Application of Monte Carlo method with forward and adjoint midway coupling to radiation transport calculation

Abstract

Forward and adjoint Monte Carlo coupling technique has been developed for analysing detector response in a very highly absorbing system or in a system with small detector and small source. Multiplying the forward transport equation by adjoint flux, and the adjoint transport equation by forward flux, and subtracting the two equations, and then integrating over all variables, and then finally appling Gauss Theorem, we obtain the general reciprocity equation. Integrating this reciprocity equation at some boundary, we can obtain the detector response. Forward and adjoint fluxes are scored at some boundary called midway, inclosing the source or the detector region. The detector response is calculated by coupling the calculated forward and adjoint flux at the midway. By coupling the forward and the adjoint fluxes at the midway, this method makes the problem independent of the detector size, which is very important for the calculation efficiency. This method eliminates particles that are absorbed and do not contribute to the detector and calculates a special kind of particles called contributons, which are never absorbed and contribute to the detector response. Using this method in deep penetration calculations can be advantageous, since classical Monte Carlo method gather large amount of irrelevant infromation. These contributons are emitted from the source and must pass through the midway between the source and the detector. The mathematical basis for this theory is shown as well as the physical meaning of the contributon. The reliability and efficiency for this method were shown by solving a sample photon and neutron problem, with a point detector, and source region relatively small compared to the midway region. Finally, an application of this method to shielding analysis to Korea Superconducting Tokamak Advanced Research(KSTAR) is demonstrated, showing an increase in calculation efficiency, depending on the distance between the neutron source and the detector.