  A linear theory of dust acoustic (DA) and dust ion-acoustic (DIA) waves in a
self-gravitating collisional dusty plasma contaminated by variable-charge
impurities is presented for a self-consistent closed system. The ion-drag force
arising from the ion orbital motion as well as momentum transfer from all the
ions and self-gravitation are taken into consideration. The physical processes,
viz., dust-charge relaxation, ionization, recombination and collisional
dissipations are also taken into account self-consistently. The generalized
dispersion relation describing the coupling of the acoustic modes with the
dust-charge relaxation mode (CRM) and damping of the waves is derived and
analyzed numerically.
