Cherenkov radiation by a particle moving with a non-uniform velocity

Energy loss by a charged particle moving with non-uniform velocity in a uniform dielectric medium is investigated. Assuming constant deceleration, an expression is derived for radiation emitted in an arbitrary distance x, and the case of Cerenkov radiation is discussed in detail. Expressions are presented for energy radiated per unit frequency interval and for Cerenkov angle containing first-order terms in retardation.