The electron density dependence of polar mesospheric summer echoes

Many of the expressions for the reflectivity of polar mesospheric summer echoes (PMSE) predict that the echo strength is controlled by the electron density. We present several observations made using the Poker Flat Incoherent Scatter Radar which are difficult to explain based on those expressions, including observations at night with no detectable incoherent scatter below 90 km and during aurora where the reflectivity shows no response to abrupt changes in ionization. We derive a new expression for the reflectivity and are still able to explain all of these observations as scatter from free electrons. When the electron density is much smaller than the ice density the reflectivity is a strong function of electron density. In the opposite limit the reflectivity is solely controlled by the ice density because only a fraction of the electron density variance generated at the largest scales can get convected to sufficiently small scales.