Methods for Solving Adjoint Equations in Nonlinear Conditionally-Critical Problems

Abstract

The special features of methods for calculating the neutron value functions with respect to functionals which are determined by solving a nonlinear conditionally-critical neutron transport equation are examined. The adjoint equations for these functions are written in an abstract operator form and contain additional, compared with linear problems, terms which are orthogonal to the neutron flux. These terms take account of the contribution due to the change in the properties of the medium when neutrons are introduced into the reactor into the balance of the values. The operators of the adjoint problem are analyzed and criteria ensuring that the proposed iteration methods converge are formulated. The satisfaction of the criteria is checked for the solution of problems where the nonlinearity of the emission equations is due to the dependence of the concentration of fuel nuclei on the neutron flux. It is noted that the iteration processes converge rapidly.