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Journal Article

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

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Pétri,  Jérôme
Prof. Heinrich J. Völk, Emeriti, MPI for Nuclear Physics, Max Planck Society;

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Kirk,  John G.
Division Prof. Dr. Werner Hofmann, MPI for Nuclear Physics, Max Planck Society;

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Citation

Pétri, J., & Kirk, J. G. (2007). Growth rates of the Weibel and tearing mode instabilities in a relativistic pair plasma. Plasma Physics and Controlled Fusion, 49(11), 1885-1896. doi:10.1088/0741-3335/49/11/009.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-7BE6-E
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.