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handout2 - 8 Radiation transport emission and absorption...

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Unformatted text preview: 8. Radiation transport, emission and absorption coefficients 8.1 The radiation transport equation Let us first define a few quantities. Assume a area element dA perpendicular to incoming radiation. All rays through dA , whose direction is within the solid angle elemnt d Ω, transport the energy dE through dA in the time interval dt and frequency interval dν . We define I ν = dE dA dt dν d Ω specific intensity (8 . 1) Averaging over solid angle yields J ν = 1 4 π I I ν d Ω mean intensity (8 . 2) The energy density spectrum per solid angle element then is u ν (Ω) = dE dV dν d Ω = dE c dt dA dν d Ω = I ν c (8 .. 3) And the total energy density spectrum u ν = I u ν (Ω) d Ω = I I ν c d Ω = 4 π c J ν (8 . 4) If radiation passes through matter, its specific intensity may change. Energy may be added by emission or taken from the radiation field by absorption processes. Let us define the spontaneous emission coefficient dV = dA ds as j ν = dE dV dt dν d Ω = dE ds dA dt dν d...
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