Large-signal theory of gyro traveling wave tubes at cyclotronharmonics

A nonlinear theory of gyrotron traveling wave tubes (gyro-TWTs) at cyclotron harmonics has been developed taking into account the electron velocity spread and the possibility of operating with significant Doppler frequency up-shift (CARM operation). It is shown that the orbital efficiency of the relativistic gyro-TWT operating at the second cyclotron harmonic with large frequency up-conversion may exceed 60%. It is also shown that the influence of the axial inhomogeneity of the wave field on the relation between amplitudes of electric and magnetic fields of the wave causes small changes in the efficiency of gyro-TWTs. The results obtained demonstrate the sensitivity of the harmonic gyro-TWT efficiency with respect to electron velocity spread at different axial wave numbers. The expressions for the gain are derived and discussed,