Wavenumber space analysis of oscillations in weakly non-uniform magnetoplasmas

A differential equation in wavenumber space is used to find the electric field excited by an external source in a weakly non-uniform, low-β, neutral magneto- plasma slab (with B perpendicular to _n). The analysis is general enough to allow one to judge the accuracy of previously used long-wavelength methods. Electrostatic waves which propagate across the magnetic field parallel to the density gradient are considered, and the impedance of a grid-plasma system is determined. The calculation is specialized to the case of a low density plasma with applied frequencies near the upper hybrid.