A simulator for charged particle guns and lenses

Abstract

An algorithm is presented that extends the application of ray optics to charged particle guns, where particles are emitted with a wide range of angles and relative energies. The extension is made possible by replacing the ray tangent as a coordinate with the directional sine, which remains finite for all take-off angles, and if necessary, by simulating the ray optics for multiple segments of the energy distribution. Consequently, an electron gun comprising a cathode, an extractor, and an anode, for example, may be characterized by its focal length, the location of its image plane, the magnification of the emission spot at this plane, and the primary and higher-order aberrations of the module, which reshape this spot. This description is realized by modeling the particle trajectories as a power series in their initial conditions and by using standard algebraic techniques, namely, the binomial and Taylor expansions, to transform the relativistic Newton’s equation, which describes the evolution of the trajectories in the electromagnetic fields of the gun, into a differential equation for the evolution of the series coefficients. In addition to providing the optical parameters, the series coefficients produce an algebraic map between the particle coordinates along the gun axis and their initial values at the plane of emission, thereby circumventing the need to launch a multitude of trajectories in a particle simulator to model the source that the gun presents to the optical elements downstream. The algorithm may be enhanced in the future by incorporating some effects of space charge from the emission current.