Estimating local plasma sheet PV5/3 from single-spacecraft measurements

The theory of plasma transport in Earth's plasma sheet depends critically on the entropy parameter PV5/3, where P is particle pressure and V is the volume of a closed flux tube containing one unit of magnetic flux. Theory suggests that earthward moving flow bursts that inject plasma into the inner magnetosphere consist of flux tubes that have PV5/3 values that are lower than those of neighboring slow-moving flux tubes. However, there is no way to measure flux tube volume from one spacecraft or a small number of spacecraft. We propose a formula for estimating local PV5/3 from a single spacecraft in the plasma sheet based on a simple two-dimensional analytic model of plasma in force equilibrium, with some parameters set from local measurements at a spacecraft and other parameters set to fit a series of equilibrated Tsyganenko models. To gain an idea of the expected error, the resulting formula is then tested against various relaxed Tsyganenko models, an equilibrium magnetic field/plasma model with a depleted channel and also a thin-filament MHD calculation. The formula is used to estimate the entropy parameter of flux tubes injected in two substorms, using spacecraft measurements near X = -10 R-E in the central plasma sheet.