On the smoothed Tamm problem

To remove obstacles against an instantaneous acceleration and deceleration of charge in the Tamm problem, we consider charge motion on a finite space interval with finite acceleration and deceleration. When the charge velocity coincides with the velocity of light in medium, a new shock wave (in addition to the Cherenkov shock wave) arises which propagates with the light velocity in medium. The angular distribution of the emitted radiation crucially depends on the radius of the sphere on which the observations are made