Velocity Ratio Measurement Using the Frequency of the Gyro Backward-Wave

The operating diagram of a low quality factor, 8 GHz TE-degrees-01 gyrotron exhibits oscillations between 6.8 and 7.3 GHz. These oscillations are identified as the backward wave component of the TE-degrees-21 traveling mode. As the resonance condition of this mode depends on the average parallel velocity of the beam electrons (omega-BW approximately-or-equal-to OMEGA-c/gamma-k parallel-to ), the measurement of omega-BW for given OMEGA-c and gamma is used as a diagnostic for the beam electrons velocity ratio alpha = /. The values of alpha, deduced from omega-BW through the linear dispersion relation for the electron cyclotron instability in an infinite waveguide, are unrealistic. A nonlinear simulation code gives alpha 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 upsilon-perpendicular-to and upsilon-parallel-to increases omega-BW. This effect explains part of the discrepancy between the values of alpha inferred from omega-BW without velocity dispersion and the expected values.