Normal modes of a loss cone plasma slab with steep density gradient

The electrostatic flute-like normal modes were found for a collisionless loss cone plasma in a uniform magnetic field with density varying sinusoidally in one direction in space. A local method, appropriate to kLvery-much-greater-than1, where k is the wavenumber and L is the scale length, and a nonlocal method, appropriate to kLapproximately-less-than1, where both used; the ion Larmor radius a/sub i/ was not assumed to be small. The usual drift cone mode was found when a/sub i/very-much-less-thanL; other instabilities were found for a/sub i/approximately-greater-thanL. In principle, the methods could be applied to other configurations of plasma