Extension of the noise propagation matrix method for higher mode solutions

The noise propagation matrix method (NPMM) has been extended to get higher mode solutions. Previous studies show that the NPMM can be used to compute the dominance ratio of a system. It is essentially the same as the Coarse Mesh Projection Method (CMPM), both of which use the noise propagation matrix (NPM) to determine the dominance ratio, either after finishing the Monte Carlo simulation or on-the-fly during the simulation. Since only the fundamental fission source information is explicitly utilized while the higher mode information is implicitly contained in the statistical noises, the NPMM can usually only give an approximate estimation of the dominance ratio after thousands of cycles. In this study, the NPMM is extended by simulating the higher modes explicitly, so that the dominance ratio estimation can be more accurate and efficient. Besides, the higher mode solutions can be obtained at the same time with good accuracy and efficiency.