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Research in the University of Maryland at College Park's Gyroklystron (GKL) Project has recently centered around the development of a high-power high-gain frequency-doubling 17.136-GHz system. The current tube is a four-cavity (input, buncher, penultimate, and output) coaxial frequency-doubling system that will be used to drive a linear accelerator structure. This paper presents the design, simulation, optimization, cold test methodology, and performance data of a proposed radial extraction output cavity in which the microwave energy is extracted through an inner coaxial conductor in the TE01 circular mode. The positioning of dielectrics in the drift spaces and the effect of axial and radial misalignments between the inner and outer walls of the cavity were studied in depth. One advantage of this topology is that it reduces the size and complexity of the output waveguide chain otherwise needed to convert the TE02 circular mode from the GKL into the standard rectangular waveguide mode for injection into the Haimson Research Corporation accelerator structure. Cold test results show that this new cavity, which has a Q of 458 and a resonant frequency of 17.112 GHz, is a viable replacement for the output cavity currently in the system, as long as the cavity is well aligned.