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Bret A.,University of Castilla - La Mancha | Bret A.,Campus Universitario Of Ciudad Real | Gremillet L.,CEA DAM Ile-de-France | Dieckmann M.E.,Linkoping University
Physics of Plasmas | Year: 2010

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 beam) 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. © 2010 American Institute of Physics. Source

Bret A.,University of Castilla - La Mancha | Gremillet L.,Campus Universitario Of Ciudad Real | Benisti D.,CEA DAM Ile-de-France
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

Following a recent Letter by Bret [Phys. Rev. Lett. 100, 205008 (2008)], we present a detailed report of the entire unstable k spectrum of a relativistic collisionless beam-plasma system within a fully kinetic framework. In contrast to a number of previously published studies, our linear analysis makes use of smooth momentum distribution functions of the Maxwell-Jüttner form. The three competing classes of instabilities, namely, two-stream, filamentation, and oblique modes, are dealt with in a unified manner, no approximation being made regarding the beam-plasma densities, temperatures, and drift energies. We investigate the hierarchy between the competing modes, paying particular attention to the relatively poorly known quasielectrostatic oblique modes in the regime where they govern the system. The properties of the fastest growing oblique modes are examined in terms of the system parameters and compared to those of the dominant two-stream and filamentation modes. © 2010 The American Physical Society. Source

Bret A.,University of Castilla - La Mancha | Bret A.,Campus Universitario Of Ciudad Real
Physics of Plasmas | Year: 2014

The filamentation (Weibel) instability plays a key role in the formation of collisionless shocks which are thought to produce Gamma-Ray-Bursts and High-Energy-Cosmic-Rays in astrophysical environments. While it has been known for long that a flow-aligned magnetic field can completely quench the instability, it was recently proved in 2D that in the cold regime, such cancelation is possible if and only if the field is perfectly aligned. Here, this result is finally extended to a 3D geometry. Calculations are conducted for symmetric and asymmetric counter-streaming relativistic plasma shells. 2D results are retrieved in 3D: the instability can never be completely canceled for an oblique magnetic field. In addition, the maximum growth-rate is always larger for wave vectors lying in the plan defined by the flow and the oblique field. On the one hand, this bears consequences on the orientation of the generated filaments. On the other hand, it certifies 2D simulations of the problem can be performed without missing the most unstable filamentation modes. © 2014 AIP Publishing LLC. Source

Bret A.,University of Castilla - La Mancha | Bret A.,Campus Universitario Of Ciudad Real
Physics of Plasmas | Year: 2016

The instabilities triggered when two counter-streaming pair beams collide are analyzed. A guiding magnetic field is accounting for, while both beams are considered identical and cold. The instability analysis is conducted over the full k-spectrum, allowing to derive the hierarchy map of the dominant unstable modes, in terms of the initial beams energy γ0 and a magnetic field strength parameter ΩB. Four different regions of the (Ω B, γ 0) phase space are identified, each one governed by a different kind of mode. The analysis also unravels the existence of a "triple point," where 3 different modes grow exactly at the same rate. A number of analytical expressions can be derived, either for the modes growth-rates or for the frontiers between the 4 regions. © 2016 Author(s). Source

Bret A.,University of Castilla - La Mancha | Bret A.,Campus Universitario Of Ciudad Real
Physics of Plasmas | Year: 2015

The motion of a particle in a spatially harmonic magnetic field is a basic problem involved, for example, in the mechanism of formation of a collisionless shock. In such settings, it is generally reasoned that particles entering a Weibel generated turbulence are trapped inside it, provided their Larmor radius in the peak field is smaller than the field coherence length. The goal of this work is to put this heuristic conclusion on firm ground by studying, both analytically and numerically, such motion. A toy model is analyzed, consisting of a relativistic particle entering a region of space occupied by a spatially harmonic field. The particle penetrates the magnetic structure in a direction aligned with the magnetic filaments. Although the conclusions are not trivial, the main result is confirmed. © 2015 AIP Publishing LLC. Source

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