Calculation and verification of neutron irradiation damage with differential cross sections

TL;DR

This paper proposes a direct method for calculating neutron irradiation damage using energy-angular distributions, introduces numerical verification techniques, and assesses the impact of angular distribution assumptions on damage calculations.

Contribution

It introduces a direct calculation method for DPA using energy-angular distributions and verifies numerical integration techniques for improved accuracy.

Findings

Direct trapezoidal integration and interpolation are accurate for DPA calculations.

Assuming isotropic angular distributions overestimates DPA cross sections.

Two orders of Legendre polynomials suffice for fission reactors, four for fusion reactors.

Abstract

The Displacement per Atom (DPA) rate is conventionally computed with DPA cross sections in reactor applications. The method of direct calculation with energy-angular distributions given in the Center of Mass (CM) frame is proposed and recommended in the present work. The methods for refining and verifying the calculations of DPA cross sections are proposed: (i) Gauss-Legendre-Quadrature-based Piecewise Integration (GLQPI) for ensuring the numeric convergence of integral over emission angle due to the discontinuity of integrand; (ii) verification of the convergence for trapezoidal integration over the secondary energy; (iii) interpolation of double-differential cross sections. For 56Fe of JEFF-3.1.1, the current numeric integration over emission angle is shown not convergent, whereas the direct trapezoidal over the secondary energy and the direct interpolation of energy-angle-integrated damage are shown accurate. On the other hand, it is shown that the DPA cross sections are overestimated if isotropic angular distributions are assumed. However, the DPA cross section is not sensitive to the high-order Legendre polynomials because the former is an angle-integrated quantity. Numerical results of neutron elastic scattering show that 2 orders of Legendre polynomials can give the DPA rates of 56Fe within 0.5% overestimation for fission reactors, while 4 orders are required for fusion reactors. For neutron inelastic scatterings-induced DPA, the first order Legendre polynomial is sufficient for both fission and fusion reactors.