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Introduction:Minor actinides transmutation is a potential solution which is currently investigated for long-term management of nuclear waste. In the case of a closed plutonium fuel cycle, minor actinides are the main responsible for long-term radiotoxicity and short-term decay heat of the nuclear waste package. In the transmutation process, neptunium, americium and eventually curium, which are the three main minor actinides produced in nuclear reactors, are submitted to a neutron flux in order to turn them into shorter-lived fission products by fission or successive captures followed by fissions. This way, radiotoxicity levels can be lowered up to a factor 200 in the best case [1] and a reduction of a factor 3 of the final repository footprint can be achieved [2].Various options have been proposed so far for minor actinides transmutation, including thermal reactors [3], ADS [4] and fast reactors [5]. We will focus here on the fast reactor option as targeted by French R&D programs. Two approaches have been discussed for transmutation in fast reactors, namely the homogeneous one and the heterogeneous one. A complete comparison of these two options can be found in [6] and a small breakdown of the most salient points for each case is done below.

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.