Abstract: A method and apparatus for producing X-rays utilizing the Compton backward scattering effect. The X-rays are electronically steerable for scanning, and also have a very narrow angle of divergence for precise positioning. The X-rays have a narrow bandwidth, and are tunable to permit an object to be irradiated with only the desired beneficial radiation. The X-rays are polarized for trace element analysis. The X-rays are suitable for medical diagnostic and therapeutic, and industrial testing, purposes.