Record high-gradient SRF beam acceleration at Fermilab

Many modern and future particle accelerators employ high gradient superconducting RF (SRF) to generate beams of high energy, high intensity and high brightness for research in high energy and nuclear physics, basic energy sciences, etc. In this paper we report the record performance large-scale SRF system with average beam accelerating gradient matching the ILC specification of 31.5MV/m. Design of the eight cavity 1.3 GHz SRF cryomodule, its performance without the beam and results of the system commissioning with high intensity electron beam at FAST (Fermilab Accelerator Science and Technology) facility are presented. We also briefly discuss opportunities for further beam studies and tests at FAST including those on even higher gradient and more efficient SRF acceleration.