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Differential form valued forms and distributional electromagnetic sources

The design of charged particle accelerators requires the solution of complex problems in electrodynamics. This paper presents a new analytic scheme for modelling spatially confined moving electromagnetic sources using modern methods of distributional geometry. The use of differential forms in this context is novel and powerful with wide applicability for solving and bench-marking problems in and beyond accelerator science. Results have led to interaction with scientists and engineers and an EPSRC-funded collaboration between the Cockcroft Institute and Lancaster’s Environment Centre (EP/K504026/1) for the construction and deployment of a tabletop device, based on magnetic field suspended ferrofluids, for polluted water remediation.