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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.
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