Higher-order variational perturbation expressions in fixed source problems using Monte Carlo trial functions

Higher-order variational expressions are used to assess the e€ects of perturbing the absorption cross-section of an in®nite non-multiplying homogeneous system on the response of an in®nite plane detector of ®nite thickness placed at a certain distance from an in®nite plane source. For this speci®c problem the number of equations to be satis®ed by the weighting functions is reduced to six instead of eight. Two approaches are used to obtain these functions. One is by using Greenʹs function approach for both the forward and back- ward ®elds and subsequently the other weighting functions. The other approach is to use trial functions provided by Monte Carlo. A methodology of utilizing virtual sampling to obtain the di€erent weighting functions from one Monte Carlo run was demonstrated. The results revealed for this problem show that higher-order variational expressions gave more accurate estimates of the e€ects of perturbation than ®rst-order expressions and the conventionally used Correlated Sampling