Can Charged Dust Explain Polar Mesospheric Summer Echoes? Theory and Experiments

Simultaneous and collocated measurements of Polar Mesospheric Summer Echoes (PMSE) and electron density in the D- and E-regions of the ionosphere with the EISCAT radars have allowed to make accurate absolute calibrations of the PMSE scattering cross sections at 224 MHz (Bragg wavelength of 67 cm) and at 930 MHz (Bragg wavelength of 16 cm). These measurements give volume scattering cross sections of 5250×10-18\ and\ 3.5×10-18 m-1 for the VHF and UHF radars respectively. These unprecedented measurements allow to make a crucial test to the theory of PMSE that asserts that electron turbulence induced by neutral air turbulence can be maintained at the necessary scale lengths by an extension of the Kolmogorov spectrum due to the presence of charged nanometer size ice dust particles which cause an enhancement of the Schmidt number. Using a model of of the Kolmogorov spectrum proposed by Hill that incorporates the Schmidt number, it has been possible to fit to the model the Schmidt number and the dissipation rate of electron density variance, given the two measurements of the volume scattering cross sections. Assuming the most favorable theoretical initial condition, namely that the slow diffusion mode completely dominates the dissipation of electron density variance, Schmidt numbers of a few thousands are possible with low charge numbers; or equivalently, dust radii up to a few tens of nanometers can sustain the required Schmidt numbers. However, it is argued that the assumed most favorable condition is not prevalent in nature.