Application of complex-step derivative method for k-eigenvalue sensitivity calculation in neutron transport models

Abstract This paper paves the way to numerically solve the k-eigenvalue neutron transport equation with complex variable arguments, and then employs the developed complex variable transport solver to calculate the k-eigenvalue sensitivities with respect to nuclear cross sections using the complex-step derivative method (CDM). CDM utilizes the Taylor series expansion in the complex plane whereby the imaginary component of the complex solution space can be directly used to represent the sensitivity derivative. CDM offers a robust numerical avenue to calculate accurate sensitivities not susceptible to subtractive cancellation errors. Numerical examples with one-dimensional k-eigenvalue neutron transport models in both one-group and multigroup formulations were employed to demonstrate the feasibility of CDM in reactor problems. The CDM sensitivity results received good agreements to the reference solutions from the conventional forward-based and adjoint-based sensitivity methods. These preliminary results confirmed the viability and accuracy of CDM for k-eigenvalue sensitivity calculation in neutron transport models.