Are Gamma‐Ray Burst Shocks Mediated by the Weibel Instability?

Lyubarsky, Yuri; Eichler, David

doi:10.1086/505523

Cited by 90 publications

(104 citation statements)

References 23 publications

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“…As we will see below, this is confirmed by the simulations. The implication is that the field growth is not stopped by the magnetization of the electrons, as conjectured by Lyubarsky & Eichler (2006), because the electrons are at all times only marginally magnetized. The essential reason the electrons get heated as much as they do is that the energy of the electrons keeps pace with the field growth, and so they never become highly magnetized.…”

Section: Electron Heating Estimatementioning

confidence: 94%

“…In particlular, the Weibel instability (Weibel 1959), which causes fast growth of a strong magnetic field at small scales in the anisotropic plasma flow, has received much attention as the main isotropization mechanism leading to the shock transition in free-streaming ejecta from violent astrophysical events (Medvedev & Loeb 1999;Wiersma & Achterberg 2004;Lyubarsky & Eichler 2006;Achterberg & Wiersma 2007;Bret 2009;Yalinewich & Gedalin 2010;Shaisultanov et al 2012;Shukla et al 2012). As the dominant modes of the Weibel instability are less than the ion gyroradius, which renders them inefficient scatterers of ions, the long standing question concerning its role in collisionless shocks has been how well it competes with other mechanisms (e.g., Galeev et al 1964;Blandford & Eichler 1987;Lyubarsky & Eichler 2006). Clearly, mechanisms that require a pre-existing magnetic field are questionable when the magnetic field is weak.…”

Section: Introductionmentioning

confidence: 99%

“…The same electric field that decelerates ions should also accelerate electrons (Blandford & Eichler 1987;Lyubarsky & Eichler 2006;Gedalin et al 2008Gedalin et al , 2012. However, the details of the electric field and the acceleration mechanism have not been worked out.…”

Section: Introductionmentioning

confidence: 99%

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Electron Heating in a Relativistic, Weibel-Unstable Plasma

Kumar

Eichler

Gedalin

2015

ApJ

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The dynamics of two initially unmagnetized relativistic counter-streaming homogeneous ion-electron plasma beams are simulated in two dimensions (2D) using the particle-in-cell (PIC) method. It is shown that current filaments, which form due to the Weibel instability, develop a large-scale longitudinal electric field in the direction opposite to the current carried by the filaments as predicted by theory. This field, which is partially inductive and partially electrostatic, is identified as the main source of net electron acceleration, greatly exceeding that due to magnetic field decay at later stages. The transverse electric field, although larger than the longitudinal field, is shown to play a smaller role in heating electrons, contrary to previous claims. It is found that in one dimension, the electrons become strongly magnetized and are not accelerated beyond their initial kinetic energy. Rather, the heating of the electrons is enhanced by the bending and break up of the filaments, which releases electrons that would otherwise be trapped within a single filament and slow the development of the Weibel instability (i.e., the magnetic field growth) via induction as per Lenz's law. In 2D simulations, electrons are heated to about one quarter of the initial kinetic energy of ions. The magnetic energy at maximum is about 4%, decaying to less than 1% by the end of the simulation. The ions are found to gradually decelerate until the end of the simulation, by which time they retain a residual anisotropy of less than 10%.

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Section: Electron Heating Estimatementioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Electron Heating in a Relativistic, Weibel-Unstable Plasma

Kumar

Eichler

Gedalin

2015

ApJ

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“…Alternative estimates of the stabilized magnetic field can be derived by equating the cyclotron frequency to the growth rate or the gyroradius to the modu- lation wavelength. 82,113,[185][186][187] The dominant filamentation mode at saturation may be determined by computing Eq. ͑54͒ over the whole unstable spectrum.…”

Section: Filamentation Instabilitymentioning

confidence: 99%

Multidimensional electron beam-plasma instabilities in the relativistic regime

2010

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The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell-Jüttner model distributions. The main properties of the competing modes ͑developing parallel, transverse, and oblique to the beam͒ are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.

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“…Depending on the background magnetic field strength, for a symmetric distribution function it was shown that there exists either one or two neutral points that divide the wavenumber range into stable and unstable intervals. Medvedev & Loeb (1999), as well as Lyubarsky & Eichler (2006), investigated only the case of an unmagnetized plasma. However, the external shocks due to the interaction of the fireball with the ambient medium carry a strong magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Plasma Instabilities in Gamma‐Ray Bursts: Neutral Points and the Effect of Mode Coupling

Tautz

Lerche

2006

ApJ

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The method of determining neutral points, corresponding to vanishing frequency in wavenumber space, is applied to the case of gamma-ray bursts (GRBs) to determine low-frequency instabilities. If a particular particle distribution function permits the existence of neutral points, instability is guaranteed on one side or the other of the neutral point. By using the rest frame of the GRB jets, only perpendicular particle motion has to be taken into account. The discussion is limited to the cases of a monoenergetic electron-proton plasma with stationary protons and also to a symmetric electronpositron plasma. In the limiting case of wave propagation perpendicular to a homogeneous background magnetic field, taken to be parallel to the streaming direction of the jet, it is shown that to lowest order in the wave frequency, unstable aperiodic fluctuations occur that grow very rapidly on timescales comparable to or smaller than the characteristic times of the GRB, leading to the conclusion that the jets most likely consist mainly of electron-proton plasmas for the cases investigated. Furthermore, high electron Lorentz factors, as well as the coupling effect between longitudinal and transverse modes, are shown to stabilize the system.

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Are Gamma‐Ray Burst Shocks Mediated by the Weibel Instability?

Cited by 90 publications

References 23 publications

Electron Heating in a Relativistic, Weibel-Unstable Plasma

Electron Heating in a Relativistic, Weibel-Unstable Plasma

Multidimensional electron beam-plasma instabilities in the relativistic regime

Plasma Instabilities in Gamma‐Ray Bursts: Neutral Points and the Effect of Mode Coupling

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