Fundamental damper power calculation of the 56 MHz SRF cavity for RHIC

At each injection period during RHIC's operation, the beam's frequency sweeps across a wide range, and some of its harmonics will cross the frequency of the 56MHz SRF cavity. To avoid excitation of the cavity at these times, we designed a fundamental damper for the quarter-wave resonator to damp the cavity heavily. The power extracted by the fundamental damper should correspond to the power handling ability of the system at all stages. In this paper, we discuss the power output from the fundamental damper when it is fully extracted, inserted, and any intermediate point. A Fundamental Damper (FD) will greatly reduce the cavity's Q factor to ∼300 during the acceleration phase of the beam. However, when the beam is at store and the FD is removed, the cavity is excited by both the yellow and the blue beams at 2 x 0.3A to attain the required 2MV voltage across its gap. The cavity then is operated to increase the luminosity of the RHIC experiments. Table 1 lists the parameters of the FD. Figure 1 shows the configuration of the FD fully inserted into the 56MHz SRF cavity; this complete insertion is defined as the start location (0cm) of FD simulation, an assumption we make throughout this paper. The power consumed by the cavity while maintaining the beam's energy and its orbit is compensated by the 28MHz accelerating cavities in the storage ring. The power dissipation of the external load is dynamic with respect to the position of the FD during its extraction. As a function of the external Q and the EM field in the cavity, the power should peak with the FD at a certain vertical location. Our calculation of the power extracted is detailed in the following sections. Figure 2 plots the frequency change in the cavity, and the external Q against the changes in position of the FD. The location of the FD is selected carefully such that the frequency will approach the designed working point from the lower side only. The loaded Q of the cavity is 223 when the FD is fully inserted. The simulation was carried out with Microwave Studio 2010.