Near Fields of Twin Circular Silver Nanotubes Exited by Electron Beam Moving between Them

A movement of harmonically modulated beam of electrons of other charged particles moves near an obstacle is known to be accompanied by the diffraction radiation (DR). We study DR for a beam flowing between two circular nanotubes of the same metal and geometry. The electromagnetic field of such a beam is a slow H-polarized wave, which propagates along the beam trajectory and decays exponentially off the trajectory. To analyze DR, we use the boundary conditions and the field expansions in the local polar coordinates supplemented with the addition theorems for Bessel functions. This leads to a matrix equation for the field expansion coefficients. Its conversion to the Fredholm second-kind form guarantees controlled accuracy in the computation of the far and near field patterns, which demonstrate resonance behavior. As we have shown, deviation of the beam trajectory from the central, i.e. symmetric, position is accompanied with the excitation of additional resonances. This phenomenon can be exploited in the design of non-invasive optical-range beam position nanomonitors.