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A new quantitative representation of the generalized Kirchhoff's law relating the emission from each propagating branch to the absorption along the corresponding branch is established, including for the first time the effects of inhomogeneous magnetic fields on cyclotron and synchrotron radiation from mode conversion theory. The concept of optical depth is revised to include effects of reflection and conversion in addition to transmission. Via the use of a variational principle, the source distribution function for the inhomogeneous emitting layer is calculated.
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Swanson et al. (1992) studied this question.
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