1. Introduction

Thermionic emission is the process taking place in hot metals where the electrons can achieve enough energy to surpass the confining extraction barrier. A simple model for a metallic conductor considers the system as a potential well where the electrons can freely move but cannot get out. At room temperature, electrons in a metal are prevented from escaping through its surface due to a potential energy barrier (work function energy), that the electrons can surpass if the metal is heated enough. To model this process we have considered a classical gas confined into a box where the particles can go out when they are close to the surface and get kinetic energy (associated to the velocity component perpendicular to that surface) greater than the specified work function of the metal. This model does not correspond to the real system because we deal with particles obeying classical statistical laws (instead of confined electrons subjected to Fermi-Dirac statistics). This not real model results in a change of the Richardson Dushman (Owen 1929) law for the emitted current, that can be analytically justified in terms of the differences above mentioned. For this work we have reworked the obtaining of the corresponding Richardson Dushman law in terms of the proposed model and describe the results obtained with the simulation, which totally agree with the theory.
In addition, we have modeled the process taking place in a vacuum tube diode, composed of two parallel plate electrodes, the thermionic emitting cathode and the anode connected to a given potential in respect to the cathode, under space charge regime. To do this we have considered the electrons emitted by the cathode and flying to the anode as electrically interacting through Coulomb's Law and additionally subjected to the externally applied electric field associated to the anode-cathode potential difference. In a simple model, where we have not imposed the constancy in the potential of the two metallic electrodes, a similar behavior to the Child Langmuir law (Child 1911) is obtained, showing the saturation behavior when the anode applied voltage is large enough.
All simulations have been developed with Ejs (Easy Java Simulations) (Ejs 2009), an authoring tool developed by F. Esquembre from the CoLoS (Conceptual Learning of Science) Murcia group, that facilitates the work to people not experts in programming.