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

Abstract

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 $\tfrac{1}{2}\leq (\omega_{\rm J}/\omega_{\rm pd})^2\leq 1$. However, when $(\omega_{\rm J}/\omega_{\rm pd})^2 > 1$ or $(\omega_{\rm J}/\omega_{\rm pd})^2 < \tfrac{1}{2}$, the Jeans instability does not occur for the domain of the wave number $k_z \lambda_{\rm D} > (\omega_{\rm J}/\omega_{\rm pd})|[(\omega_{\rm J}/\omega_{\rm pd})^2 - 1]/[2(\omega_{\rm J}/\omega_{\rm pd})^2 - 1]|^{1/2}$. It is also found that the phase velocity of the surface wave decreases with increasing Jeans frequency.