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A singular perturbation analysis of theoretical models for warm inhomogeneous plasmas

Published online by Cambridge University Press:  13 March 2009

Robert M. Miura
Courant Institute of Mathematical Sciences, New York University
Eugene M. Barston
Courant Institute of Mathematical Sciences, New York University


Owing to the complexity of the Vlasov–Maxwell equations for inhomogeneous plasmas, it is of general interest to investigate simpler approximate models. We compare three specific models, proposed in the literature in connexion with the high frequency oscillations of such plasmas, by means of a singular perturbation expansion in powers of E = (λD/L)⅔, where λD and L are appropriate electron Debye and equilibrium scale lengths, respectively. Explicit formulas are obtained for the eigenfrequencies (to second order) and for the electric field eigenfunctions (to leading order), and the computation of these quantities for various equilibrium parameters becomes very simple indeed. We find that, whereas the electric field eigenfunctions differ in zero order for the three models, the eigenfrequencies are identical through first order.

Research Article
Copyright © Cambridge University Press 1971

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