Calculation of Higher-Order Fluxes in Symmetric Cores—I: Theory

In neutron chain systems with material symmetries, various k-eigenvalues of the neutron balance equation beyond the dominant one may be degenerate. Eigenfunctions can be partitioned into several classes according to their invariance properties with respect to the symmetry operations (mirror symmetries and rotations) keeping the material distribution in the system unchanged. Their calculation can be limited to a fraction of the system (sector) provided that innovative boundary conditions matching the symmetry classes are used, and whole-system eigenfunctions can then be unfolded from the solutions obtained over the sector. With power iteration as the method for searching k-eigenvalues, this use of the material symmetries to split the global problem into a variety of smaller-sized problems has several computational advantages: lower computation times and memory requirements, increased dominance ratios, lowered possible degeneracies in each subproblem, and possible parallel (separated) treatment of the subproblems. The implementation is discussed in a companion paper using diffusion and transport theories.