Transition and parametric radiators are proposed as sources for EUVL and XRL. Collimated soft x-rays and extreme UV (EUV) radiation can be generated using electron beams with moderate electron-beam energies, unlike synchrotron radiators, which require energies of greater than 300 MeV. Earlier work focused on using transition radiation in the 0.5-3.0 keV range with electron beam energies between 17-100 MeV for output wavelength around 1.4 nm. However, tunable quasi-monochromatic emission in the EUV as well as x-ray regions can be also obtained using parametric radiators. We propose that a compact betatron be used to recycle the beam through these radiators for higher x-ray efficiency. Experiments using storage rings and simulations using known betatron parameters are presented here that demonstrate the electron beam can be recycled through the thin radiators up to 300 times. With this increase in efficiency, the source output power is expected in the range of 100 mW.
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