  Nuclear reactor cores achieve sustained fission chain reactions through the
so-called 'critical state' -a subtle equilibrium between their material
properties and their geometries. Observed at macroscopic scales during
operations, the resulting stationary neutron field is tainted by a noise term,
that hinders various fluctuations occurring at smaller scales. These
fluctuations are either of a stochastic nature (whenever the core is operated
at low power) or related to various perturbations and vibrations within the
core, even operated in its power regime. For reasons that are only partially
understood using linear noise theory, incidental events have been reported,
characterized by an increase of the power noise. Such events of power noise
growth, sometimes up to seemingly unbounded levels, have already led in the
past to volontary scramming of reactors. In this paper, we will extend the
findings of \cite{percolation_pre} (where a statistical field theory of
critical processes was employed to model stochastic neutron noise) by
incorporating the effects of power noise. We will show that the evolution of
the neutron field in a reactor is intimately connected to the dynamic of
surface growths given by the Kardar-Parisi-Zhang equation. Recent numerical
results emerging from renormalization group approaches will be used to
calculate a threshold in the amplitude of the reactor noise above which the
core could enter a new criticality state, and to estimate the critical
exponents characterizing this phase transition to rough neutron fields. The
phenomenology of this roughening transition will be correlated and compared to
data of misunderstood reactor noise levels and reactor instabilities, and will
be shown to provide both qualitative and quantitative insights into this
long-standing issue of reactor physics.
