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Singular Eigenfunction Expansion Solution for Time-Dependent Neutron Transport with Delayed Neutrons

Jeffery D. Densmore

Nuclear Science and Engineering / Volume 191 / Number 3 / September 2018 / Pages 231-247

Technical Paper /

Received:February 9, 2018
Accepted:April 14, 2018
Published:August 16, 2018

We develop an analytic solution for time-dependent neutron transport with delayed neutrons using the singular eigenfunction expansion method. Our approach is based on a technique for solving time-dependent neutron-transport problems without delayed neutrons (Case and Zweifel, Linear Transport Theory, Addison-Wesley, 1967), which we effectively generalize to include the presence of delayed-neutron precursors. In particular, we obtain eigenfunctions composed of two parts: one corresponding to the neutron angular flux and one corresponding to the delayed-neutron precursor concentration. We further demonstrate that these eigenfunctions are complete. We also provide numerical results for an example problem.