A Parametric Investigation on the Cyclotron Maser Instability Driven by Ring-beam Electrons with Intrinsic Alfv\'en Waves

The electron-cyclotron maser is a process that generates intense and coherent radio emission in plasma. In this paper, we present a comprehensive parametric investigation on the electron-cyclotron-maser instability driven by non-thermal ring-beam electrons with intrinsic Alfv\'en waves which pervade the solar atmosphere and interplanetary space. It is found that both forward propagating and backward propagating waves can be excited in the fast ordinary (O) and extraordinary (X) electromagnetic modes. The growth rates of X1 mode are almost always weakened by Alfv\'en waves. The average pitch-angle $\phi_0$ of electrons is a key parameter for the effect of Alfv\'en waves on the growth rate of modes O1, O2 and X2. For a beam-dominated electron distribution ($\phi_0 \lesssim 30^\circ$ ), the growth rates of the maser instability for O1, O2 and X2 modes are enhanced with the increase of Alfv\'en wave energy density. In other conditions, the growth rates of O1, O2 and X2 modes weakened with increasing Alfv\'en wave intensity, except that the growth of O1 mode may also be enhanced by Alfv\'en waves for a ring distribution. The results may be important for us in analyzing the mechanism of radio bursts with various fine structures observed in space and astrophysical plasmas.