Stability of Bound Eigenmode Solutions for the Collisionless Universal Instability

Abstract

The collisionless universal instability in slab geometry with a sheared magnetic field is considered. It is shown from the differential eigenvalue equation that no bound growing eigensolutions exist. The method of solution consists of first assuming that exponentially growing eigenmodes exist and then forming quadratic quantities from which a contradiction is obtained. The relation between the eigenmodes and convective modes is discussed.