  Free-electron lasers (FELs) have been built ranging in wavelength from
long-wavelength oscillators using partial wave guiding through ultraviolet
through hard x-ray FELs that are either seeded or start from noise (SASE).
Operation in the x-ray spectrum has relied on single-pass SASE due either to
the lack of seed lasers or difficulties in the design of x-ray mirrors.
However, recent developments in the production of diamond crystal Bragg
reflectors point the way to the design of regenerative amplifiers (RAFELs)
which are, essentially, low-Q x-ray free-electron laser oscillators (XFELOs)
that out-couple a large fraction of the optical power on each pass. A RAFEL
using a six-mirror resonator providing out-coupling of 90% or more through a
pinhole in the first downstream mirror is proposed and analyzed using the
MINERVA simulation code for the undulator interaction and the Optics
Propagation Code (OPC) for the resonator. MINERVA/OPC has been used in the past
to simulate infrared FEL oscillators. For the present purpose, OPC has been
modified to treat Bragg reflection from diamond crystal mirrors. The six-mirror
resonator design has been analyzed within the context of the LCLS-II beamline
under construction at the Stanford Linear Accelerator Center and using the HXR
undulator which is also to be installed on the LCLS-II beamline. Simulations
have been run to optimize and characterize the properties of the RAFEL, and
indicate that substantial powers are possible at the fundamental (3.05 keV) and
third harmonic (9.15 keV).
