Application of the Monte Carlo methods and variational procedure for optimizing time-of-flight neutron diffractometer characteristics

Based on variational calculus, a procedure for the optimal approximation of detector surface of the time-of-flight neutron diffractometer has been suggested. The exact solution for a point sample and zero thickness detector has been obtained. Using the shape of the detector surface, an optimized Monte Carlo simulation has been performed for the parameters of the spectrometer depending on the sample size and detector thickness, its azimuthal and Bragg’s angular dimensions, and taking into account the neutron absorption in the sample and detector.