## Computation — Transport and Diffusion Theory

The information required to calculate the group fluxes and importances by solving equations 1.27 and 1.30 consists of the specification of the reactor and the nuclear cross-sections. The latter are available in the form of data from thousands of measurements stored in data libraries such as the USA Evaluated Nuclear Data File (ENDF), the OECD Joint Evaluated Fission File (JEFF), the Japanese Evaluated Nuclear Data Library (JENDL), the Chinese Evaluated Nuclear Data Library (CENDL) and the Russian Evaluated Nuclear Data Library (BROND). Microscopic cross-section data from these files are then used, together with data about the specification, to calculate fine-group macroscopic cross-sections for each region. Fundamental-mode calculations in about 1000 fine groups are then performed to give group macroscopic cross-sections for spatial calculations, usually in 30 or 40 groups.

Equations 1.27 are solved by a double iterative method such as that described by Greenspan, Kelber and Okrent (1968). There are “inner” iterations to find the flux distribution and “outer” iterations to determine the eigenvalue, because the multigroup equations have no solution for ф until the correct value of к has been found. This outer iteration can be done in either of two ways. The composition and dimension of the reactor may be kept constant while the value of к is altered until the equations are solved. This is equivalent to finding the reactivity of a reactor that may not be exactly critical. Alternatively the composition (for example the concentration of plutonium in the core) or the dimensions (say the radius of the core) may be altered to make к = 1.

In the initial stages of design when the broad features of performance are being determined the three-dimensional reactor can often be represented adequately by a two-dimensional model in (r, z) cylindrical polar coordinates, but for the purposes of detailed design and for calculations in support of an operating reactor a three-dimensional model is required, usually in (hex, z) or (tri, z) geometry (i. e. with the transverse planes covered by a hexagonal or triangular mesh).

Again, in the initial stages of design, diffusion theory is adequate but when it comes to the details transport theory is necessary. A typical transport theory code would use a nodal formulation of the transport equation with hexagonal nodes, each node corresponding to an individual core position occupied by a fuel subassembly, a control rod or an incineration target, etc. The code would calculate the average flux in each node and then determine the fine structure within the node in terms of spherical harmonics in angle and polynomials in space. The average flux would enable properties such as the power generated in the subassembly to be predicted, and the fine structure would give the power of individual fuel elements within the subassembly.

A typical approach to operational calculations is given by Wardle- worth and Wheeler (1974).