Efficiency of frequency up-shifted gyrodevices: cyclotron harmonics versus CARM´s

For gyrodevices with a given operating frequency and a fixed value of the external magnetic field two kinds of operation are compared: Doppler frequency up-shifted operation at the fundamental cyclotron resonance and cyclotron harmonic operation. When the electron velocity spread is negligibly small the maximum efficiency of the Doppler up-shifted operation exceeds that of harmonic operation. However, as the velocity spread grows the Doppler up-shifted efficiency degrades faster. The relevant quantity when deciding between fundamental, Doppler up-shifted, and harmonic operation turns out to be the velocity spread divided by the square root of the beam current. If this quantity is small, fundamental, Doppler upshifted operation is more efficient than harmonic operation; if it is large harmonic operation is more efficient. The efficiency dependence of both kinds of operation on electron velocity spread is studied. A comparative analysis of designs relevant to the planned University of Maryland experiments with relativistic gyro-amplifiers is done