Velocity ratio measurement using the frequency of the gyro backward wave

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Abstract
The operating diagram of a low quality factor, 8 GHz TE°01 gyrotron exhibits oscillations between 6.8 and 7.3 GHz. These oscillations are identified as the backward wave component of the TE°21 traveling mode. As the resonance condition of this mode depends on the average parallel velocity 〈v∥〉 of the beam electrons (ωBW≂Ωc/γ−k∥〈v∥〉), the measurement of ωBW for given Ωc and γ is used as a diagnostic for the beam electrons velocity ratio α=〈v⊥〉/〈v∥〉. The values of α, deduced from ωBW through the linear dispersion relation for the electron cyclotron instability in an infinite waveguide, are unrealistic. A nonlinear simulation code gives α values that are in very good agreement with the ones predicted by a particle trajectory code (+10% to +20%). It is found numerically that the particles’ velocity dispersion in v⊥ and v∥ increases ωBW. This effect explains part of the discrepancy between the values of α inferred from ωBW without velocity dispersion and the expected values.