In spherical coordinates, the ions produced in a volume element dV₁ (solid red sector) travel outwards, and the volume containing them expands with r² to reach a magnitude dV at r (dashed red sector). The neutral number density n decreases with r⁻² (Haser 1957) so the ion production rate (per cubic meter) decreases but the number of ions produced in each element of constant solid angle is conserved.