\section*{Problem 4}

The power trajectory would be exponentially positive as the reactor would become
prompt critical. One would analyze the transient by using a robot to examine the
reactor soup after the steam bomb goes off in the containment. 

But being serious, one may examine the power transient by evaluating \(\rho\)
over time using the partial addition formula we used in the last problem.
Because the reactor is prompt critical, we can essentially ignore the delayed
neutrons. The point kinetic equations can also be used, but honestly a decent
approximation will be a first order exponential growth with time constant
derived from the prompt neutron lifetime.

For a high enrichment fuel, the growth of the curve will be impeded by basically
nothing. Fuel and moderator temperature effects will be minimal. For a low
enrichment fuel, moderator temperature and fuel temperature effects will slow
the exponential growth as temperature increases, but depending on reactor
design, will not prevent catastrophic failure.
