A novel theory of relativistic crossed-field limiting current

Summary form only given. Strictly speaking, the maximum injected current for a time-independent cycloidal flow in a relativistic, magnetically insulated diode has never been correctly solved. Lovelace and Ott (1974) assumed the space charge limited (SCL) condition on the cathode surface in their classic paper. They included the self electric and magnetic fields of the cycloidal flow. Their result is often considered to be the maximum emission current density for time-independent flows, because in a nonmagnetized diode, the maximum emission current density is indeed given by the SCL condition if the electrons are assumed to be emitted with a zero velocity. Adopting the SCL condition for a magnetically insulated gap was thus a natural assumption. We extend the analytical theory of Lovelace-Ott by relaxing the SCL assumption. Our theory reduces to Christianson\´s results in the deeply non-relativistic regime, and to the Lovelace-Ott results under the SCL assumption. A set of "universal curves" for the limiting current density has been obtained at various gap voltages, ranging from the deeply nonrelativistic to relativistic.