Exact relativistic kinetic theory of the full unstable spectrum of an electron-beam–plasma system with Maxwell-Jüttner distribution functions

Bret, Antoine; Grémillet, L.; Bénisti, Didier

doi:10.1103/physreve.81.036402

Cited by 74 publications

(95 citation statements)

References 84 publications

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“…While early results on obliquely oriented modes have been obtained through the longitudinal approximation 8,9 ͑which, as shown in Ref. 110, allows for an accurate characterization of the dominant modes in the broad parameter range governed by oblique modes͒, the general kinetic dispersion relation was first numerically solved by Lee and Thode 111 for a special class of diluted, angularly spread monoenergetic beams. The first picture of the full 2D spectrum was obtained a decade later in the cold-fluid regime by Califano et al 28,112,113 Once a real wave vector k has been chosen, the dispersion equation follows from Eqs.…”

Section: ͑8͒mentioning

confidence: 99%

“…When the inequality is reversed, the instability enters the hot ͑or kinetic͒ regime characterized by weaker growth rates. 26,110 A given configuration can therefore be cold with respect to the two-stream instability, and "hot" with respect to filamentation. Note also that the effective velocity spread involved in Eq.…”

Section: ͑27͒mentioning

confidence: 99%

“…135 For the Maxwell-Jüttner distribution in the weak-temperature limit, the factor is rather ␥ b . 110 Now, the sensitivity of unstable modes to a given thermal spread depends on their orientation. Transverse spreads do not detune beam electrons from beam-aligned modes, which are therefore weakly affected.…”

Section: ͑27͒mentioning

confidence: 99%

“…Such stabilization can be achieved for waterbag 15,16,52,105 or Maxwellian-like 59,104 distributions, but not with Maxwell-Jüttner functions. 110 Furthermore, the cancelation threshold, when it exists, can be very sensitive to the background plasma distribution ͑see Ref. 136 and discussion in Sec.…”

Section: -10mentioning

confidence: 99%

“…The temperature-dependent analysis 18,110 brings in at least two additional parameters, namely, the beam and plasma temperatures. The introduction of both transverse and parallel thermal spreads would lead to a daunting sixdimensional parameter space.…”

Section: B Maxwell-jüttner Kinetic Theorymentioning

confidence: 99%

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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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Section: ͑8͒mentioning

confidence: 99%

Section: ͑27͒mentioning

confidence: 99%

Section: ͑27͒mentioning

confidence: 99%

Section: -10mentioning

confidence: 99%

Section: B Maxwell-jüttner Kinetic Theorymentioning

confidence: 99%

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Multidimensional electron beam-plasma instabilities in the relativistic regime

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On the ordinary mode Weibel instability in space plasmas: A comparison of three‐particle distributions

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Electromagnetic wave fluctuations driven by temperature anisotropy in plasmas are of interest for solar flare, solar corona, and solar wind studies. We investigate the dispersion characteristics of electromagnetic wave propagating perpendicular to the uniform magnetic field which is derived by using multiple particle distribution functions: Maxwellian, bi‐kappa, and product bi‐kappa. The presence of temperature anisotropy in which the parallel plasma kinetic energy density exceeding by a sufficient amount can lead to Weibel‐like electromagnetic instability. A general description is made to calculate the growth/damping rates of Weibel‐like modes when the temperature anisotropy and nonthermal features are associated with these distributions. We demonstrate that for the zeroth cyclotron harmonic, our results for bi‐Maxwellian and bi‐kappa overlap with each other, while the product bi‐kappa distribution shows some dependence on parallel kappa index. For higher harmonics, the growth rates vanish and the damping prevails.

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Relativistic Shocks: Particle Acceleration and Magnetization

Sironi¹,

Keshet²,

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2016

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We review the physics of relativistic shocks, which are often invoked as the sources of non-thermal particles in pulsar wind nebulae (PWNe), gamma-ray bursts (GRBs), and active galactic nuclei (AGN) jets, and as possible sources of ultra-high energy cosmic-rays. We focus on particle acceleration and magnetic field generation, and describe the recent progress in the field driven by theory advances and by the rapid development of particle-in-cell (PIC) simulations. In weakly magnetized or quasi parallel-shocks (i.e. where the magnetic field is nearly aligned with the flow), particle acceleration is efficient. The accelerated particles stream ahead of the shock, where they generate strong magnetic waves which in turn scatter the particles back and forth across the shock, mediating their acceleration. In contrast, in strongly magnetized quasi-perpendicular shocks, the efficiencies of both particle acceleration and magnetic field generation are suppressed. Particle acceleration, when efficient, modifies the turbulence around the shock on a long time scale, and the accelerated particles have a characteristic energy spectral index of s γ 2.2 in the ultra-relativistic limit. We discuss how this novel understanding of particle acceleration and magnetic field generation in relativistic shocks can be applied to high-energy astrophysical phenomena, with an emphasis on PWNe and GRB afterglows.All authors contributed equally to this review.

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Exact relativistic kinetic theory of the full unstable spectrum of an electron-beam–plasma system with Maxwell-Jüttner distribution functions

Cited by 74 publications

References 84 publications

Multidimensional electron beam-plasma instabilities in the relativistic regime

Multidimensional electron beam-plasma instabilities in the relativistic regime

On the ordinary mode Weibel instability in space plasmas: A comparison of three‐particle distributions

Relativistic Shocks: Particle Acceleration and Magnetization

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