Control Rod Worth Integral & Differential Calculator
Compute differential rod worth curve (dρ/dz), integral S-curve worth, axial flux peaking, and reactor Shutdown Margin (SDM).
Control Rod Bank & Core Geometry
Rod Worth & Shutdown Margin (SDM)
Recommended Tools & Equipment
Tested hardware and components for high reliability
Control Rod Reactivity Physics & S-Curves
Control rod reactivity worth is governed by neutron importance theory. In an unrodded core, the fundamental axial flux distribution is cosine-shaped, peaking at core midplane ($z = H/2$). Since neutron capture effectiveness is proportional to the square of the local flux ($\Phi^2$), rod differential worth ($d\rho / dz$) follows a $\sin^2(\pi z / H)$ curve.
Stuck Rod Criterion & Shutdown Margin
Nuclear Technical Specifications mandate that the reactor can be brought to subcriticality from any operating condition with the highest-worth control rod completely stuck in the fully withdrawn position. The Shutdown Margin ($\text{SDM}$) is the net amount of negative reactivity by which the core is subcritical with that single failure assumed.