Assessment of Techniques for Determining Space-Charge Limited Current in Nonplanar Crossed-Field Diodes

Space-charge limited current (SCLC) is the maximum current for a diode and is essential for numerous applications, including nano vacuum transistors, electric thrusters, multipactor, and time-resolved electron microscopy [1] . Crossed-field diodes (CFDs), where an external magnetic field B is applied perpendicular to the electric field, may also be characterized by a maximum current both for BB H [3] , where B H is the Hull cutoff magnetic field for magnetic insulation. A recent study extended these calculations to a concentric cylindrical diode by using variational calculus [4] ; however, the Euler-Lagrange formulation used in the derivation is not readily amenable to more complicated geometries. This motivates an assessment of more flexible techniques for determining SCLC for nonplanar CFDs.