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Magnetohydrodynamic plasma instability driven by Alfvén waves excited by cosmic rays

Published online by Cambridge University Press:  13 March 2009

J. F. McKenzie  and
G. M. Webb
J. F. McKenzie
Affiliation:
Department of Mathematics and Applied Mathematics, University of Natal, Durban, Natal, South Africa
G. M. Webb
Affiliation:
Max-Planck-Institut für Kernphysik, Heidelberg, W. Germany
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Abstract

Hydrodynamical equations describing the mutual interaction of cosmic rays, thermal plasma, magnetic field and Alfvén waves scattering the cosmic rays used in cosmic ray shock acceleration theory (e.g. McKenzie & Völk 1982; Drury 1983; Webb 1983) are analysed for long-wavelength linear compressive instabilities. The Alfvén wave field may contain a pre-existing component as well as a component excited by the cosmic ray streaming instability. In the case of no Alfvén wave damping, adiabatic wave growth and Alfvén wave generation by the cosmic ray streaming instability, it is found that the backward propagating slow magneto-acoustic mode is driven convectively unstable by the pressure of the self-excited Alfvén waves, provided the thermal plasma β is sufficiently large. The equations are also analysed for the case where the Alfvén wave growth is balanced by some nonlinear damping mechanisms. In the latter case both the forward and backward propagating slow magneto-acoustic modes may be driven unstable if the plasma β is sufficiently small. The conditions under which the instabilities occur are delineated, and sample calculations of growth rates given. Possible applications of the instabilities to astrophysical situations are briefly discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 31 , Issue 2 , April 1984 , pp. 275 - 299
Copyright
Copyright © Cambridge University Press 1984

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