Cell-average flux
\phi_{\ell g}(V) = \sum_{i \in {\rm cell}} \frac{\phi_{\ell g}(v_i)\,v_i}{V}~~,
and
Cell-average macroscopic cross section
\Sigma_{\ell g}(V) = \sum_{i \in {\rm cell}} \sum_j \frac{\rho_j(v_i)\,\sigma^j_{\ell g}(v_i)\,\phi_{\ell g}(v_i)\,v_i} {\phi_{\ell g}(V)\,V}~~.
In these equations, the $v_i$ are the region volumes, $V$ is the cell volume, $\rho_j(v_i)$ is the number density for material $j$ in region $i$, and $\sigma^j_{\ell g}(v_i)$ is the microscopic cross section for material $j$ in region $i$.
These calculations of cell-averaged quantities require a good knowledge of the region fluxes by group. These fluxes can be obtained in the form of a CCCC standard-interface file from a separate transport calculation and read into TRANSX. A typical procedure is to do a simple one-dimensional calculation for a reactor pin cell, and then to use the flux from this calculation to prepare cell-averaged cross sections to be used for a reactor-core calculation. An example of this process will be found in the next section of this report.
It is often necessary to obtain a ``constituent'' of a mixture like this, for example, the microscopic cross section for the U-235 in the uranium oxide in the fuel region of a reactor pin. Other times, the user may need the microscopic cross section averaged over the cell. TRANSX calls the first type of constituent cross section a ``region constituent'' and the second type a ``cell constituent.''
Region constituents are useful when the transport calculation is going to be done using the detailed region-wise geometry of the cell and when the user needs to make the mixtures in the transport code (e.g., to do concentration searches). Real material densities must be used with region constituents.
Cell constituents include the effects of any flux depression (``disadvantage factors'') or flux enhancement in the regions of the cell. Therefore, they are needed when the transport calculation is going to be made using a simplified geometry and when the user needs to make the mixtures in the transport code. Cell-averaged densities must be used with cell constituents.
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