  Electron storage rings used for the production of synchrotron radiation (SR)
have an output photon brightness that is limited by the equilibrium beam
emittance. By using interleaved injection and ejection of bunches from a source
with repetition rate greater than 1 kHz, we show that it is practicable to
overcome this limit in rings of energy ~1 GeV. Sufficiently short kicker pulse
lengths enable effective currents of many milliamperes, which can deliver a
significant flux of diffraction-limited soft X-ray photons. Thus, either
existing SR facilities may be adapted for non-equilibrium operation, or the
technique applied to construct SR rings smaller than their storage ring
equivalent.
