Numerical solution of the linear dispersion relation in a relativistic pair plasma

Abstract

We describe an algorithm that computes the linear dispersion relation of waves and instabilities in relativistic plasmas within a Vlasov-Maxwell description. The method used is fully relativistic and involves explicit integration of particle orbits along the unperturbed equilibrium trajectories. We check the algorithm against the dispersion curves for a single component magnetised plasma and for an unmagnetised plasma with counter-streaming components in the non-relativistic case. New results on the growth rate of the Weibel or two-stream instability in a hot unmagnetised pair plasma consisting of two counter-streaming relativistic Maxwellians are presented. These are relevant to the physics of the relativistic plasmas found in gamma-ray bursts, relativistic jets and pulsar winds.

Accepted by Plasma Physics and Controlled Fusion

References in corpus (3)

• The Physics of Gamma-Ray Bursts
• Are GRB shocks mediated by the Weibel instability?
• Magnetic field generation in relativistic shocks - An early end of the exponential Weibel instability in electron-proton plasmas

Cited by in corpus (6)

• Theory of pulsar magnetosphere and wind
• Particle Energization in 3D Magnetic Reconnection of Relativistic Pair Plasmas
• Growth rates of the Weibel and tearing mode instabilities in a relativistic pair plasma
• The filamentation instability driven by warm electron beams: Statistics and electric field generation
• Simulation study of the filamentation of counter-streaming beams of the electrons and positrons in plasmas
• Electric field generation by the electron beam filamentation instability: Filament size effects