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We carried out a series of 2D simulations to study the beam instability and cyclotron maser instability (CMI) with the initial condition that a population of tenuous energetic electrons with a ring-beam distribution is present in a magnetized background plasma. In this paper, weakly relativistic cases are discussed with the ring-beam kinetic energy ranging from 25 to 100 keV. The beam component leads to the two-stream or beam instability at an earlier stage, and the beam mode is coupled with Langmuir or whistler mode, leading to excitation of beam-Langmuir or beam-whistler waves. When the beam velocity is large with a strong beam instability, the initial ring-beam distribution is diffused in the parallel direction rapidly. The diffused distribution may still support CMI to amplify the X1 mode (the fundamental X mode). On the contrary, when the beam velocity is small and the beam instability is weak, CMI can amplify the Z1 (the fundamental Z mode) effectively while the O1 (the fundamental O mode) and X2 (the second harmonic X mode) modes are very weak and the X1 mode is not excited. In this report, different cases with various parameters are presented and discussed for a comprehensive understanding of ring-beam instabilities

A 2D simulation study of Langmuir, whistler, and cyclotron maser instabilities induced by an electron ring-beam distribution