Fundamental and harmonic mode competition in gyrotron oscillator

Summary form only given. We present a theoretical study of the competition between fundamental and harmonic interactions in the gyrotoron oscillator. It is shown through the particle-in-cell simulation that, in the nonlinear stage, the fundamental harmonic interaction possesses a significant advantage over the harmonic interaction, which can become a deciding factor in the competition process. The beam-wave coupling coefficient is given by H_sm=J²_s-m(k_mnr_c)J´²_S(k_mnr_L), where s is the cyclotron harmonic number, J_n(x) is a Bessel function of order n, x_mn = k_mn/r_w, and x_mn is the nth nonzero root of J_s´(k_mnr_L). H_sm of a higher harmonic mode decreases much faster than a lower harmonic mode as the electron Larmor radius decreases. Hence, in saturated operation, H_sm (averaged over all electrons) of a higher har-monic mode decreases rapidly along the interaction structure as the electron transverse energy is depleted, while H_sm of a fundamental harmonic mode remains near its original value. This suggests an inherent advantage for fundamental harmonic mode.