On the P_N Method in Spherical Geometry: A Stable Solution for the Exterior of a Sphere

Abstract

A numerically stable version of the P_N method for solving the one-speed problem of neutron transport in the exterior of a sphere is developed. A transformation is used to obtain a plane-geometry-like neutron transport equation, where the angular derivative part of the streaming term in spherical geometry is considered as a source. In this way, conventional P_N solutions developed for plane geometry can be used to solve the problem and avoid having to deal with ill-conditioned solutions expressed in terms of the modified spherical Bessel functions of the third kind.

Keywords:

• Neutron transport
• spherical geometry
• P_N method
• Volterra integral equations

Acknowledgments

The author is indebted to W. J. Vieira for providing the MCNP6 result reported in Section 5.

Additional information

Funding

This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under grant 306231/2014-0.