Finite-element methods for electron gun design

Summary form only given. The finite-element method for numerical field solutions is philosophically different from the finite difference approach. Rather than solve the limiting differential equations, the idea is to apply integral conservation laws over small elements of the solution volume. The author reviews finite-element principles for electric and magnetic field solutions and emphasizes advantages for vacuum electron devices. Because solutions on conformal triangular meshes give accurate field values on curved electrodes, they are ideally suited to field-emission guns. For space-charge-limited emission, novel numerical methods give significantly improved accuracy compared to conventional finite difference approaches. Design procedures for power tubes and vacuum micro-electronic devices are illustrated with solutions from TRAK, a ray tracing program for quasi-steady-state gun design. Development of the code was supported in part by an SBIR Grant through Northstar Research Corporation. The goal of the program was to study high-power vacuum tubes for voltage control in Heavy Ion Fusion induction linacs.