Thermal design studies in niobium and helium for superconducting radio frequency cavities

Liquid helium is now a common refrigerant for superconducting radio frequency (SRF) technology. It helps in cooling the niobium (Nb) made SRF cavities below their superconducting transition temperature (Tc). Testing of these cavities is routinely done in saturated liquid helium-I (He-I) for low field measurements and in saturated liquid helium-II (He-II) for high field measurements. The thermal design studies of these cavities involve two thermal parameters, namely the temperature dependant thermal conductivity of Nb at low temperatures and the Nb-He interface heat transfer coefficient. During the fabrication process of the SRF cavities, Nb sheet material is plastically deformed through a deep drawing process to obtain the desired shape. The effect of plastic deformation on low temperature thermal conductivity as well as heat transfer coefficients in the two states (He-I and He-II) has been studied. Strain induced due to the plastic deformations reduces the thermal conductivity in its phonon transmission regime, which may explain the performance limitations of the SRF cavities during their high field operations. The effect of annealing the Nb samples at two different temperatures to restore the phonon peak in the thermal conductivity curve has also been studied. Measurements of heat transfer coefficient for nucleate pool boiling liquid helium are in agreement with the theoretical predictions as well as with the existing experimental data. These measurements reveal higher heat transfer for rough surfaces as compared with smoother ones. Kapitza conductance measurements for Nb - He-II interface for rough surfaces with surface index (SI) more than 3 as compared with the flat and smooth surfaces have also been carried out before and after the annealing. Here, SI is defined as the ratio of exposed surface area to that of projected area. These measurements provide helpful insight in understanding the problem of Kapitza conductance for different surface topologies where the rough and annealed surface revealed increased Kapitza conductance.