Described is a reactor for irradiating ultraviolet light into a fluid reaction medium (3). The reactor consists of at least one housing (15) which encloses a tubular cavity, with a radiation source (1) for generating ultraviolet light and an inner tube (2) which, together with the housing (15), forms an irradiation chamber (26) which, in particular, is of annular shape, the irradiation chamber (26) being connected at least with an inlet (13) and an outlet (14) for the reaction medium (3) and is perfused by reaction medium (3) in the longitudinal direction of the tube (2), the irradiation chamber (26) being equipped with means (6, 25) for generating an additional radial flow routing of the reaction medium (3).