Zemskov E.A.
A.I. Leypunsky Institute for Physics and Power Engineering, Obninsk, Russia
The article presents the results of using a sequential matrix approach for analyzing the system of diffusion equations for nuclear reactors in which solutions are constructed with the involvement of a complete system of eigenvectors and eigenvalues.
The criticality calculation reduces to the generalized eigenvalue problem. In addition to the basic solution (Keff and the principal eigenvector), all the dominant relations characterizing the iterative processes are determined. It is shown how such an approach makes it possible to determine the optimal relationship between internal and external iterations.
The matrix representation of the equations of neutron kinetics with allowance for delayed neutrons is treated as a Cauchy problem whose solutions are expressed in terms of a fundamental solution matrix made up of eigenvectors and the exponential operator of the evolution matrix. Knowledge of such solutions allows one to analyze in detail with good accuracy many transient processes, including a pulsed experiment to determine the subcriticality of a medium with fissile materials. These statements are illustrated by calculations of the damping decrement and dynamic reactivity in the model problem.
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