Low frequency responses, and wave dispersion in dusty plasmas

The self-consistent dusty-plasma response found in the kinetic theory [V. N. Tsytovich and U. de Angelis, Phys. Plasmas 6, 1093 (1999)] is generalized to include collisions of all species with neutrals, a situation often important in the experiments, and used to derive a new dispersion relation for low-frequency waves in dusty plasmas. An estimate of the differences with previous results is given for the particular case of dust-acoustic waves without the effects of collisions with neutrals: the present theory reproduces the result of Rao, Shukla, and Yu [Planet. Space Sci. 38, 543 (1990)] only for low dust density and small wavelengths, but strong deviations occur at larger wavelengths and dust densities.