We derive self-consistent formalism for the description of multi-component partially ionized solar plasma, by means of the coupled equations for the charged and neutral components for an arbitrary number of chemical species, and the radiation field. All approximations and assumptions are carefully considered. Generalized Ohm's law is derived for the single-fluid and two-fluid formalism. Our approach is analytical with some orderof-magnitude support calculations. After general equations are developed we particularize to some frequently considered cases as for the interaction of matter and radiation.

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Over the last decades, realistic 3D radiative-MHD simulations have become the dominant theoretical tool for understanding the complex interactions between the plasma and the magnetic field on the Sun. Most of such simulations are based on approximations of magnetohydrodynamics, without directly considering the consequences of the very low degree of ionization of the solar plasma in the photosphere and bottom chromosphere. The presence of large amount of neutrals leads to a partial decoupling of the plasma and the magnetic field. As a consequence of that, a series of nonideal effects (ambipolar diffusion, Hall effect and battery effect) arises. The ambipolar effect is the dominant one in the solar chromosphere. Here we report on the first three-dimensional realistic simulations of magneto-convection including ambipolar diffusion and battery effects. The simulations are done using the newly developed Mancha3D code. Our results reveal that ambipolar diffusion causes measurable effects on the amplitudes of waves excited by convection in the simulations, on the absorption of Poynting flux and heating and on the formation of chromospheric structures. We provide a low limit on the chromospheric temperature increase due to the ambipolar effect using the simulations with battery-excited dynamo fields.