On the validity of magnetohydrodynamics for ionic mixtures

The collective mode spectrum of the magnetized ionic mixture consisting ofs components is studied by starting from the microscopic balance equations and the fluctuation formulas for the microscopic densities. Apart from a heat mode ands-1 diffusion modes with frequencies of second order in the wavenumber, four modes with complex finite frequencies for vanishing wavenumber are found. If the mixture consist of particles with equal ratios of charge and mass, these four modes become similar to the gyroplasmon modes of the magnetized one-component plasma of which the frequencies are real in lowest order in the wavenumber. Green-Kubo relations are derived for the transport coefficients which appear in the frequencies of the heat mode and the diffusion modes. The long-time behavior of the integrands of the Green-Kubo expressions is evaluated with the help of mode-coupling theory. The static transport coefficients are found to be finite unless the mixture consists of species with equal ratios of charge and mass. It is concluded that the presence of species with different charge-mass ratios is essential for the validity of magnetohydrodynamics for an ionic mixture.