Space-Charge-Limited Current in Finite Concentric Cylindrical Diodes

Characterizing space-charge-limited current (SCLC), the maximum current that can flow in the steady-state operation of a diode, is important for numerous applications including high-current vacuum devices and high-power microwaves [1]. The Child-Langmuir (CL) law describes SCLC in one-dimensional (10) planar diodes. We previously extended the CL law to analytically derive SCLC in nonplanar diode geometries using variational calculus and conformal mapping [2]. We also recently incorporated nonzero injection velocity into SCLC by using Lie point symmetries [3] and the fringing electric fields in multiple dimensions by using vacuum capacitance for planar diodes [4].