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5.5: The Equation of Transfer

Last updated

Mar 5, 2022
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- 5.4: Optical Depth
- 5.6: The Source Function (Die Ergiebigkeit)

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The equation of transfer deals with the transfer of radiation through an atmosphere that is simultaneously absorbing, scattering and emitting.

alt
$\text{FIGURE V.1}$

Suppose that, between $x$ and $x + dx$ the absorption coefficient and the scattering coefficient at frequency $\nu$ are $\alpha (\nu)$ and $\sigma (\nu)$ , and the emission coefficient per unit frequency interval is $j_{\nu} d\nu$ . In this interval, suppose that the specific intensity per unit frequency interval increases from $I_{\nu}$ to $I_{\nu} + dI_{\nu}$ ( $dI_{\nu}$ might be positive or negative). The specific intensity will be reduced by absorption and scattering and increased by emission. Thus:

$dI_{\nu} = - [I_{\nu} \alpha (\nu) + I_{\nu} \sigma (\nu) - j_{\nu} (\nu) ] dx. \label{5.5.1} \tag{5.5.1}$

This is one form - the most basic form - of the equation of transfer. Notice that $\alpha$ and $\sigma$ do not have a subscript.

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