RF Defocusing in Super-Conducting Structure with Constant Geometry

Due to higher accelerating gradient in the super-conducting linear accelerator the RF defocusing factor plays significant role in the beam dynamics. Together with the space charge it is a main reason for the stability loss. Usually the RF defocusing is estimated in frame of the travelling wave formalism with synchronous motion. However, the super-conducting cavity is desirable to have the constant geometry, when synchronous motion is absent. In this case the quasi-synchronous phase velocity is adjusted by RF phasing. In this paper we investigate RF defocusing factor in absent of synchronism between the beam and the accelerating structure.