Space charge limited current for bipolar flow in a crossed-field vacuum gap

In this paper, a numerical iteration approach is proposed to make an investigation of the influence of a transverse magnetic field on the space charge limited bipolar flow in a planar vacuum diode. By employing the method, the unknown limiting current density and potential distribution can be simultaneously determined. Considering a planar ion vacuum diode with a transverse magnetic field B parallel to the electrodes surface, we investigated the limiting current density as a function of B. Numerical calculations show that the limiting current density of the crossed-field vacuum diode may be approximately given by J(e) = J(CL)[a(B/B-H)(b) + F], where J(CL) is the CL law and BH the Hull cutoff magnetic field, and a and b are the function of the ion current density, respectively. The physical meaning of F may be interpreted as the 1D current density enhancement factor due to the effect of ions for B = 0. In the absence of ions, the limiting current solution is recovered in a crossed-field vacuum gap.