Implementation of the modified power iteration method to two-group Monte Carlo eigenvalue problems

In nuclear engineering field, the Monte Carlo method has been used to solve the eigenvalue or criticality problem for many years. The theoretical basis for solving the eigenvalue problem is the power iteration method, which exhibits slow convergence when the dominance ratio of the system is close to one. To overcome this drawback, a modified power iteration method, which could compute the first two eigenpairs at the same time, was proposed and its validity was exemplified for one-dimensional mono-energetic problems. In this paper, we implemented this method to one-dimensional two-group problems and proved its validity for these problems. This work indicates the capability of the modified power iteration method to solve practical multi-group or continuous energy problems.

Research highlights
► We implemented the modified power iteration method convergence acceleration.
► The method is capable to solve keff for one-dimensional two-group problems.
► The fundamental eigenfunction can be estimated at the same time.
► Fission density is used for the purpose of weight cancellation.
► The second eigenvalue and eigenfunction are also available by using the method.