  The instability of the dust-acoustic waves driven by drifting electrons and
ions in a dusty plasma is investigated by the kinetic theory. All the plasma
components (electrons, ions and dust particles) are assumed to be the
Lorentzian kappa-distributions. The spectral indexes kappa of the
kappa-distributions for the three plasma components are different from each
other. The obtained instability growth rate depends on the physical quantities
of the plasma not only, but on the spectral indexes. The numerical results for
the kappa-effect on the instability growth rate show that, if the normalized
wave number is small, the index of electrons has a stabilized effect on the
dust acoustic waves and the index of ions has an instability effect on the
waves, but if the normalized wave number is large, they both nearly have no any
effect on the waves. In reverse, the index of dust grains has nearly no any
effect on the instability growth rate if the normalized wave number is small,
but it has a stabilized effect on the dust waves if the normalized wave number
is large.
