Apparatus for the controllable downhole production of ionizing radiation (12), the apparatus including at least a thermionic emitter (11) which is arranged in a first end portion (7a) of an electrically insulated vacuum container (9), and a lepton target (6) which is arranged in a second end portion (7b) of the electrically insulated vacuum container (9); the thermionic emitter (11) being connected to a series of serially connected negative electrical-potential-increasing elements (141, 142, 143, 144), each of said electrical-potential-increasing elements (141, 142, 143, 144) being arranged to increase an applied direct-current potential (δV0, δV1, δV1+2, . . . , δV1+2+3) by transforming an applied, driving voltage (VAC), and to transmit the increased, negative direct-current potential (δV1, δV1+2, . . . , δV1+2+3+4) and also the driving voltage (VAC) to the next unit in the series of serially connected elements (141, 142, 143, 144,5), and the ionizing radiation (12) exceeding 200 keV with a predominant portion of the spectral distribution within the Compton range.