A finite element approach to the electromagnetic interaction with rotating penetrable cylinders of arbitrary cross section

A method for evaluating the fields excited by an obliquely incident plane wave inside and outside a rotating cylinder is presented. A differential formulation of the problem is developed with respect to the comoving reference frame of the scatterer on a closed circular domain including the scatterer cross section; the boundary conditions account for the far-field conditions through a series expansion of the total field on the domain contour. The results at oblique incidence are then particularized for normal incidence and a hybrid finite element numerical solution is presented and discussed for TM incidence. The present FEM approach and the related computer code are directly applicable to the study of rotating piecewise-homogeneous cylinders at normal incidence, as well as metallic cylinders coated by layers of penetrable materials. Through a comparison, for normal incidence, between the quasi-stationary and the Galileian relativistic approach, a method for approximately reconstructing the Doppler frequency shift in the quasi-stationary method is derived. Far-field and near-field numerical results for circular and arbitrarily shaped (metallic or dielectric) cylinders are presented