High-frequency behavior of the crossed-field potential minimum

A time-domain analysis of the high-frequency currents in a crossed-field potential minimum is presented. The distinctions between ordinary and crossed-field potential minimums are discussed and a one-dimensional model for the crossed-field case is described. The general form of the solution is given as an infinite array of coupled integral equations and the required expressions for the coefficients are developed. A reduced array of equations is used for a numerical analysis of a diode with a 100-gauss transverse magnetic field. The numerical analysis revealed only a minor modification of the current fluctuations as a result of the transverse magnetic field, although experiments have shown excess-energy crossed-field currents related to the potential minimum with magnetic fields lower than this.