Parametric coupling of whistler waves with gyrating ion beam in a complex plasma

This manuscript examines the non‐linear interaction between the negative energy beam cyclotron mode and the high‐frequency whistler waves. The negative energy beam mode is supported in the vicinity of the beam gyro‐frequency harmonics by a gyrating ion beam with ring‐shaped velocity distribution. Using a gyrating ion beam, we have examined how dust charge variations affect the parametric up‐conversion of high‐frequency whistler waves (WWs) into a side band wave and a low‐frequency mode. For the linked modes, a non‐linear dispersion relation is obtained. It is demonstrated that the WWs divided by beam gyro‐frequency harmonics are up‐converted by a gyrating ion‐beam frequency. An expression for the ion cyclotron mode wave growth rate has been obtained. The estimation of the turbulence growth rate takes into account for the typical parameters of existing dusty plasma. It has been observed that an increased growth rate is reported with a rise in the pump wave amplitude, beam gyro‐frequency, number density of dust grains, and the relative density of dust grains. However, a decline in the growth rate has been observed with increasing gyrating ion beam density and dust grain's size.