Quench propagation in the HOM damper of the 56 MHz cavity

The aim of this report is to summarize a study of the propagation of a quench in a HOM damper probe of the 56 MHz superconducting storage cavity for RHIC and provide guidance for machine protection. The 56 MHz cavity (1) is designed to operate as a beam-driven superconducting quarter-wave resonator in the RHIC ring. Four Higher Order Mode (HOM) dampers (2) are used to prevent beam instabilities (3) in RHIC. These are inserted in the back wall of the cavity (the high magnetic field region) through ports that also serve for rinsing the cavity with high-pressure deionized water as well as the fundamental power coupler and pick-up ports. Figure 1 shows the outline of the cavity (4,5). The HOM damper probe has a magnetic coupling loop which penetrates the cavity as shown in Figure 2 (5). The loop is cooled by conduction to the 4.3K helium system, thus any sudden, significant amount of heat dumped on the loop will cause local heating. The peak magnetic field on the loop can reach about 7.4 x 104 amperes per meter at a cavity voltage of 2.5 MV (5). The scenario we present here is that a small region on the loop quenches. We can calculate the current driving the cavity using the RHIC parameters and get the magnetic field as a function of the current, the cavity's intrinsic Q and detuning parameter, however it turns out that within the time relevant for the quench development (a fraction of a second) the cavity field does not change sufficiently to warrant this extra computation. Thus we can assume that the field over the loop is constant. The damper loop dimensions are not so important, however its cross section is. In the following we assume that the loop's cross-section is 2 cm by 0.3 cm. It is actually rounded in cross section (sharp corners avoided) but we will approximate it as square. The material parameters taken for the niobium loop (assuming high RRR of about 200) are given in the following stepwise linear approximations. The surface resistivity in ohms as a function of temperature in degrees Kelvin is given in Figure 3, the thermal conductivity in watt per degree meter as a function of temperature is given in Figure 4 and the heat capacity in Joule per kg as a function of temperature is given in Figure 5.