The neutron point kinetics equation: Suppression of fractional derivative effects by temperature feedback. (January 2016)

• Record Type: Journal Article
• Authors: Schramm, M.; Bodmann, B.E.J.; Alvim, A.C.M.; Vilhena, M.T.
• Is Part Of: Annals of nuclear energy. Volume 87:Part 2(2016:Jan.)
• Page Start: 479
• Page End: 485
• Publication Date: 2016-01
• Subjects: Neutron point kinetics -- Fractional derivative -- Temperature feedback; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; 621.4805
• DOI: 10.1016/j.anucene.2015.10.003
• Languages: English
• ISSNs: 0306-4549

Abstract

Highlights: A Riemann–Liouville fractional derivative point kinetics model is discussed. A nonlinear temperature feedback is considered. A solution in analytical representation for the neutron density is derived. The solution is valid for any fractional order and relaxation time scale. Temperature feedback effects suppress the fractional derivative contributions. Abstract: A Riemann–Liouville fractional derivative point kinetics model is discussed with additional temperature feedback. The choice for the Riemann–Liouville definition is justified by preservation of homogeneity and integral transform properties. An analytical representation for the time dependent neutron density is derived for any fractional order and any relaxation time scale by the use of a recursive decomposition scheme. Without temperature effects scenarios with constant positive and negative, linear and oscillatory time dependent reactivity are presented. The case with additional temperature effects is solved and results are presented. The latter case showed that for a selection of fractional derivative parameter effects on the neutron density are completely suppressed.