The temperature and density conditions in the magnetized photosphere and chromosphere of the Sun lead to a very small degree of atomic ionization. In addition, at particular height, the magnetic field may be strong enough to give rise to a cyclotron frequency larger than the collisional frequency for some species, while for others the opposite may happen. These circumstances influence the collective behavior of the particles and some of the hypotheses of magnetohydrodynamics may be relaxed, giving rise to non-ideal MHD effects. In this paper we discuss our recent developments in modeling non-ideal plasma effects derived from the presence of a large amount of neutrals in the solar photosphere and the chromosphere, as well as observational consequences of these effects.
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