Decay Instability of a Dust-Acoustic Wave in a Magnetized Dusty Plasma

The three-wave nonlinear decay instability of a dust-acoustic wave (DAW) into a dust-lower-hybrid wave and a low-frequency electromagnetic wave in a homogeneous, magnetized, and collisionless dusty plasma has been investigated analytically. Fluid equations coupled with Maxwell's equations have been employed to find the nonlinear response of the plasma particles. An expression for the undamped growth rate of the three-wave parametric instability is derived. It is found that a large amplitude DAW undergoes a considerable decay instability in the magnetized dusty plasma. The growth rate of the wave instability is found to be highly sensitive to some plasma parameters, like external static magnetic field, ion number density, electron/ion temperature, etc. The importance of this paper to space dusty plasma environments is also pointed out.