  In this paper, we present a new kind of high power and high efficiency
free-electron laser oscillator based on the application of the tapering
enhanced stimulated superradiant amplification (TESSA) scheme. The main
characteristic of the TESSA scheme is a high intensity seed pulse which
provides high gradient beam deceleration and efficient energy extraction. In
the oscillator configuration, the TESSA undulator is driven by a high
repetition rate electron beam and embedded in an optical cavity. A
beam-splitter is used for outcoupling a fraction of the amplified power and
recirculate the remainder as the intense seed for the next electron beam pulse.
The mirrors in the oscillator cavity refocus the seed at the undulator entrance
and monochromatize the radiation. In this paper we discuss the optimization of
the system for a technologically relevant example at 1 $\mu$m using a 1~MHz
repetition rate electron linac starting with an externally injected igniter
pulse.
