Page 26 - Dynamics and Control of Nuclear Reactors

CHAPTER

The point reactor kinetics

equations 3

3.1 Neutronics
The neutron population in a nuclear reactor is a function of time, position, direction
of motion, and energy. Neutrons appear at some position in the reactor as a result of
a fission reaction between uranium or plutonium and a neutron from a previous
generation. The neutron emerges from the fission reaction with a large kinetic
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energy (an energy of around 3MeV or a speed of around 3 10 cm/s). These
neutrons undergo elastic and inelastic scattering events with materials in the
reactor core (fuel, structure, cladding, coolant, moderator, etc.) and, as a result,
lose energy.
Most current-generation reactors include a moderator, a material with a high
probability of slowing neurons by scattering collisions while absorbing few
neutrons. Typical moderators are water, heavy water, and graphite. Reactors with
moderators are called thermal neutron reactors. In these reactors, most of the
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neutrons slow to energies less than 0.1eV (a speed of around 4 10 cm/s). Fast
reactors have no moderator and rely on fissions with fast neutrons. In a thermal
reactor, thetimebetween aneutron’sbirth and eventual absorption by a target
nucleus is typically 10 to 30 microseconds, andevenfasterin a reactorwithafast
neutron spectrum.
The most complete neutronic description of a reactor is the Boltzmann transport
equation. This equation gives the neutron population as a function of seven indepen-
dent variables (time, three position coordinates, energy and two direction vectors).
The neutron diffusion model is one-step simpler. In diffusion theory, the direction
dependence is removed, leaving a model with five independent variables. Further
simplification occurs with eliminating the spatial dependence (treating the reactor
as a “point”) and reducing the energy treatment to a single energy group. These
simplifications may seem extreme, but the simplified neutronics model has proved
suitable for a wide range of reactor simulations.
Appendix C provides a brief discussion of basic reactor physics for those who
need familiarization or review.

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Dynamics and Control of Nuclear Reactors. https://doi.org/10.1016/B978-0-12-815261-4.00003-2
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