Abstract: A free electron laser (FEL) is described which is used for generating high ower radiation in a region of increasing guiding magnetic field before injection into an undulating low magnetic field. It includes an electron beam propagating along a guiding magnetic field B.sub.0 (approximately 10 kilo gauss) inside a hollow metallic tube used as a wave guide. Around the path of the beam, an undulator in the form of a bifilar helical winding or the like produces a periodic magnetic field B.sub.1 (approximately 0.5 to 1.0 kG). The electron motion accordingly has a substantial transverse component and the motion at the cyclotron and undulator frequencies occurs. Due to the energy exchange between the gyrating component of electron motion and an electromagnetic wave already present in the hollow tube, radiation of a calculable frequency is amplified.