Motion-induced radiation from electrons moving in Maxwell's fish-eye

In \u{C}erenkov radiation and transition radiation, evanescent wave from motion of charged particles transfers into radiation coherently. However, such dissipative motion-induced radiations require particles to move faster than light in medium or to encounter velocity transition to pump energy. Inspired by a method to detect cloak by observing radiation of a fast-moving electron bunch going through it by Zhang {\itshape et al.}, we study the generation of electron-induced radiation from electrons' interaction with Maxwell's fish-eye sphere. Our calculation shows that the radiation is due to a combination of \u{C}erenkov radiation and transition radiation, which may pave the way to investigate new schemes of transferring evanescent wave to radiation.