Wake field of an electron bunch moving parallel to a dielectric cylinder -art. no. 056503

The wake field of an electron bunch moving parallel to the axis of a dielec tric cylinder is being considered. It is shown that for a relativistic bunc h (gamma much greater than1) the circular harmonic of order zero contribute s a decelerating force inversely proportional to gamma, whereas the circula r harmonics of nonzero order contribute a gamma -independent force. Moreove r, the wake linked to the circular harmonic of order zero may grow in space in case the dielectric cylinder consists of an active medium; however. thi s growth rate does not depend on the value of gamma. On the other hand, no growth is anticipated for the case of circular harmonics of nonzero order.