Non-relativistic boundary conditions and scattering in the presence of arbitrarily moving media and objects: Cylindrical problems

Recently non-relativistic boundary conditions, based on the Lorentz force formulas, have been investigated. It was shown that to the first order in the relative velocity v/c the results for scattering problems are in agreement with the exact relativistic formalism. Examples for scattering by material objects moving in free space have been discussed. Presently the feasibility of non-relativistically solving scattering problems involving arbitrary material media is investigated. For concreteness, two representative canonical problems were chosen: scattering by a uniformly moving circular cylinder, and the related problem of a cylinder at rest, comprised of a uniformly moving medium in the cylindrical cross-sectional plane. The investigation demonstrates that solving such problems is feasible, and indicates the complexity involved in such an analysis. The main highlights are that we need to evaluate the phases and amplitudes of waves at the scatterer's surface, employing formulas based on the Lorentz force formulas and the Fresnel drag concept. The explicit solutions for the scattering problem display velocity-dependent interaction of the scattering coefficients.