  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.
