A study of coherent scatter from mid-latitude sporadic-E layers

Common volume observations with the Cornell University Portable Radar Interferometer (CUPRI) coherent scatter radar and the Arecibo Observatory incoherent scatter radar (AO-ISR), as well as sounding rocket data obtained during the NASA El Coquí campaigns of 1992 and 1997, are used to study the causes of coherent radar backscatter at midlatitudes. The common volume CUPRI/AO-ISR data reveal that coherent scatter echoes are obtained from sporadic E (E_s) layers that exhibit little or no gravity wave altitude modulation and possess high densities and sharp gradients. The echoes are independent of geomagnetic activity but are associated with larger than typical F-region south-perpendicular electric fields coincident with greater than unity height integrated Pedersen conductivity ratios, $SPF/SPE$. The echoes appear to come from the linearly unstable side of the E_s layers even though the usual local linear theory is invalid at midlatitudes. In-situ electric field measurements from the Sodium Atom Layer (SAL) sounding rocket reveal relatively short wavelength perturbations (wavelengths of 10s of meters) coming from the linearly unstable side of a E_s layer.; Non-local shorting effects along magnetic field lines play a crucial role at midlatitudes, and we have developed a theory that takes this into account. The unstable eigen modes are a sum of plane waves with k vectors varying vertically about pure perpendicular propagation by a few degrees (allowing for the spatial localization of the modes on the top or bottom of the layer). The k vectors are also approximately aligned with the $E\times B$ drift. While both density and potential modes peak in amplitude on the unstable side of the layer, the density mode peaks closer to the maximum of the layer than does the potential mode. The separation and shape of the modes is determined by the profile of the vertical scale length, $Lz=Ne/ddzNe$; convergent growing solutions are found when the scale length profile exhibits a deep local minimum (steep gradient). We used a narrow Gaussian layer superimposed on a constant background density. Perhaps surprisingly, the constant background is essential for the numerical calculations. It can be small but not zero.