Abstract　 　　  

  The parametric decay of a monochromatic Alfven wave in a low beta plasma is found to decay into a forward propagating density mode and a backward propagating daughter Alfven wave mode. In this paper, by performing one-dimensional (1-D) hybrid simulations, we detailedly analyze the parametric instabilities of the Alfven waves with a spectrum in a low beta plasma. The results show that the parametric instabilities have two stages. In the first stage, the density wave modes are excited due to the modulation of the pump Alfven waves, and then magnetic fluctuations appear after these density modes interact with the pump Alfven waves. In the second stage, each pump Alfven wave will decay into a density mode and a daughter Alfven wave mode, as in the parametric decay of a monochromatic Alfven wave.