Adjoint Monte-Carlo method with fictitious scattering in deep penetration and long-distance detector calculations

Abstract

Deep penetration transport problems in complex systems joint to hetere geneous source (Q) sampling give rise to some difficulties in evaluating leakage and fluxes on a detector point.

To overcome these difficulties we have solved both the adjoint Boltzmann flux (ф*) equation and the following scalar-dual equation:

$$\smallint Q\phi *dP - \smallint Q\phi *dP = \smallint \phi \phi *\Omega \cdot n d\sum d\Omega dE dt + \smallint \frac{{[\phi \phi *]_0^T }}{v} dr d\Omega dE$$

With a suitable choice for the domain , for Q* and for the boundary conditions, an adjoint flux calculation allows us to obtain simultaneously the Q-source contribution and the detection (or leakage) spectrum.

Compared to direct methods with importance sampling, the adjoint methods give very low-cost and faithful results.