Particle trajectory tracing for electrostatic and magnetostatic fields

This work reports a numerical method for single charged particle trajectories computation in 2D electrostatic and magnetostatic stationary fields, in other words, fields that do not change in time. This is approached by the finite element method domain discretisation, and numerical computation of particle trajectory, calculated by the two step centred in time method, which calculates the particle position on the next step using a dummy step in order to increase the accuracy for the same step size. Given particle's coordinates, the finite element that contains that particle is found based on Lohner's algorithm. The examples used to test the method are a electric deflector for the electric case and cyclotron for the magnetic case. Both are very important devices to science and technology, being used in a variety of domestic and industrial appliances and in several scientific and technologic researches. Other particle optics devices can benefit of the method proposed in this paper, as beam bending devices and spectrometers, among others. This method can be easily extended for particle trajectories computation in 3D domains, can be extended also for dynamic fields and for the relativistic case, which is ideal for the typical speed involved when working with particles near the atomic level