Abstract
The density conditions under which low-threshold parametric decay instabilities occur are analyzed by a physical model. Calculations show that low-threshold parametric decay instabilities occur in the density region. Magnetic field effects on the density region are analyzed. The maximum width of the density region is found. The plasma temperature has little effect on the density region. In order to avoid the low-threshold parametric decay instabilities, the daughter wave's frequency must be far from the UH frequency inside magnetic island. It's the key to control the magnetic field inside the magnetic island.