Eur. Phys. J. Plus (2019) 134: 516
https://doi.org/10.1140/epjp/i2019-13045-9

Regular Article

On Fick’s law in asymptotic transport theory

¹ INFN, Sezione di Genova, Via Dodecaneso, 33, 16146, Genova, Italy
² Centro Fermi, Piazza del Viminale, 1, 00184, Roma, Italy
³ Politecnico di Torino, Dipartimento Energia, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy
⁴ INFN, Sezione di Torino, Via P. Giuria, 1, 10125, Torino, Italy

^* e-mail: Nicholas.Chentre@ge.infn.it

Received: 21 February 2019
Accepted: 7 July 2019
Published online: 17 October 2019

Abstract

The spatial asymptotic approach is used to derive expressions for the diffusion coefficient from the neutron transport equation to improve the standard P₁-based formula. A general explicit analytical expression is obtained in the frame of the P_N model, which also allows an easy evaluation of the coefficient in the limit for . The analytical formulae are presented at any order of the scattering anisotropy. An alternative formula is derived through the interpretation of the diffusive contribution of the exact transport solution obtained by means of Case’s method applied to a plane configuration in the presence of isotropic scattering. Some numerical results are presented to illustrate the performances of the different formulations once they are used in the diffusion model for the solution of source-injected and critical problems.