes at long time scales. A fundamental question in plasma physics concerns the stability of a given plasma configuration. Unstable plasma configurations are ubiquitous and constitute important dissipation sites via the operation of plasma instabilities, which typically convert plasma kinetic energy into thermal and electric or magnetic field energy. Plasma instabilities can occur at microscopic (particle kinetic) and macroscopic [magnetohydrodynamic (MHD)] scales, and are generally studied separately using simplified frameworks that focus on a particular scale and neglect the other. This approach conceals the role that microscopic processes may have on the macroscopic plasma dynamics, which in many scenarios cannot be disregarded. It is now recognized, for instance, that collisionless plasma instabilities operating on the electron scale in unmagnetized plasmas, such as the Weibel [1] and streaming instabilities [2], play a crucial role in the formation of (macroscopic) collisionless shocks in astrophysical [3][4][5][6][7] and laboratory conditions [8,9]. These microscopic instabilities result from the bulk interpenetration between plasmas and are believed to be intimately connected to important questions such as particle acceleration and radiation emission in astrophysical scenarios [10,11].Sheared plasma flow configurations can host both microscopic and macroscopic instabilities simultaneously, although the former have been largely overlooked. Sheared flow settings have been traditionally studied using the MHD framework [12][13][14], where the Kelvin-Helmholtz instability (KHI) is the only instability known to develop [15]. Only very recently have collisionless unmagnetized sheared plasma flows been addressed experimentally [16] and using particle-in-cell (PIC) simulations, revealing a rich variety of electron-scale processes, such as the electron-scale KHI (ESKHI), dc magnetic field generation, and unstable transverse dynamics [17][18][19][20][21][22]. The generated fields and modif...

EVOLUTION OF GLOBAL RELATIVISTIC JETS: COLLIMATIONS AND EXPANSION WITH kKHI AND THE WEIBEL INSTABILITY

“…In the limit, n n Alves et al (2015). While the ESKHI has ahigher growth rate than the MI for nonrelativistic flows, for relativistic flows the MI growth rate declines as jt Alves et al 2015). Provided that initial perturbations for both instabilities are similar, the MI is the dominant electron-scale instability in relativistic shear flows.…”

“…The fastest growth of this unstable branch (∂ k Γ=0) is found at k y  ¥ (finite thermal effects and/or smooth velocity shear profiles introduce a cutoff at finite k). In the limit, n n Alves et al (2015). While the ESKHI has ahigher growth rate than the MI for nonrelativistic flows, for relativistic flows the MI growth rate declines as jt Alves et al 2015).…”

“…In the low-wavenumber limit (kc=ω p ) with v am =0 and γ am =1, relevant to the numerical simulations, an analytic solution to the dispersion relation is given by * w g µ -, and wavenumber, k * , at maximum growth. Alves et al (2015) analyzed the stability of electromagnetic perturbations in the transverse plane of a collisionless plasma sheared flow with velocity profile v v x e z 0 0 ( ) = .…”

“…They labeled this the Mushroom instability (MI) owingto the mushroom-like structures that emerge in the electron density. While the ESKHI (kKHI) has higher growth rates than the MI for subrelativistic cases, the MI growth rate scales with jt 1 2 g -and declines slower than the ESKHI, which scales with jt 3 2 g - (Alves et al 2015). Here γ jt is the Lorentz factor of jet particles.…”

“…Recently, Alves et al (2015) reported electron-scale surface waves in the transverse plane of a counter-streaming sheared flow in an initially unmagnetized collisionless plasma. They labeled this the Mushroom instability (MI) owingto the mushroom-like structures that emerge in the electron density.…”