Stability and gravitational effects on surface dust-acoustic waves in self-gravitating semi-bounded dusty plasmas

The stable conditions and gravitational effects on the surface dust-acoustic wave are investigated in self-gravitating semi-bounded dusty plasmas. The dispersion relation of the surface dust-acoustic wave is obtained by the plasma dielectric function with the specular reflection boundary condition. It is shown that the surface dust-acoustic wave become unstable for any values of the wave number when tfrac{1}{2}≤ (omega_J/omega_pd)(2≤) 1. However, when (omega_J/omega_pd)(2) > 1 or (omega_J/omega_pd)(2) < tfrac{1}{2}, the Jeans instability does not occur for the domain of the wave number k_z lambda_D > (omega_J/omega_pd)|[(omega_J/omega_pd)(2) - 1]/[2(omega_J/omega_pd)(2) - 1]|(1/2) . It is also found that the phase velocity of the surface wave decreases with increasing Jeans frequency.