Cherenkov radiation of a fast vortex from the surface of a waveguide coupled to a Josephson junction

A system of equations for phase differences of the superconducting order parameter describing the coupled Josephson junction, waveguide, and semi-infinite dielectric medium is obtained. For such a layered structure, the Cherenkov radiation of a fast vortex emitted from the surface of the superconducting sandwich into the dielectric is described. In such a structure, the fast vortex moves with velocity close to the Swihart velocity of the waveguide, which can significantly exceed the velocity of an ordinary Josephson vortex. The characteristic emission frequencies and radiation losses of the fast vortex are determined.