The Multiple Scattering of Waves by Weak Random Irregularities in the Medium

I. D. Howells
1960 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
In part II, the general solution of the equation of transfer for a spatially homogeneous radiation field, varying with time, is given first, and compared with Lighthill's result for the angular distri bution of radiation in terms of the length of path travelled. The much more difficult problem of a steady-state field with spatial variation has been treated by Chandrasekhar (1950), who gives many exact solutions for special types of scattering (such as isotropic and Rayleigh scattering). But his
more » ... methods are not well suited to some other types, especially small-angle forward scattering. Most of part II is devoted to finding approximate solutions for this case, first generalizing Fejer's solu tion for a slab of scattering medium which produces a small total angular deviation of the radiation, and then deriving an approximate partial differential equation of transfer to treat problems where the total angular deviation is not small. Methods of solving this equation by eigenfunction expan sions are explained, and some numerical results are given, especially angular distributions of emergent and reflected radiation for a semi-infinite scattering region.
doi:10.1098/rsta.1960.0011 fatcat:z5imy7472vguhhvy6jmulhwisi