Transverse space-charge flow in four magnetically insulated transmission lines

Electromagnetic field theory and electron motion conservation equations are used to derive numerical model of transverse space-charge flow and magnetically insulated critical condition in the four usual transmission lines: planes, cylinders, cones and discs. Through numerical simulation, the dependence of the transverse space-charge flow on the geometrical configurations parameters of the transmission lines is quantitatively obtained. The space-charge flow decreases as the geometrical factor increases for cylinders or as the geometrical factor and the angle between anode and cathode increase and the cathode polar angle decreases for cones. This work provides theoretical basis for engineering design.