The linear excitation of surface dust-ion-acoustic waves in a semi-bounded dusty plasma and a dusty plasma slab comprising Tsallis distributed electrons and ions is studied. The propagation properties of surface modes (in semi-bounded dusty plasma) and both symmetric and antisymmetric modes (in the dusty plasma slab) are investigated. It is found that the nonextensivity increases the phase velocities of surface modes in both dusty plasma structures, whereas the magnitude of the dust grain charge reduces the wave frequency. In the dusty plasma slab, the wave frequency of both symmetric and anti-symmetric modes decreases with the increasing number density of dust grains, also it leads to a decrease in the separation between two modes. The present investigation contributes to the physics of electrostatic surface wave structures in Saturn’s E-ring or Gring magnetosphere in which plasma components with Tsallis distribution exist.
