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Interpretation of dispersion relations for bounded systems

Published online by Cambridge University Press:  13 March 2009

T. D. Rognlien  and
S. A. Self
T. D. Rognlien
Affiliation:
Institute for Plasma Research, Stanford University
S. A. Self
Affiliation:
Institute for Plasma Research, Stanford University
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Abstract

A treatment is given of the problem of constructing normal modes for anarbitrarily bounded system from roots of the linear dispersion relation D( ω, k) = 0 for the corresponding infinite or periodically bounded system. For a system described by continuous macroscopic variables, and of general cylindrical form (uniform along an axis z, say), each transverse eigenmode gives rise to a set of axial normal modes constructed from a pair of dominant roots kαz(ω) of D = 0 satisfying the boundary conditions which are characterized by complex reflexion coefficients for the dominant waves. The implications of the results for the interpretation of experiments on plasma waves and instabilities on finite cylinders are discussed, with particular reference to the effects of end-plate damping and axial current on Q-machines.

Type
Research Article
Information
Journal of Plasma Physics , Volume 7 , Issue 1 , February 1972 , pp. 13 - 48
Copyright
Copyright © Cambridge University Press 1972

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