  Zirconium alloys are widely used as the fuel cladding material in pressurised
water reactors, accumulating a significant population of defects and
dislocations from exposure to neutrons. We present and interpret synchrotron
microbeam X-ray diffraction measurements of proton-irradiated Zircaloy-4, where
we identify a transient peak and the subsequent saturation of dislocation
density as a function of exposure. This is explained by direct atomistic
simulations showing that the observed variation of dislocation density as a
function of dose is a natural result of the evolution of the dense defect and
dislocation microstructure driven by the concurrent generation of defects and
their subsequent stress-driven relaxation. In the dynamic equilibrium state of
the material developing in the high dose limit, the defect content distribution
of the population of dislocation loops, coexisting with the dislocation
network, follows a power law with exponent $\alpha \approx 2.2$. This
corresponds to the power law exponent of $\beta \approx 3.4$ for the
distribution of loops as a function of their diameter that compares favourably
with the experimentally measured values of $\beta$ in the range $ 3 \leq \beta
\leq 4$.
