An investigation of methods suitable for electron trajectory tracing in digital computer programmes

Abstract

Integration of the equations of motion of an electron by various numerical techniques is discussed in the context of computer simulations of electron guns. Methods considered are of the Runge-Kutta, predictor-corrector and Taylor series type. All employ an automatically adjusted time step which is controlled by the truncation error of the process. Various degrees of approximation are tested for each method and their relative efficiencies are considered for different specified tolerances. It is concluded that a set of Runge-Kutta formulae proposed by Fehlberg exhibits distinct advantages over other methods both in the required number of steps and computer time. Results are obtained with reference to a typical electron flow problem.