A self-consistent approach to the analysis of thermionic devices

Research in thermionics has been reinvigorated recently by the advent of nanotechnology and nanomaterials. Thermionic energy convertors are commonly modelled using the Poisson-Vlasov system of equations under various limitations and approximations. With the ever-growing demands of emergent thermionic devices, more comprehensive approaches are needed in order to be able to treat a broader range of device configurations and operational parameters. Here, we propose a self-consistent approach that, by iterating between the Poisson and Vlasov equations, does not rely on the existence of an analytical solution to the latter. Specifically, we present a particle-tracing implementation of this method for solving the system numerically in an efficient manner. In the case where an analytical solution does exist, we present an asymptotic expansion of the ill-behaving functions that arise; this approach improves the effectiveness of the method in the deep space-charge mode. We also demonstrate the applicability of thi...