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We consider diffusion caused by a combined influence of the Hall effect and electric currents, and argue that such diffusion forms chemical inhomogeneities in plasma. The considered mechanism can be responsible for the formation of element spots in laboratory and astrophysical plasmas. Such current-driven diffusion can be accompanied by the propagation of a paticular type of waves which have not been considered earlier. In these waves, the impurity number density oscillates alone and their frequency is determined by the electric currents and sort of impurity ions. These compositional waves exist if the magnetic pressure in plasma is much greater than the gas pressure. Such waves lead to local variations of chemical composition in plasma and, hence, can manifest themself by variations of the emission in spectral lines.