An electron cyclotron maser based on anomalous Doppler effect (ADECM) with an initially axial beam velocity is considered,and the nonlinear equation of beam-wave interaction is presented.With the numerical methods,the nonlinear dynamics of the ADECM is investigated.It is shown that the saturated interaction efficiency of the ADECM approaches 90％ and the interaction length for the saturated efficiency spans about 5-20cm.The results may be of importance for designing a compact device in applications in microwave generations or microwave heating of ceramic laminates.In the late 1950s,the theoretical studies on the instability of electron cyclotron maser based on normal Doppler effect (NDECM) were performed almost simultaneously by Gaponov,[1] Twiss,[2] and Schneider.[3] Their discoveries have resulted in the most successful fast-wave devices such as the gyrotron and variants.[4,5] The possible applications of microwaves span a wide range of technologies such as in thermonuclear fusion energy,charged particle accelerations,radar systems,and processing of advanced ceramics.[6-16]