VARIATIONAL PRINCIPLE FOR CROSSED-FIELD DEVICES

We present a Rayleigh-Ritz variational model of the electron sheath in crossed-field devices. Using laminar layer orbits, this model predict s equilibria in agreement with the classical Brillouin model. Other pr edictions include the existence of existence of non-classical, stable equilibria as well as limit cycles. This variational model also predic ts the existence of a stable propagating diocotron mode, which is abse nt from the Brillouin model but is present in tile double-box model of Kaup and Thomas. Comparisons of these results with those of the cold- fluid theory are discussed.