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Cell["\<\
Nuclear Reactor Physics
J.A. McNeil
April 2008\
\>", "Text",
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The Fuchs model attempts to describe the response of a nuclear reactor to a \
supercritical reactivity intertion.  We assume the time scale of the pulse \
event is short compared to the delayed neutron precursor lifetimes; so this \
term is neglected.  The time dependent one-group flux equation becomes:\
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To model the pulse, we assume the transient rod is withdrawn instantaneously \
giving a large positive reactivity, \[Rho]0 > \[Beta].   We next assume that \
the time behavior of the reactivity is due to the rise in temperature in the \
fuel and is linear in the deviation of the temperature from some reference \
value, T0.\
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where \[Alpha] is the temperature coefficient of reactivity.  The temperature \
rise is due to the energy released by fission.  The process is much faster \
than the thermal transport time; so we treat the fuel rod as adiabatic.  \
Therefore, if C is the heat capacity of the fuel rod and \[Gamma] is the \
energy released per fission, we have\
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Putting this altogether gives the Fuchs equation (Hansen form):\
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Take the derivative, y'[t],  solve for \[Phi][t], and plug it into the Fuchs \
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where \[Kappa]^2 is the integration constant which we solve using the initial \
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