Theory and simulations of a thermionic emissions in a plain diode

The problem of biased diodes with thermionic emission has been first presented by Langmuir¹ with a theoretical solution predicting the dependence on diode current on bias voltage in plane and cylindrical geometries. It has been shown that increase of density of emitting particles naturally leads to potential barrier with a non-monotonic potential profile. For many years, the value of potential minimum and its position have been considered as free parameters of this problem. Analytic, i.e. explicit, expressions for these parameters have been found only many years later². However, the question of a stability of such a structure, with the potential bias as external control parameter, has not been fully investigated. In this paper we deal with this problem using grid-less tree-code method, in similar manner as was already done by Christlieb³ and Krek⁴ for the case of short-cut diode. The last investigations where focused into confirming high reliability of tree-code method, i.e. the same as in direct summation method, while in the present investigation, we apply our method to particular cases of engineering importance. Namely, we use same cases as exploited in Refs. [1, 2], which, in addition, implies cases with an arbitrary finite diode bias voltages ranging from zero (short-cut) to values much higher that the emitted particles thermal energy.