# Variation of the plasma-sheet polytropic index along the midnight meridian in a finite-width magnetotail

## Abstract

The polytropic index is obtained as a function of distance along the midnight meridian in the terrestrial magnetotail. As our purpose is to establish the effects of the finite width of the magnetotail, we use a simple theoretical model of plasma sheet convection, i.e., two-dimensional field structure and adiabatic inward convection of a uniform distant tail source. Particle orbits are treated independently for portions of the phase space distribution on shells of constant energy. On the midnight meridian, the moments of the distribution are parameterized by tau, the ratio of half the cross-tail potential energy to the characteristic Maxwellian energy of a distant down-tail plasma source. We infer from the model the plasma pressure, P, and the number density, n, along the midnight meridian as a function of tau. P and n define locally an effective polytropic index. Gamma ranges between 5/3 and 1, depending on the value of tau and on geocentric distance. The qualitative differences between the recent empirical determinations of the polytropic index by Baumjohann and Paschmann and Huang et al. may be accounted for in part by this simple model.

## Department

Physics

## Publication Date

8-15-1990

## Document Type

Report

## Recommended Citation

Spence, Harlan E. and Kivelson, M. G., "Variation of the plasma-sheet polytropic index along the midnight meridian in a finite-width magnetotail" (1990). *Physics & Astronomy*. 284.

https://scholars.unh.edu/physics_facpub/284