The parametric decay of dust ion acoustic waves in non-uniform quantum dusty magnetoplasmas

The parametric decay instability of a dust ion acoustic wave into low-frequency electrostatic dust-lower-hybrid and electromagnetic shear Alfven waves has been investigated in detail in an inhomogeneous cold quantum dusty plasma in the presence of external/ambient uniform magnetic field. The quantum magnetohydrodynamic model of plasmas with quantum effect arising through the Bohm potential and Fermi degenerate pressure has been employed in order to find the linear and nonlinear responses of the plasma particles for three-wave nonlinear coupling in a dusty magnetoplasma. A relatively high frequency electrostatic dust ion acoustic wave has been taken as the pump wave. It couples with two other low-frequency internal possible modes of the dusty magnetoplasma, viz., the dust-lower-hybrid and shear Alfven waves. The nonlinear dispersion relation of the dust-lower-hybrid wave has been solved to obtain the growth rate of the parametric decay instability. The growth rate is at a maximum for a small value of the e...