A Theory for the Sparkover Time of a Low Pressure Magnetic Switch

In this paper the theory developed by the author for the formative time lags of gases on the right-hand side of Paschen´s minimum in crossed electric and magnetic fields has been extended to cover the left-hand side of the Paschen minimum. A coaxial cylindrical geometry has been considered and the theory takes into account the radial change of the electric field and of Townsend´s first ionization coefficient. The temporal and spatial growth of current in oxygen has been calculated in electric fields only, as a first step and good agreement is shown to exist between the theory and experiment. The theory is then extended to a magnetic switch which operates on the left-hand side of the Paschen minimum by considering the influence of a magnetic field on the transverse drift velocity of electrons and on Townsend´s first ionization co efficient. An increase in the applied magnetic field has been shown to reduce the sparkover time at a constant applied voltage, and reach a minimum value. On further increas, e in the applied magnetic field, the sparkover time begins to rise and a cut-off magnetic field strength at which breakdown is not possible at all is shown to exist at these low pressure ranges. An increased ap plied voltage causes breakdown at the cut-off magnetic field strength and at this operating point a higher cut-off magnetic field strength exists.