Parallel Electric Fields and Double Layers in Downward Auroral-Current Regions from Theory and Satellite Data

A method for determining the parallel electric field (E_ƒìƒì) and the presence of double layers for downward auroral-current regions that includes wave-particle interactions is given. We derive the multi-constituent fluid equations for a weakly inhomogeneous, magnetized plasma where the Vlasov-Maxwell hierarchy is used to treat the particle dynamics and the Fokker-Planck method is used to calculate the momentum (anomalous resistivity) and energy (anomalous heating) transfer rates between the waves (turbulence) and the particles. Two major assumptions are necessary: (1) a renormalized kinetic theory for the turbulence either exists or can be developed; and (2) both the length and frequency scales between the single-particle distributions and the fluctuations are separable. For downward currents, we may approximate the momentum and energy transfer rates by using FAST satellite data for the renormalized spectral density of the fluctuating electric field, the conservation laws, and a scaling assumption for the renormalized dielectric screening function. Using FAST data for the particle velocity moments as a boundary condition, we integrate the fluid equations both upward and downward from the satellite altitude in order to determine the potential and the particle velocity moments as functions of distance along the geomagnetic field line. We analyzed a winter FAST satellite pass near local midnight at ∼4130 km which shows a downward current region having a latitudinal width of about 45 km. At each subinterval ( ∼1.5 km) along the pass, we found a double layer (DL) below the satellite altitude; a transition region (TR) just above the DL where strong electron thermalization and intense ion heating occur; and a long range potential region (LRPR) extending from the top of the TR to several earth radii and beyond. In the LRPR, ion conics are produced and further electron thermalization occurs. The average altitude of the DL/TR is in good agreement with experimental observations. Our analysis suggests that the formation of the DL, the particle dynamics, and the turbulence are intermittent in space and time. We also calculated the anomalous resistivity in the LRPR and showed that it has a very small effect on E_ƒìƒì (< few %) and that E_ƒìƒì is determined primarily by the velocity-space anisotropy and pressure gradient terms in the momentum balance equation.