An electron emission model for use with 3D electromagnetic finite element simulation

Abstract

Using commercial 3D finite element (FE) simulation packages it is now possible to model the self-consistent behaviour of charged particle beams in electromagnetic fields within a complex problem geometry. However, in many cases the accuracy of the simulation is restricted by the accuracy of the particle emission models traditionally in use. Most such models date back to the time when problem complexity was limited by what could be solved. Artifacts of this early work in, for example, vacuum tubes, led to the development of simplified models like those by Child and Langmuir aiming to describe space charge limited electron emission from thermionic cathodes. Such models, which are still in use, have the twin disadvantages of their formulation being dependent on the problem geometry and their reliance on a “characteristic dimension” to specify the distance over which the space charge limited flow is to be computed. These disadvantages can make their application to general problem geometry in a FE simulation environment difficult and in some cases misleading. With the recent introduction of facilities to specify the initial particle dynamics in commercial space charge solvers there is no longer a need to rely on the above traditional but restricted emission models. This paper describes one method of implementing a completely general model for thermionic electron emission which utilizes the new facilities. The new methodology is applicable to any type of electron emission including thermionic, field and photoemission and depends only on the ability of the user to specify the starting conditions of the particle trajectories. The details of our approach are illustrated in the simulation of initial beam formation from a thermionic cathode in a thin CRT. In the example simulations, the use of a characteristic dimension is precluded. The emission characteristics are derived solely from the Maxwell–Boltzmann distribution which provides the electron velocities, and the Richardson–Dushman law which provides the saturation current density. Many problems require the solution to simultaneously include the total cathode emission current and yet cope with a large dynamic range of beam current. Methods developed to permit such solutions whilst keeping computation time within practical limits are discussed. The paper also discusses the effect the coupling of the particle beam to the model has on solution convergence.