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NUGN580: Ends report 3 and creates report 4
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| %% This BibTeX bibliography file was created using BibDesk. | ||
| %% http://bibdesk.sourceforge.net/ | ||
| %% Saved with string encoding Unicode (UTF-8) | ||
| @misc{reactor01, | ||
| title = {{USGS} Reactor Lab: Control rod calibration}, | ||
| author = {\vspace{0mm}T. Debey}, | ||
| howpublished = {Handouts}, | ||
| note = {Accessed: 2016-09-28} | ||
| } |
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NUGN580/Report4_Control-Rod-Calibration/chapters/appendices/app0A.tex
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| % | ||
| % file: localoperator.tex | ||
| % author: Victor Brena | ||
| % description: Briefly describes properties of the local operator. | ||
| % | ||
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| \chapter{Delayed neutrons} | ||
| \label{app:app01} | ||
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| \initial{T}his appendix presents the importance of the delayed neutrons in a nuclear reactor. It presents, without going into detailed mathematics, the impact of their non-existence of a nuclear chain reaction. | ||
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| \section{Neutron lifetime} | ||
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| First, let's talk about the neutron lifetime. In a PWR reactor, it is $10^{-5}$ seconds ($10^{-7}$ seconds in a BWR). This means that after this time on average, the neutron will have disappeared (absorbed, absorbed to induce fission, or leaked out of the reactor). | ||
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| \section{Multiplication factor} | ||
| The multiplication factor k leads to the critical, subcritical and supercritical states. | ||
| $k < 1$ : Subcritical, the chain reaction dies | ||
| $k = 1$ : Critical, the chain reaction is nice, the power is constant | ||
| $k > 1$ : Supercritical, the neutron population increases with each generation, the power increases. No good. | ||
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| \section{A world without delayed neutrons} | ||
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| If we do not consider the delayed neutrons into the kinetics equation, and a multiplication factor equals to 1.001 (quite close to 1, we all agree) then we have the following evolution of the neutron population with time: | ||
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| \begin{equation}\label{eq6} | ||
| n(t) = N*e^{k-1}*e^{\frac{t}{X}} | ||
| \end{equation} | ||
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| Where X is the mean lifetime of the neutrons inside the reactor. So, in a PWR for example, and considering k = 1.001 (difficult to get closer to criticality in real operations): | ||
| \begin{equation}\label{eq7} | ||
| n(t) = N*e^{k-1}*e^{\frac{t}{10^{-5}}} | ||
| \end{equation} | ||
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| This gives us : | ||
| \begin{equation}\label{eq8} | ||
| n(t) = N*e^{100t} | ||
| \end{equation} | ||
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| This means that the neutron population is *not at all* under control. After 1 second, we have the original population (N) multiplied by $e^{100}$ (gigantic number). So the power in the reactor would increase very quickly, even though the multiplication factor is as close as possible to 1. | ||
| So, what are we missing ? The \emph{delayed neutrons}. | ||
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| \section{The real world, with delayed neutrons} | ||
| Where do they come from ? To answer that, we must be sure to understand where the neutrons come from in a reactor. Several possibilities : | ||
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| \begin{enumerate} | ||
| \item Fission induced neutrons (mainly uranium-235 gets hits by a low energy neutron, and produce on average around 2 neutrons) | ||
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| \item External sources | ||
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| \item Different decay reactions (instead of undergoing fission, an atom, uranium-235 for example, would absorb one neutron and release two neutrons, and some other reactions like that) | ||
| \end{enumerate} | ||
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| So, what are we missing ? Well, the fission of an atom creates two smaller atoms. Those are the ones (called precursors) that will release neutrons later, by decaying. Thus \emph{delayed neutrons}. Indeed, the mean lifetime of a precursor neutron is 13 seconds roughly (compared to the $10^{-5}$ seconds in a PWR). | ||
| Delayed neutrons represents around 700 pcm (0.7\%) of the whole neutrons "produced" during a generation. This very small difference is what actually allow us to control the chain reaction in a nuclear reactor. | ||
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