The effect of dust charge-gradient and dust polarization forces on the Jeans instability in a collisional magnetized dusty plasma

Abstract

A theoretical investigation of Jeans instability has been done incorporating dust charge gradient and dust polarization forces in a collisional magnetized dusty plasma. The dispersion relation is derived using three fluid theory by employing Boltzmann distribution of ions and electrons and retaining the complete dynamics of positively charged dust. To signify the effects of each parameter on Jeans instability the obtained general dispersion relation is further deduced considering parallel and perpendicular modes of propagation. It has been analyzed analytically as well as numerically that the growth rate of gravitational instability decreases with simultaneous presence of charge gradient force, collision frequency, thermal velocity and external magnetic field, but increases with the dust polarization force. The existence of dust charge gradient force and dust polarization force (along with external magnetic field) have been found to improve the criterion for Jeans instability. The relevance of the work to the collapse of dusty clouds has been discussed.