Looking for a new light source, especially short-wavelength coherent light source has attracted much attention. A possibility and basic conditions are discussed by using crystalline undulator field radiation as a short-wavelength laser; it is pointed out that the short-wavelength laser has not yet been available so far which is due to not only technical reasons, but also physical reasons. In this paper, the physical problem is analyzed by using parametric excitation method. Introducing the sine-squared potential, the particle motion equation is reduced to a pendulum equation with a damping term and parameter excitation term in the framework of classical mechanics and the dipole approximation. A stability of the system is discussed using Melnikov method, and the critical condition of the system is also analyzed. The results show that the stability of the system relates to its parameters. By adjusting these parameters appropriately, the stability of the system can be ensured in principle.