Growth rates of the Weibel and tearing mode instabilities in a relativistic pair plasma

Abstract

We present an algorithm for solving the linear dispersion relation in an inhomogeneous, magnetised, relativistic plasma. The method is a generalisation of a previously reported algorithm that was limited to the homogeneous case. The extension involves projecting the spatial dependence of the perturbations onto a set of basis functions that satisfy the boundary conditions (spectral Galerkin method). To test this algorithm in the homogeneous case, we derive an analytical expression for the growth rate of the Weibel instability for a relativistic Maxwellian distribution and compare it with the numerical results. In the inhomogeneous case, we present solutions of the dispersion relation for the relativistic tearing mode, making no assumption about the thickness of the current sheet, and check the numerical method against the analytical expression.

arXiv commentAccepted by PPCF

References in corpus (5)

• The Physics of Gamma-Ray Bursts
• The theory of pulsar winds and nebulae
• 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
• Numerical solution of the linear dispersion relation in a relativistic pair plasma

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• PIC simulations of the Thermal Anisotropy-Driven Weibel Instability: Field growth and phase space evolution upon saturation
• Relativistic Tearing and Drift-kink Instabilities in Two-fluid Simulations
• High-energy pulses and phase-resolved spectra by inverse Compton emission in the pulsar striped wind - Application to Geminga
• Simulation study of the filamentation of counter-streaming beams of the electrons and positrons in plasmas
• PIC Simulations of the Temperature Anisotropy-Driven Weibel Instability: Analyzing the perpendicular mode
• Evolution of three-dimensional Relativistic Ion Weibel Instability: Competition with Kink Instability
• Collisionless tearing instability in relativistic non-thermal pair plasma and its application to MHD turbulence
• Collisionless tearing instability in a relativistic pair plasma with a power-law distribution function