A novel magnetron achieves increased power output at high frequencies by replacing a typical resonant cavity with a slow-wave waveguide structure. Waveguides built into the anode body sustain oscillations having phase change coefficients of 2*pi*n radians per section, where n is a positive integer. The magnetron is capable of supporting RF oscillations at frequency harmonics of the fundamental frequency, permitting it to operate at frequencies double or quadruple that of a similarly sized conventional magnetron.