A general dispersion relation for non-uniform magnetized plasmas

A general dispersion relation is derived for linear waves in a non-uniform, magnetized plasma using the polarized co-ordinate system. An equilibrium distribution function with general gradients in density and temperature (and differing parallel and perpendicular temperatures) is proposed using polarized tensors. A compact conductivity tensor is derived in terms of tensor quantities, including certain tensor moment integrals whose elements may be evaluated separately from a given problem. This is of importance in computational applications. The derivation is under the restrictions ( a ) small gradients, ( b ) the local approximation of Krall & Rosenbluth, and ( c ) β ⊥ ≪ 1. Conditions for coupling of electrostatic and electro-magnetic modes are investigated.