Stochastic Eigenvalues in Multiplying Systems

A new approach is developed for solving stochastic eigenvalue problems that arise when uncertainty is present in the cross-section data in a critical assembly. The method has been shown to agree with values obtained from a direct quadrature. The new approach, which uses a polynomial chaos expansion (PCE), does not involve the nonlinear equations associated with the classical method of PCE, but rather a linear equation obtained by considering an equivalent time-dependent problem; it therefore leads to much simpler calculational procedures. The convergence of the method is rapid, and it is illustrated by numerical examples based upon a criticality problem and also by comparison with a problem that uses the nonlinear method.