skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Relativistic Weibel instability

Abstract

The relativistic Weibel instability has received much attention because of its potential application to astrophysical problems. The purpose of this paper is to correct certain erroneous expressions in the author's early paper on the subject [P. H. Yoon, Phys. Fluids B 1, 1336 (1989)], to discuss further properties of the relativistic Weibel instability, and to compare with its nonrelativistic counterpart.

Authors:
 [1]
  1. Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)
Publication Date:
OSTI Identifier:
20974854
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 2; Other Information: DOI: 10.1063/1.2646285; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ASTROPHYSICS; COMPARATIVE EVALUATIONS; PLASMA INSTABILITY; RELATIVISTIC PLASMA; RELATIVISTIC RANGE

Citation Formats

Yoon, Peter H. Relativistic Weibel instability. United States: N. p., 2007. Web. doi:10.1063/1.2646285.
Yoon, Peter H. Relativistic Weibel instability. United States. doi:10.1063/1.2646285.
Yoon, Peter H. Thu . "Relativistic Weibel instability". United States. doi:10.1063/1.2646285.
@article{osti_20974854,
title = {Relativistic Weibel instability},
author = {Yoon, Peter H.},
abstractNote = {The relativistic Weibel instability has received much attention because of its potential application to astrophysical problems. The purpose of this paper is to correct certain erroneous expressions in the author's early paper on the subject [P. H. Yoon, Phys. Fluids B 1, 1336 (1989)], to discuss further properties of the relativistic Weibel instability, and to compare with its nonrelativistic counterpart.},
doi = {10.1063/1.2646285},
journal = {Physics of Plasmas},
number = 2,
volume = 14,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • Detailed properties of the classical electromagnetic Weibel instability in a relativistic unmagnetized plasma are investigated for a fully relativistic bi-Maxwellian distribution. In particular, exact analytical expressions for the range of unstable wavenumbers, conditions for the instability, and the growth rate of the unstable mode for weak anisotropy are derived. The analysis shows that relativistic effects tend to stabilize the Weibel instability.
  • Detailed properties of the Weibel instability in a relativistic unmagnetized plasma are investigated for a particular choice of anisotropic distribution function F(p/sub perpendicular//sup 2/,p/sub z/) that permits an exact analytical solution to the dispersion relation for arbitrary energy anisotropy. The particular equilibrium-distribution function considered in the present analysis assumes that all particles move on a surface with perpendicular momentum p/sub perpendicular/ = p-circumflex/sub perpendicular/ = const and are uniformly distributed in parallel momentum from p/sub z/ = -p-circumflex/sub z/ = const to p/sub z/ = +p-circumflex/sub z/ = const. (Here, the propagation direction is the z direction.) The resulting dispersionmore » relation is solved analytically, and detailed stability properties are determined for a wide range of energy anisotropy.« less
  • Analyzing the production of a weakly relativistic plasma produced by microwave fields with circular polarization in the adiabatic approximation, the electron distribution function is obtained, which is nonequilibrium and anisotropic. Furthermore, it is shown that the produced plasma is accelerated in the direction of propagating microwave electric fields. The electron velocity in this direction strongly depends on electron origination phase, electric field phase, and amplitude of the microwave electric field. Making use of the dielectric tensor obtained for this plasma, it is shown that the Weibel instability develops due to the anisotropic property of the distribution function. It is shownmore » that the growth rate in the relativistic case is higher than that obtained for the nonrelativistic case by a factor depending on the electric field strength and plasma frequency.« less
  • We present three-dimensional, fully relativistic, fluid simulations of the dynamics of inhomogeneous counter streaming beams with the aim of understanding the magnetic structures that can be expected to form as a consequence of the development of the so-called Weibel instability. Ringlike structures in the transverse direction are generated as a consequence of the development of a spatially resonant mode. We describe the structures generated by beams of equal initial density and velocity and by a fast, less dense beam compensated by a slower, denser beam. We consider these two cases as schematic models of a laser produced beam propagating inmore » a plasma with nearly equal density and in a plasma much denser than the injected beam.« less
  • A general description is developed of the kinetic Weibel [Phys. Rev. Lett. 2, 83 (1959)] instability in relativistic plasmas for arbitrary plasma distribution functions. Then general conditions for the existence of the relativistic instability are given as well as the influence of limits on the wave-number range and so on the instability rate. A comparison with previous works on bi-Gaussian distributions is also provided. Furthermore, ultrarelativistic and also weakly anisotropic relativistic distributions are investigated in general. Finally, isolated Weibel modes (in which both the frequency and wave number are fixed) are derived for asymmetric relativistic plasma distributions and constraints onmore » these isolated modes are presented.« less