AbsiractThe tllcoretical design of a second harmonic gyroklystron amplifier at a voltage near 500 kV is presented. Because of the relat,ively high voltage the beam tunnel must be large, so the radiation is not, cutoff in the drift tub?. To avoid feedback we operate the input, cavity at the f~lnd;rment,al, which is cutoff in the drift tube, and design a con~plt~ output cavity t,hat emits very little radiation back into 111~ drift tube. The outpllt, cavity is described in detail, and t,he overall gain and efficiency is given.