This paper presents the conceptual design of a high power radiation source with laser-like characteristics in the ultraviolet spectral range at the TESLA Test Facility (TTF). The concept is based on the generation of radiation in a regenerative FEL amplifier (RAFEL). The RAFEL described in this paper covers a wavelength range of 200-400nm and provides 200fs pulses with 2mJ of optical energy per pulse. The linac operates at 1% duty factor and the average output radiation power exceeds 100W. The RAFEL will be driven by the spent electron beam leaving the soft X-ray FEL, thus providing minimal interference between these two devices. The RAFEL output radiation has the same time structure as the X-ray FEL and the UV pulses are naturally synchronized with the soft X-ray pulses from the TTF FEL. Therefore, it should be possible to achieve synchronization close to the duration of the radiation pulses (200fs) for pump-probe techniques using either an UV pulse as a pump and soft X-ray pulse as a probe, or vice versa.