The interaction of a beam with a cavity and a generator in cyclic accelerators or storage rings is investigated. Application of Maxwell's equations together with the nonuniform boundary condition allows one to get an equivalent circuit for a beam-loaded cavity. The general equation for beam loading is obtained on the basis of the equivalent circuit, and the beam admittance is calculated. Formulas for power consumption by a beam-loaded cavity are derived, and the optimal tuning and coupling factor are analyzed.
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