One way to define reactor power that is commonly covered in the undergraduate nuclear

engineering curriculum is:

$P=P_0{e}^{\frac{t}{T}}$

where $P$ is reactor power, $P0$ is the initial reactor power, $t$ is time, and $T$ is reactor period. The

reactor period, $T,$ is defined as that length of time required to change reactor power $($or neutron

density$)$ by a factor of $e.$

An alternative representation of reactor power is given by

$P=P_0{10}^{\frac{?}{\text{b}\text{a}\text{r}}(SUR)t}$

Where $\frac{?}{\text{b}\text{a}\text{r}}(SUR)$ is the average startup rate $($in decades per minute, or DPM$)$ over the time $t.$ The

second equation is somewhat more intuitive as one would imagine that a negative startup rate

means that reactor power will go down over time $($e$.$g$.$ a shutdown$)$ and a positive startup rate

will coincide with rising reactor power $($e$.$g$.$ a startup$).$ Let's explore these relationships in more

detail.

a$.$ What sort of SUR protection do you think you would want on a reactor $-$ do you think you would

want to protect against a large positive, large negative, small positive, or small negative startup

rate? $[5$ pts$]$

b$.$ What sort of period protection do you think you would want on a reactor $-$ large positive, large

negative, small positive, small negative? $[5$ pts$]$

c$.$ Write an expression that relates SUR to period T$.[10$ pts$]$

d$.$ When we shut down the reactor, reactor neutron level is maintained by the decay of delayed

neutron sources. The shorter lived fission products will decay, leaving longer$-$ lived isotopes

that will control the period$/$SUR observed. An operator is taught to look for a certain

period$/$SUR during a shutdown to validate appropriate behavior and this value is driven by the

decay of $Br-87,$ which has a half$-$life $t_{\frac{1}{2}}$ of $56s.$ Thus, $P{P}_0{e}^{-t}$ with $$ the effective decay

constant of $Br-87.$

i$.$ Assuming that $ln20\mathrm{.}7,$ calculate the approximate reactor period $T$ corresponding to this

decay $($note that $Br-87$ undergoes exponential decay$).($Hint: $=ln\frac{2}{t_{\frac{1}{2}}})[5$ pts$]$

ii$.$ Assuming $log10(e)=0\mathrm{.}4$ and $ln(10)=2\mathrm{.}3,$ show that the SUR ~~$-0\mathrm{.}3$ DPM for a

shutdown. $($hint: use the result from di$)[5$ pts$]$