Tuning possibilities of the longitudinal beam shape of a racetrack microtron

The beam shape in the longitudinal phase plane at the extraction point of an RTM strongly depends on the choice of the stable phase of the accelerating cavity. This is due to the fact that the main longitudinal focusing force is the derivative of the accelerating potential with respect to time (or phase). Furthermore, this focusing force is applied to the electron beam each turn, such that the output beam shape in the longitudinal phase plane is significantly affected. This effect can for instance be used in order to minimise the bunch length or the energy spread of the output beam of the RTM. For this paper we have used the lay-out of the Eindhoven RTM for the calculations of the stable-phase variations, which have been studied in a linear approximation. The stable phase area for this RTM equals 18 degrees. It will be shown that stable-phase variations in the order of 1 degree already have a significant impact on the longitudinal beam shape. Furthermore, some remarks are made on the consequences of nonlinear beam dynamics in relation to stable-phase variations