RF power requirements for a high intensity proton collider

In the new generation of circular accelerators or colliders where the average beam currents are pushed up to their ultimate limits, the power exchanged between the RF power source and the beam becomes much larger than the losses in the RF system itself (cavity, amplifier, circulator load). This situation of high beam loading has been analyzed previously with respect to the stability of the radiofrequency system. Without any electronic loops, one obtains the well known high current Robinson stability limit, which is somewhat modified by the presence of the phase, amplitude and tuning loops. To go beyond these limits the usual recipe is to employ RF feedback around the power amplifier-cavity combination. The beam current thresholds are simply increased by the RF feedback loop gain, without changing the static RF power balance. However when transient effects are considered, the peak RF power demanded by RF feedback may dominate the static power requirements, in particular for hadron storage rings where φB (synchronous phase angle) equals zero. During acceleration or storage periodic transient beam loading is due to the non-uniform structure of the beam. With high RF feedback gains and therefore large equivalent cavity bandwidths this effect becomes more and more important, especially for large machines with a low revolution frequency. In addition, non-periodic transient beam loading effects occur during the filling phase of the machine, when newly injected particles are added to the already circulating beam