Role of magnetic flux expulsion to reach Q0>3×1010 in superconducting rf cryomodules

When a superconducting radiofrequency cavity is cooled through its critical temperature, ambient magnetic flux can become ``frozen in'' to the superconductor, resulting in degradation of the quality factor. This is especially problematic in applications where quality factor is a cost driver, such as in the cw linac for LCLS-II. Previously, it had been unknown how to prevent flux from being trapped during cooldown in bulk niobium cavities, but recent R studies showed near-full flux expulsion can be achieved through high temperature heat treatment and cooling cavities through the superconducting transition with a spatial thermal gradient over the surface. In this paper, we describe the first accelerator implementation of these procedures, in cryomodules that are currently being produced for LCLS-II. We compare the performance of cavities under different conditions of heat treatment and thermal gradient during cooldown, showing a substantial improvement in performance when both are applied, enabling cryomodules to reach and, in many cases, exceed a ${Q}_{0}$ of $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{10}$.