Abstract
In this paper a method is described to study the collisionless tearing mode properties in cases where complicated orbit integrals must be evaluated. The method is based on a quadratic form of a self-adjoint integrodifferential operator. No approximations are made for equilibrium orbits and perturbed fields in evaluating the necessary orbit integrals. The objective of the paper is to provide a rigorous theoretical basis for the method. Application to physical systems is demonstrated for the collisionless tearing mode in a non-Maxwellian neutral sheet. This method may be applied to other Vlasov instabilities and is particularly suited for problems where the numerical evaluation of orbit integrals is time consuming. In such cases, the present method can yield stability criteria with minimal computation.
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