Saturation of relativistic Weibel instability and the formation of stationary current sheets in collisionless plasma

Martyanov, Vladimir; Kocharovsky, Vl. V.

doi:10.1134/s1063776108120145

Cited by 11 publications

(10 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Filamentation Instabilitymentioning

confidence: 99%

Multidimensional electron beam-plasma instabilities in the relativistic regime

2010

View full text Add to dashboard Cite

show abstract

“…Mirroring the non-relativistic solution [9][10][11] , where the properties of the pressure tensor were exploited, the energy-momentum tensor T αβ was wielded in an equivalent role 27 , allowing the calculation of the equilibrium. In our Alternative methods of studying relativistic VM equilibria have also been developed [28][29][30][31][32][33][34] . Suzuki explored possible equilibria by describing the deviation of the distribution function from a Maxwell-Jüttner distribution using orthogonal polynomial series 28 .…”

Section: Discussionmentioning

confidence: 99%

“…Using this novel method a new, two dimensional equilibrium was reported. Kocharovsky and co-workers use the method of invariants of particle motion to find exact solutions of the VM system for arbitrary particle energy distributions [29][30][31] . There technique allows for the description of multicomponent plasmas, that may be relativistic or not, for a general magnetic geometry 29 .…”

Section: Discussionmentioning

confidence: 99%

Collisionless distribution function for the relativistic force-free Harris sheet

Stark

Neukirch

2012

Physics of Plasmas

View full text Add to dashboard Cite

A self-consistent collisionless distribution function for the relativistic analogue of the force-free Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the non-relativistic collisionless force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)] as it has the same dependence on the particle energy and canonical momenta.We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed.

show abstract

“…Yet, there were almost no attempts to analytically construct a stationary filamentary equilibrium, in a way, similar to the building of a Harris current sheet. Recently, an attempt to derive a GradShafranov-type equation for such equilibrium has been made (Mart'yanov et al 2008). In doing this, the authors failed to make one of their basic assumptions consistent with Maxwell equations, thus losing an important constraint, which has to be satisfied.…”

Section: Introductionmentioning

confidence: 99%

Relativistic filamentary equilibria

et al. 2010

View full text Add to dashboard Cite

Abstract. Plasma filamentation is often encountered in collisionless shocks and inertial confinement fusion. We develop a general analytical description of the two-dimensional relativistic filamentary equilibrium and derive the conditions for existence of potential-free equilibria. A pseudopotential equation for the vectorpotential is constructed for cold and relativistic Maxwellian distributions. The role of counter-streaming is explained. We present single current sheet and periodic current sheet solutions, and analyze the equilibria with electric potential. These solutions can be used to study linear and nonlinear evolution of the relativistic filamentation instability.

show abstract

Saturation of relativistic Weibel instability and the formation of stationary current sheets in collisionless plasma

Cited by 11 publications

References 38 publications

Multidimensional electron beam-plasma instabilities in the relativistic regime

Multidimensional electron beam-plasma instabilities in the relativistic regime

Collisionless distribution function for the relativistic force-free Harris sheet

Relativistic filamentary equilibria

Contact Info

Product

Resources

About