Nuclear Science and Engineering / Volume 191 / Number 3 / September 2018 / Pages 231-247
Technical Paper / dx.doi.org/10.1080/00295639.2018.1466542
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.