Eigenmodes and growth rates of relativistic current filamentation instability in a collisional plasma

Honda, M.

doi:10.1103/physreve.69.016401

Cited by 61 publications

(49 citation statements)

References 46 publications

(84 reference statements)

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“…156,217 The simplicity of the Krook approach makes it widely employed in spite of its known drawbacks ͑no relaxation to a Maxwellian, nonconservation of particle number, etc.͒. More elaborate treatments for the filamentation 219 155,217,222 others find they only modify the existing collisionless unstable branch. A general trend, observed regardless of the number of branches, is that collisions tend to generate larger filaments by displacing the fastest growing filamentation modes toward the lower k's.…”

Section: -29mentioning

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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Section: -29mentioning

confidence: 99%

Multidimensional electron beam-plasma instabilities in the relativistic regime

2010

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“…The role of collisions on the instability growth rates in the regime of interest for FI has been recently addressed analytically by a linear fluid normal mode analysis in Ref. [12] and by a linear and quasilinear kinetic approach in the limit of purely transverse modes in Ref. [13].…”

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confidence: 99%

Three-Dimensional Magnetic Structures Generated by the Development of the Filamentation (Weibel) Instability in the Relativistic Regime

2006

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“…Setting then ∇P i = 3k B T i ∇n i [12,22] if dealing only with electronic motion, one only needs to add to the notebook entries 4 and 5 the terms (i 2 = −1)…”

Section: Comments and Conclusionmentioning

confidence: 99%

Beam-plasma dielectric tensor with Mathematica

Bret

2007

Computer Physics Communications

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We present a Mathematica notebook allowing for the symbolic calculation of the 3 × 3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Program summary Title of program: TensorCatalog identifier: ADYT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, Spain Operating system under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of bytes in distributed program, including test data, etc.: 33 439 No. of lines in distributed program, including test data, etc.: 3169 Distribution format: tar.gz Nature of the physical problem:The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables. Method of solution:The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère-Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the dimensionless variables. Restrictions on the complexity of the problem: Temperature effects are limited to small, i.e. non-relativistic, temperatures. The kinetic counterpart of the present Mathematica will usually not compute the required integrals. Typical running time: About 1 minute on a Intel Centrino 1.5 GHz Laptop with 512 MB of RAM. Unusual features of the program: None.

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Eigenmodes and growth rates of relativistic current filamentation instability in a collisional plasma

Cited by 61 publications

References 46 publications

Multidimensional electron beam-plasma instabilities in the relativistic regime

Multidimensional electron beam-plasma instabilities in the relativistic regime

Three-Dimensional Magnetic Structures Generated by the Development of the Filamentation (Weibel) Instability in the Relativistic Regime

Beam-plasma dielectric tensor with Mathematica

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