Steady dust-tail continuity equation ($n(s)\dot{s}=\dot{N}P(t(s))$)

For a single-stream dust tail with injection rate $\dot{N}$, monotone angular distance $s(t)$, and survival probability $P(t)$, the number per unit angle is $n(s)=\dot{N}P(t(s))/\dot{s}$. A vanishing angular drift creates an idealized density enhancement; velocity dispersion rounds it.

A zero of the angular drift in a cold single-grain-size dust tail produces a formally divergent number density per unit angle. The divergence is integrable when the exact local angle-to-age map is retained. A spread of launch velocities or radiation-pressure coefficients removes the singularity.