Dispersion relation for the dust-acoustic wave in a Lorentzian plasma

The electrostatic mode of dust-acoustic (DA) surface waves propagating on the interface between a vacuum and a complex plasma is kinetically investigated by using the dispersion relation based on the Vlasov-Maxwell equations. The complex plasma consists of Lorentzian (kappa) electrons and ions, and cold dusty particles. The results show that in the long wavelength limit ($k_{x}$\textit{$\lambda $}$_{D}\to $ 0), the frequency of the wave is reduced to\textit{ $\omega $ }$\approx $ (\textit{$\mu $}$_{\kappa })^{1/2}k_{x}C_{D}$ where \textit{$\mu $}$_{\kappa }$ is a kappa (spectral index) dependent factor and $C_{D}$ = \textit{$\omega $}$_{pd}$\textit{$\lambda $}$_{D}$ is the well known dust acoustic speed. We see that the frequency increases as the ratio of dust density to ion density increases. Some interesting results of the DA surface waves supported by the Lorentzian plasma are discussed.