Abstract
The van Kampen-Case treatment of the linearized Vlasov equation is generalized to cases of non-uniform plasmas in non-uniform equilibrium fields. This is done by transforming the Vlasov operator into the representation of the eigenfunctions of the streaming operator. The Vlasov operator is thus reduced to the form of a multiplication operator perturbed by an integral operator so that the continuum eigenfunctions may be constructed by adapting a method originally devised in neutron transport theory. The calculation leads to solving a non-singular Fredholm-type integral equation. Various kinds of degeneracy of the continuous spectrum are discussed and an example is given.
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