In this paper, the kinetic power theorem is used for solving the problem of interaction between a relativistic electron beam moving in a static magnetic field and a travelling electromagnetic wave. The electron bunching function suggested here is specially suitable for analyzing the electron bunching process in this amplifier. By using numerical calculation, the whole process of energy exchange between the gyrating electrons and waves in the interaction region is analysed. The results of calculation show that the imaginary part of the axial wa-venumber is not a constant, so that the gain characteristics is nonlinear. Under the situation of high efficiency and high power output operation, very high stability is required for the static magnetic field. By adjusting the operation parameters to lower the output power, the high stability requirement may be somewhat.relaxed By analysing the electron bunching process, these properties of this amplifier can be well explained.