# Analytic solutions of the multigroup space-time reactor kinetics equations in multiregion slab and spherical geometry

## Abstract

Analytic solutions of the multigroup space-time reactor kinetics equations are developed for a bare slab and spherical reactor, and a reflected slap and spherical reactor for the zero flux, the zero current, and the extrapolated endpoint boundary conditions. The material properties of the reactors are assumed constant in space and time, but solutions involving spatially dependent source terms and initial conditions are investigated. The development of analytic and numerical solutions to the reactor kinetics equations is reviewed. The system of partial differential equations is reduced to a set of linear ordinary differential equations by the Laplace transform method, which are solved with matrix Green's functions, yielding a general matrix solution of the neutron flux and the precursor concentration in the Laplace transform space. The detailed pole structure of the matrix solution in the Laplace transform space is investigated. The temporally and spatially dependent solutions are determined from the inverse Laplace transform using the Cauchy residue theorem, a knowledge of the detailed pole structure, and matrix operators. Solutions are evaluated for one and two groups of prompt neutrons and six groups of delayed neutron precursors.

- Authors:

- Publication Date:

- Research Org.:
- Texas A and M Univ., College Station (USA)

- OSTI Identifier:
- 5389622

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: Thesis (Ph. D.)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; REACTOR KINETICS EQUATIONS; ANALYTICAL SOLUTION; LAPLACE TRANSFORMATION; MATRICES; MULTIGROUP THEORY; NEUTRON FLUX; SLABS; SPHERICAL CONFIGURATION; CONFIGURATION; EQUATIONS; INTEGRAL TRANSFORMATIONS; NEUTRON TRANSPORT THEORY; RADIATION FLUX; TRANSFORMATIONS; TRANSPORT THEORY; 220100* - Nuclear Reactor Technology- Theory & Calculation

### Citation Formats

```
Rottler, J.S.
```*Analytic solutions of the multigroup space-time reactor kinetics equations in multiregion slab and spherical geometry*. United States: N. p., 1984.
Web.

```
Rottler, J.S.
```*Analytic solutions of the multigroup space-time reactor kinetics equations in multiregion slab and spherical geometry*. United States.

```
Rottler, J.S. Sun .
"Analytic solutions of the multigroup space-time reactor kinetics equations in multiregion slab and spherical geometry". United States.
```

```
@article{osti_5389622,
```

title = {Analytic solutions of the multigroup space-time reactor kinetics equations in multiregion slab and spherical geometry},

author = {Rottler, J.S.},

abstractNote = {Analytic solutions of the multigroup space-time reactor kinetics equations are developed for a bare slab and spherical reactor, and a reflected slap and spherical reactor for the zero flux, the zero current, and the extrapolated endpoint boundary conditions. The material properties of the reactors are assumed constant in space and time, but solutions involving spatially dependent source terms and initial conditions are investigated. The development of analytic and numerical solutions to the reactor kinetics equations is reviewed. The system of partial differential equations is reduced to a set of linear ordinary differential equations by the Laplace transform method, which are solved with matrix Green's functions, yielding a general matrix solution of the neutron flux and the precursor concentration in the Laplace transform space. The detailed pole structure of the matrix solution in the Laplace transform space is investigated. The temporally and spatially dependent solutions are determined from the inverse Laplace transform using the Cauchy residue theorem, a knowledge of the detailed pole structure, and matrix operators. Solutions are evaluated for one and two groups of prompt neutrons and six groups of delayed neutron precursors.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1984},

month = {1}

}