Near-field behavior in the method of auxiliary sources (MAS) for a simple scattering problem

It has been recently observed that, when one applies the Method of Auxiliary Sources (MAS) to scattering problems involving an infinite circular cylinder illuminated by an electric current filament, it is possible to have divergent auxiliary currents together with a convergent field. In this paper, we investigate the near-field behavior for the so-called “cylindrical problem” with discrete auxiliary sources, in the region within the critical distance, where the aforementioned divergence appears as abnormal, rapid oscillations. We provide numerical results and derive an asymptotic formula for the case of a large number of sources that reveals the properties of the near field.