A quadratic-form analysis of the collisionless tearing mode

A quadratic form method is developed to study the collisionless tearing mode properties in the neutral sheet geometry in cases where complicated orbit integrals must be evaluated even at marginal stability. The method is based on a quadratic form of a self-adjoint integro-differential operator describing the linear tearing mode. The equilibrium orbits are included exactly and analytically. The objective of the paper is to provide a rigorous theoretical basis for the method. Application to physical systems is illustrated using an example. This method is particularly suited for problems where the repeated numerical evaluation of the orbit integrals is time-consuming. In such cases, the present method can yield stability criteria with minimal computation.