Full-Wave Modeling of Beam Position Monitors on Silver Nanowires and Nanotubes: Analysis of Solution Convergence

We consider the diffraction radiation of a flat modulated beam of charged particles passing between twin circular metallic nanotubes. The beam electromagnetic field is a two-dimensional H-polarized surface wave, which propagates in the same direction as the beam, the phase velocity being the same as the beam velocity. This field excites the currents on the nanotubes and therefore a radiation happens even if the beam trajectory is off the scatterers. We reduce the diffraction radiation problem to the matrix equation with favorable features for the field expansion coefficients and compute the calculation error dependence on the matrix truncation order. The calculations confirm the convergence and show how sensitive is the error to the parameters of two configurations of scatterers: solid nanowires and nanotubes.