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Microwave tubes required to drive future 1-TeV linear colliders have challenging requirements, including 300-MW peak power at wavelengths near 3 cm. It is believed that gyrotrons have good potential for development into the high peak power, high gain, efficient amplifier required for this application. Presented here is the detailed design for a 3-cm gyroklystron amplifier at a peak power level of ~ 30 MW. This power level is approximately three orders of magnitude above the gyroklystron state of the art, and a 30-MW experimental study will be a crucial step toward achieving the 300-MW goal. Novel problems associated with a high-energy (Â¿ ~ 2) gyrotron beam are considered in detail. A new partially self-consistent nonlinear analysis is described and subsequently used to design the gyroklystron circuit. Based on the TE011 mode in cavities of circular cross section, stable operation is anticipated; the current is well below the threshold at which an unbunched electron beam would excite oscillations in the cavities and the drift spaces are designed to heavily load modes which are not cut off.