Low level RF systems for synchrotrons: part II: High Intensity. Compensation of the beam induced effects

The high intensity regime is reached when the voltage induced by the beam in the RF cavities is of an amplitude comparable to the desired accelerating voltage. In steady state this beam loading can be compensated by providing extra RF power. Transient beam loading occurs at injection or in the presence of a beam intensity that is not uniform around the ring. The transients are periodic at the revolution frequency. Without correction transient beam loading can be very harmful: The stable phase and bucket area will not be equal for all bunches. Strong beam loading often goes in pair with longitudinal instabilities because the RF cavities are a large contributor to the total ring impedance. The low level systems that reduce the effect of the transient beam loading will also increase the threshold intensity of the longitudinal instability caused by the cavity impedance at the fundamental RF frequency. Four classic methods are presented here: Feedforward, RF feedback, long delay feedback and bunch by bunch feedback. The first three fight against both effects: Transient beam loading and longitudinal instability, if caused by the cavity impedance (at the fundamental). The last one cures longitudinal instability (dipole mode) caused by any impedance in the machine but has no effect on the beam loading. These techniques have been made possible by the recent advent of fast digital circuitry and an emphasis will be put on the implementations.