Electron sheaths in a crossed-field gap-equilibrium solutions and transition to turbulence

Summary form only given, as follows. There is renewed interest in the equilibrium solutions and the transition to turbulence of electron sheaths in a crossed-field gap. In this paper, we present an analytic theory of the critical current beyond which transition from laminar to turbulent behaviour occurs, under the assumption that the electrons are released from the cathode with a nonzero mono-energetic velocity. This analytic theory is found to be in excellent agreement with the results obtained from a particle simulation code. We also find that the behaviour of the sheaths is quite different, depending on whether B>B/sub H/ or B B/sub H/, where many crossed-field amplifiers of practical significance operate, we find that there is no electrostatic potential minimum in the equilibrium solution, in sharp contrast to the BB/sub H/ cases. The spatial extent and the frequency of oscillations of this microsheath depend on the injected current and on the initial velocity. This study seems to have added substance to the notion, widely held in the community of ultra-low noise crossed-field amplifiers, that a necessary condition for quiescent behaviour in a crossed-field gap is that electron emission be limited.