Effect of polarization force on the Jeans instability of self-gravitating dusty plasma

The effect of polarization force acting on massive charged dust grains is investigated analytically on the Jeans instability of self-gravitating dusty plasma. The gravitational force acting on the massive negatively charged interstellar dust grains are considered in presence of both electrical and polarization forces. The basic equations of the problem are formulated and a general dispersion relation is obtained using plane wave approximation in low frequency wave mode. The effect of polarization force in the dispersion relation of the problem, condition of the Jeans instability and expression of the critical Jeans wave number is examined. The unstable growing modes due to self-gravitational force are studied in the situation when polarization force on the dust grain exceeds over the electrical force in magnitude. It is observed that the polarization force increases the growth rate of the system.