Entropy and plasma sheet transport

Abstract

This paper presents a focused review of the role of entropy in plasma sheet transport and also describes new calculations of the implications of plasma sheet entropy conservation for the case where the plasma pressure is not isotropic. For the isotropic case, the entropy varies in proportion to log[PV5/3], where P is plasma pressure and V is the volume of a tube containing one unit of magnetic flux. Theory indicates that entropy should be conserved in the ideal MHD approximation, and a generalized form of entropy conservation also holds when transport by gradient/curvature drift is included. These considerations lead to the conclusion that under the assumption of strong, elastic pitch angle scattering, PV5/3 should be approximately conserved over large regions of the plasma sheet, though gradient/curvature drift causes major violations in the innermost region. Statistical magnetic field and plasma models lead to the conclusion that PV5/3 increases significantly with distance downtail (pressure balance inconsistency). We investigate the possibility that the inconsistency could be removed or reduced by eliminating the assumption of strong, elastic pitch angle scattering but find that the inconsistency becomes worse if the first two adiabatic invariants are conserved as the particles drift. We consider two previously suggested mechanisms, bubbles and gradient/curvature drift, and conclude that the combination of the two is likely adequate for resolving the pressure balance inconsistency. Quantitatively accurate estimation of the efficiency of these mechanisms depends on finding a method of estimating PV5/3 (or equivalent) from spacecraft measurements. Two present approaches to that problem are discussed.