It is pointed out that magnetic fields in the radiative interior of a star cause a slight reduction in the gas pressure, by a fraction of the order of B²/8πp. The effect is a proportionate reduction in the opacity and an increase in the effective heat transport coefficient, so that magnetic inhomogeneities cast thermal shadows in the general outflow of radiant energy. The shadows involve horizontal temperature gradients, forcing convective circulation in the otherwise stably stratified radiative zone. The associated vertical mixing may have important consequences for the thermonuclear burning of ⁷Li in the outer envelope of the star.
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E. N. Parker (1984) studied this question.