Nonlinear diffuse reflection and transmission of radiative energy by a layer of finite thickness

Details Nonlinear diffuse reflection and transmission of radiative energy by a layer of finite thickness Nonlinear diffuse reflection and transmission of radiative energy by a layer of finite thickness

Apr 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010ap.....53..251p&link_type=abstract

Astrophysics, Volume 53, Issue 2, pp.251-267

Astronomy and Astrophysics

Astrophysics

Radiative Transfer, Nonlinear Diffuse Reflection And Transmission

Scientific paper

The major results for the linear problem of diffuse reflection and transmission of radiation by a layer of finite thickness are carried over to the nonlinear case by successive application of Ambartsumyan’s approach for a one dimensional anisotropic medium. Formulas are given for nonlinear addition of layers which can be used to construct recurrence calculation procedures for uniform, periodic, and arbitrary stratified media. A complete set of differential equations for invariant imbedding is derived with the aid of these formulas. These equations are used to obtain a system of total invariance equations, which, in turn, offer the possibility of reducing the nonlinear problem of diffuse reflection and transmission during irradiation of a layer from both sides to the simpler problem of illuminating this medium from only one side, with the thickness of the layer remaining only as a fixed parameter. Finally, it is shown that the results obtained for the single frequency case (two-level atom) remain valid in the polychromatic case (multilevel atom), which is important for interpreting astrophysical data.

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