Second-order stability analysis of the Vlasov–Poisson equations in the planar magnetron

Abstract

The second-order stability analysis of the Vlasov–Poisson equations for high-density, finite-temperature plasmas in the presence of inhomogeneous crossed fields and density gradients is carried out. The analysis is more general than earlier studies of high-beta inhomogeneous plasmas in that various approximations employed therein, such as the local approximation Jeffreys–Wentzel–Kramers–Brillouin, and low-frequency and small-wavelength restrictions, are not employed here. It is shown that the evolution of the particle guiding centers on the slow-time scale corresponds to an electron motion toward the anode at and above the diocotron resonance. This is in qualitative agreement with what has been observed during convective cell formation in recent particle simulations performed by Mission Research Corporation [Technical Digest—International Conference on Electron Devices (IEEE, New York, 1985), pp. 180–183]. The behavior predicted by the Vlasov–Poisson formalism is shown to be somewhat different from that obtained from the cold-fluid formalism, where the density profile for the latter evolved only at the positions of the diocotron and magnetron resonances.