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

Abstract

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.

Keywords:

• Singular eigenfunction expansion
• time-dependent transport
• delayed neutrons

Notes

^a It is possible for the denominator in Eq. (26) to vanish. However, this corresponds to a pole in the complex k plane, which can be handled when inverting the Fourier transform.