The invention relates to an X-ray source that uses a rectangular resonant cavity which is excited with a microwave mode TE10p.The invention can also be used as a cyclotron radiation source using the cylindrical cavity, but making structural changes thereto for this purpose. The system can be used to significantly increase the energy of the electronic beam by compensating the diamagnetic force via an axially symmetrical electrostatic field. The longitudinal electrostatic field is generated by ring-type electrodes placed inside the cavity, preferably in the planes of the nodes of the electric field TE11p. The electrodes must be made from a material that is transparent to the microwave field, e.g. graphite.