  We investigate the dispersion relation and Landau damping of ion acoustic
waves in the collisionless magnetic-field-free plasma if it is described by the
nonextensive q-distributions of Tsallis statistics. We show that the increased
numbers of superthermal particles and low velocity particles can explain the
strengthened and weakened modes of Landau damping, respectively, with the
q-distribution. When the ion temperature is equal to the electron temperature,
the weakly damped waves are found to be the distributions with small values of
q.
