Higher-Order Mode Loss in Stationary State

The higher-order mode loss in a stationary state in an electron storage ring is analyzed both in the time domain and in the frequency domain. The effect of multiple passage is studied carefully. It is shown that the coupling impedance of frequencies harmonic with the revolution frequency contributes to the higher-order mode loss. In a high-Q RF cavity, the loss is large when the mode frequency is close to the harmonic of the revolution frequency and is small otherwise. Statistical arguments show that the expected value of the loss in a high-Q RF cavity is equal to the energy loss in a single passage. This is a good estimate for a room-temperature RF cavity, but for a superconducting cavity, the r.m.s. error of the estimated energy loss is quite large.