Generation of Scattered Ion-Cyclotron Wave and Ion Acoustic Wave by Parametric Instability of Electromagnetic Ion-Cyclotron Wave in a Dusty Plasma

This manuscript provides the theoretical explanation of the nonlinear scattering of an EMIC into an IAW $\text{and}$ a scattered ion-cyclotron wave (SICW) in a dusty plasma using fluid theory. The low-frequency nonlinearity arises through the parallel ponderomotive force on ions and the high-frequency nonlinearity arises through $\text{the}$ nonlinear current density of ions. For the linked modes, a nonlinear dispersion relation is obtained. A formula for the SICW growth rate has been derived. The estimation of the turbulence growth rate takes into account for the typical parameters of dusty plasma. It is detected that an increased growth rate can be seen with a rise in the pump wave amplitude and the number density $n^{0d}\left({\mathrm{cm}}^{-3}\right)$ of dust grains. However, a decline in the growth rate has been reported with growing relative density $d=\frac{n^{0i}}{n^{0e}}$ $\text{of}$ dust grains, magnetic field, and the dust grain's size. Therefore, these wave modes have many applications in space and astrophysics as well as in laboratory experiments.