Mathematical description of source driven subcritical nuclear systems is substantially different from that of the critical reactors. While in the critical case the neutron flux distribution can be obtained as the eigenfunction corresponding to the largest eigenvalue of a homogenous eigenvalue problem (i.e. fundamental mode), the subcritical case requires the solution of an inhomogeneous problem which can be constructed as a linear combination of the eigenfunctions of the homogenous problem (modal analysis). Obviously, the latter also involves many higher modes excited by the given external source distribution. Although the solution of a subcritical problem with external source can be obtained directly, without the determination of the contributing eigenfunctions, but modal analyses can add a deeper insight into the kinetic behavior of the system. The presence of higher modes reduces the accuracy of the point-kinetic approximation generally used for critical reactors, introduces bias into reactivity measurements and spatial dependence in the temporal behavior. Modal analysis can be an important tool to understand and correct for these effects. Most important application of the modal analysis of subcritical systems is related to the development of Accelerator Driven Systems (ADS), e.g. the planned MYRRHA research reactor in Mol (Belgium), but it can also be useful in other cases where subcriticality is involved, e.g. in the monitoring of shut down reactor core, cooling pond, fissile material storage, etc.
Recent efforts in this field concluded that in detailed models of real systems the important higher modes lie deep inside the eigenvalue spectrum. As a result of this enormously large number of eigenfunctions need to be determined for the accurate description, while most of them do not contribute significantly to the solution. Therefore efficient, targeted calculation of the important higher modes is crucial to the feasibility of the method. Such calculation can be performed by different spectral transformations, harmonic extractions and other methods implemented in numerical libraries (e.g. SLEPc). A further promising candidate is the Dynamic Modes Decomposition (DMD), which is based on the analysis of a detailed time dependent calculations. While the targeted search for inner eigenvalues suffers from convergence problems, DMD is challenging due to the required precision of the transient calculation.
The tasks of the candidate will involve:
- detailed literature study concerning the potential methods for the efficient targeted determination of the important higher modes of an external source problem;
- implementation and testing of the most promising methods, with special focus on DMD, in different test problems with gradually increasing complexity;
- development of a calculation tool applicable for detailed neutronics modelling of realistic systems based on the above experiences;
- verification and validation of the calculation system by available benchmarks and measurement results;
- application of the developed method in the design, evaluation and interpretation of reactor physics measurements and in the analysis of ADS designs.
English language skills, reactor physics knowledge, good programming skills