Effect of inner conductor misalignment of high-$\beta$ quarter-wave resonator

Niobium sputtering the HIE-ISOLDE quarter-wave resonator at high temperatures has called for a reconsideration of the mechanical tolerances for the fabrication of the cavity. A study was launched to understand the effect of inner conductor misalignments on the beam to determine the manufacturing tolerances; in previous error studies only misalignments of the ideal cavity were considered. Systematic rf simulations of the imperfect cavity were carried out using CST Microwave Studio and kick factors calculated for each mode of misalignment. It was found, as expected, that the misalignments of the internal conductor give the same order of magnitude kick as misalignments of the entire ideal cavity. To avoid any significant perturbation to the beam, the inner conductor should be aligned to within the same tolerance as the cavity itself, i.e to within 0:3 mm [1]. The rather conservative tolerance originally set for sputtering at low temperatures can be relaxed by a factor around 10.