Finite-wavelength oscillations of a diffuse-profile, Vlasov-fluid plasma column

An equation of motion is derived which describes finite-wavelength (i.e., axial wavelength approx. plasma radius) oscillations of a Vlasov-ion, fluid-electron plasma in a diffuse, near-theta pinch geometry. The equations include simultaneous geometric and ion kinetic effects. For a screw-pinch geometry, and with isothermal electrons, these equations are shown to be equivalent to the guiding-center equations. Boundary conditions and a closed-form solution for the sharp-profile case are discussed