Efficiency enhancement of slow-wave electron-cyclotron maser by a second-order shaping of the magnetic field in the low-gain limit

Based on the anomalous Doppler effect, we put forward a proposal to enhance the conversion efficiency of the slow-wave electron cyclotron masers (ECM) under the resonance condition. Compared with previous studies, we add a second-order shaping term in the guild magnetic field. Theoretical analyses and numerical calculations show that it can enhance the conversion efficiency in the low-gain limit. The case of the initial velocity spread of electrons satisfying the Gaussian distribution is also analysed numerically.