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Electron inertia and quasi-neutrality in the Weibel instability

Part of: PLA The Vlasov Equation

Published online by Cambridge University Press:  05 June 2017

Enrico Camporeale  and
Cesare Tronci
Enrico Camporeale*
Affiliation:
Center for Mathematics and Computer Science (CWI), 1098 XG Amsterdam, The Netherlands
Cesare Tronci
Affiliation:
Department of Mathematics, University of Surrey, Guildford GU2 7XH, United Kingdom
*
†Email address for correspondence: e.camporeale@cwi.nl
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Abstract

While electron kinetic effects are well known to be of fundamental importance in several situations, the electron mean-flow inertia is often neglected when length scales below the electron skin depth become irrelevant. This has led to the formulation of different reduced models, where electron inertia terms are discarded while retaining some or all kinetic effects. Upon considering general full-orbit particle trajectories, this paper compares the dispersion relations emerging from such models in the case of the Weibel instability. As a result, the question of how length scales below the electron skin depth can be neglected in a kinetic treatment emerges as an unsolved problem, since all current theories suffer from drawbacks of different nature. Alternatively, we discuss fully kinetic theories that remove all these drawbacks by restricting to frequencies well below the plasma frequency of both ions and electrons. By giving up on the length scale restrictions appearing in previous works, these models are obtained by assuming quasi-neutrality in the full Vlasov–Maxwell system.

Keywords

plasma instabilities
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 3 , June 2017 , 705830301
Copyright
© Cambridge University Press 2017 

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