Exact and approximate solutions to the finite temperature wave equation in a one-dimensional perpendicularly stratified plasma

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Abstract
The sixth order wave equation which results from a finite temperature expansion of the Vlasov equation is solved globally in the ion cyclotron range of frequencies. A perpendicularly stratified, onedimensional slab plasma is assumed. The diamagnetic drift and the associated anisotropy are included in the unperturbed distribution function to ensure a self-adjoint system. All x-dependence in the plasma pressure and magnetic field is retained along with the electric field parallel to B⃗. Thus, Landau damping of the ion Bernstein wave is included self-consistently. Because of the global nature of the solution, the evanescent short wavelength Bernstein waves do not grow exponentially as in shooting methods. Strong variations occur in the absorption and in the structure of the wave fields as resonance topology is varied. Solutions to the complete sixth order differential equation are compared to those from an approximate second order equation based on local dispersion theory.