Abstract
Scattering effects are considered for radiative transfer within randomly distributed and binary mixtures in one dimension. The most general formalism is developed within the framework of the invariant imbedding method. The lengthL of the random sample thus appears as a new variable. One transmission coefficientT(L) suffices to specify locally the intensities. By analogy with the homogeneous situation, one introduces an effective opacity with 〈T〉=(1+σeff L)−1 fulfilling σeff<〈σ〉=p 0σ0+p 1σ1(0 and 1 refer, respectively, to the components involved in the mixture). Equality is reached whenL→0, ∞. Otherwise, σeff displays a deep transmission window. It is numerically expressed for three combinations of opacities (σ0,σ1) and average grain sizes (λ0, λ1). These results are of crucial concern in optimizing an ICF compression for a pellet nonuniformly illuminated by intense laser or ion beams.
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Vanderhaegen, D., Deutsch, C. Linear radiation transport in randomly distributed binary mixtures: A one-dimensional and exact treatment for the scattering case. J Stat Phys 54, 331–360 (1989). https://doi.org/10.1007/BF01023483
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DOI: https://doi.org/10.1007/BF01023483