THEORY OF ELECTROSTATIC FLUID MODES IN A COLD SPHEROIDAL NONNEUTRAL PLASMA

The normal modes of a magnetized spheroidally shaped pure ion plasma have recently been measured. Here the theory of these modes is presented. Although one might expect that a numerical solution is required (because the plasma dielectric is anisotropic and the plasma is inhomogeneous), the problem is actually separable in an unusual coordinate system. The result is a simple electrostatic fluid dispersion relation for modes in a cloud of any spheroidal shape.