Virtual reality for electrons in vacuum devices

Vacuum tube oscillators and amplifiers at microwave frequencies have presented a considerable challenge to CAD design engineers, since successful computer modelling of such devices can lead to considerable savings in their development costs. In principle, the vacuum tube is potentially capable of very precise mathematical simulation (virtual reality) if three basic conditions prevail. These are: (1) the devices are perfectly evacuated; (2) electrodes and waveguiding structures are perfectly conducting; and (3) electrons can be viewed as `particles´. The compilation of a computer simulation package for electron beam tubes requires the solution of two distinct field problems. Firstly, a finite difference, or finite element, representation of the Laplace of Poisson equation in the collector or gun regions of the device is required together with the observance of Lorentz forces on the electrons if magnetic focussing fields are present. Secondly, gain or oscillation in a microwave tube occurs in the beam/circuit interaction region. The `circuit´ is generally a slow-wave structure which supports a guided electromagnetic wave. The field solution for such circuits involves the numerical evaluation of the Helmholtz equation together with appropriate boundary conditions. One of the main tasks in the computer simulation of such structures entails the development of algorithms which can flexibly accommodate a wide variety of geometrical shapes