Accurately predicting electron beam deflections in fringing fields of a solenoid

Computer modelling is widely used in the design of scientific instrumentation for manipulating charged particles, for instance: to evaluate the behaviour of proposed designs, to determine the effects of manufacturing imperfections and to optimise the performance of apparatus. For solenoids, to predict charged particle trajectories, accurate values for the magnetic field through which charged species traverse are required, particularly at the end regions where fringe fields are most prevalent. In this paper, we describe a model that accurately predicts the deflection of an electron beam trajectory in the vicinity of the fringing field of a solenoid. The approach produces accurate beam deflection predictions in the fringe field region as well as in the centre of the solenoid. The model is based on a direct-line-of-action force between charges and is compared against field-based approaches including a commercially available package, with experimental verification (for three distinct cases). The direct-action model is shown to be more accurate than the other models relative to the experimental results obtained.