The traveling wave cyclotron (TWC) is defined in this paper as a cyclot ron-type interaction of a nonrelativistic electron beam with traveling waves in an inductive periodic waveguide. Experimental results and a theoretical model of the TWC interaction are presented in this paper. The TWC experiment is conducted in the microwave regime ("" 10 GHz) with a low-energy ("" 10 keV), low-current (< 1 A) electron beam. Considerable RF amplification has been observed in the TWC experiment. A TWC theoretical model presented in the paper shows that the TWC amplification observed is the result of the inductive impedance of the periodic waveguide near cutoff.