Modifications of Limiting Current and Magnetic Insulation in a Crossed-Field Diode by a Series Resistor

Adding an orthogonal magnetic field to a diode is crucial for multiple applications, including high power generation. These crossed-field diodes (CFDs) have curved electron trajectories that store current in the gap. Above a critical magnetic field referred to as the Hull cutoff, electrons emitted from the cathode fail to cross the anode-cathode gap, leading to magnetic insulation and the storage or transport of all the current. Normally, the Hull cutoff may be easily calculated from diode geometry and boundary conditions; however, dissipative effects in the circuit or the addition of a protective shunt resistor may introduce an external resistance in series that causes a mismatch between the applied voltage and the voltage drop across the gap. For non-magnetically-insulated CFDs, non-zero net current flows in the circuit due to space-charge limited current (SCLC) in the gap. In this paper, we examine several models for crossed-field SCLC below the Hull cutoff to determine the impedance of the CFD. We find that the resistor reduces the voltage drop across the gap, reducing the magnetic field necessary for magnetic insulation below the typical Hull cutoff, which in turn lowers the SCLC. One-dimensional particle-in-cell simulations show that adding the series resistor causes electron trajectories to oscillate between insulated and non-insulated states for CFDs operating within 30% of the conventional Hull cutoff; these findings are validated by further examination of the theory. Extensions to other perturbations, such as AC modulation and magnetic field tilts, are discussed.