Landau damping of the dust ion-acoustic surface waves in a Lorentzian plasma

The Lorentzian (kappa) velocity distribution function is employed to study the stability of dust ion-acoustic surface waves propagating on a boundary of semi-infinite plasma. We allow that the electrons and ions are Lorentzian but the dusts are cold. Then the dust ion-acoustic surface wave can be excited: the real and imaginary parts of the wave frequency $\omega =\omega _r +i\gamma$ are obtained as functions of \textit{$\delta $} = $n_{i}$/$n_{e}$ (ion-to-electron mass ratio) as well as the normalized wave number $k_x \lambda _e $ where $k_{x}$ is the x-component of the wave number and $\lambda _e $ is the electron Debye length. The wave exhibits resonances and the resonant frequency is strongly dependent on the value of \textit{$\delta $}. For a negatively (positively) charged dust particles, the phase velocity of the wave increases as \textit{$\delta $} increases (decreases). When \textit{$\delta $ }=1$,$ the result displays the phase velocity of a Maxwellian wave. The imaginary part of the wave frequency appears to be negative always regardless of the value of \textit{$\delta $}. Such collisionless dissipation of the wave is known as the Landau damping. We also found that the damping is enhanced as \textit{$\delta $} increases (decreases) for a negatively (positively) charged dust particles.