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The use of a cluster of cavities in frequency multiplying gyro-amplifiers is described. An analytical theory has been developed to maximize the second harmonic current and optimize the drift section length for the case of a single low-Q input cavity, operating at the fundamental cyclotron harmonic, and bunching clustered cavities operating at the second-harmonic. MAGY simulations have been conducted to benchmark the theory and further study the detailed characteristics of cluster-cavity gyro-amplifiers. The theory and MAGY code simulations agree. In the small signal regime, the bandwidth of a cluster-cavity device (with a pair of cavities in the cluster) is twice that of a single cavity device, while both have the same peak bunching. With a gyro-TWT output section, a peak power of 247 kW, efficiency of 24.2% and bandwidth of 1.08% has been simulated using a cluster of cavities as a buncher. In addition, the power-bandwidth product is 105 kW×MHz, which is double that of the single cavity buncher case. We also investigate the effect of coupling between the cavities of a cluster, and the performance of a three-cavity cluster.