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We present a theoretical comparison of multicavity gyroklystron circuits which are designed to optimize the beam-microwave interaction efficiency given a set of physical constraints imposed by the experimental system. The restrictions considered in this work are representative of realistic systems and include a cap on the maximum input power available, as well as a magnetic field defined by preexisting field coils and power supplies. The frequency doubling circuits all have input cavities which operate near the fundamental cyclotron frequency and all have output cavities which operate near the second-harmonic. Intermediate bunching cavities can be operated in either the first or second-harmonic. It was found that to maximize gain it is best to have initial buncher cavities at the fundamental harmonic and that to optimize efficiency, it is best to have the final buncher cavities at the second-harmonic. It was also found that diminishing returns are found for enhanced gain with increasing numbers of cavities, and that for the parameters of this study, a six cavity tube with three first-harmonic and three second-harmonic cavities appears to be optimal.