In a solid-fuel reactor, delayed-neutron precursor nuclei sit still and decay exactly where they were born. In a molten salt reactor the fuel is the coolant — it is pumped continuously through the core and out to an external heat exchanger loop, carrying precursor nuclei with it. Some decay outside the core, where their delayed neutrons cannot contribute to the chain reaction. This is a real, measured effect from the Oak Ridge MSRE program.
For one precursor group with decay constant λ, flowing at speed v around a loop, the steady-state concentration C(s) along path position s obeys advection–decay with an in-core source S:
v · dC/ds = S(s) − λ·C(s) (S > 0 only inside the core)
This simulation solves that equation numerically (finite-volume, upwind advection) around the closed racetrack loop shown, reaching a periodic steady state each time you change a control. The colored beads show the resulting concentration profile — bright where precursors are dense (fresh, near the core), fading to blue as they decay in transit through the external loop.
The readout β_eff/β is the fraction of that group's precursors that actually decay inside the core, versus the stationary-fuel ideal (β_eff/β = 1). Faster flow and a longer external loop both sweep more precursors out before they decay, shrinking β_eff — which is why circulating-fuel reactors have measurably different (faster) kinetic response than solid-fuel ones, and why MSR designers track this ratio per precursor group.