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.

A physical model for low-frequency electromagnetic induction in the near field based on direct interaction between transmitter and receiver electrons.

A physical model of electromagnetic induction is developed which relates directly the forces between electrons in the transmitter and receiver windings of concentric coaxial finite coils in the near-field region. By applying the principle of superposition, the contributions from accelerating electrons in successive current loops are summed, allowing the peak-induced voltage in the receiver to be accurately predicted. Results show good agreement between theory and experiment for various receivers of different radii up to five times that of the transmitter. The limitations of the linear theory of electromagnetic induction are discussed in terms of the non-uniform current distribution caused by the skin effect. In particular, the explanation in terms of electromagnetic energy and Poynting's theorem is contrasted with a more direct explanation based on variable filament induction across the conductor cross section. As the direct physical model developed herein deals only with forces between discrete current elements, it can be readily adapted to suit different coil geometries and is widely applicable in various fields of research such as near-field communications, antenna design, wireless power transfer, sensor applications and beyond.