Beam loading in high-energy storage rings

The analysis of beam loading in the RF systems olhighenergy storage rings (for example, the PEP e-e+ ring ) is complicated by the fact that the time, Tb, between the passage of successive bunches is comparable to the cavity filling time, Tf. In this paper, beam loading expressions are first summarized for the usual case in which Th << Tt. The theory of phase oscillations in the heavily-bea&loa&d case is considered, and the dependence of the synchroixon frequency and damping constant for the oscillations on beam current and cavity.tuningis calculated. Expressions for beam loading are then derived which are valid for any value of the ratio Tb/Tf. It is shown that, for the proposed PEP e-e+ ring parameters, the klystron power required is increased by about 3% over that calculated using the standard beam loading expressions. Finally, the analysis is extended to take into account the additional losses associated with the excitation of higher-order cavity modes. A rough numerical estimate is made of the loss enhancement to be expected for the PEP RF system. It is concluded that this loss enhancement might be substantial unless appropriate measures are taken in the design and tuning of the accelerating structure.