Weibel instability oscillation in a dusty plasma with counter-streaming electrons

We investigate the Weibel instability (WI) in a dusty plasma which is driven to oscillation by the addition of dust grains in the plasma. Our analysis predicts the existence of three modes in a dusty plasma. There is a high-frequency electromagnetic mode, whose frequency increases with an increase in the relative number density of dust grains and which approaches instability due to the presence of dust grains. The second mode is a damping mode which exists due to dust charge fluctuations in plasma. The third mode is the oscillating WI mode. The dispersion relation and the growth rate of various modes in the dusty plasma are derived using the first-order perturbation theory. The effect of dust grain parameters on frequency and growth rate is also studied and reported.