MODELS OF FLUX ROPES EMBEDDED IN A HARRIS NEUTRAL SHEET - FORCE-FREE SOLUTIONS IN LOW AND HIGH-BETA PLASMAS

We present two models of an array of flux ropes embedded in a Harris neutral sheet. The first solution satisfies the two-dimensional Vlasov-Maxwell equilibrium and is electromagnetically force free. Such a solution is pertinent to a plasma in which beta, the ratio of the thermal pressure to the magnetic pressure, is small. Several features of the model are in excellent agreement with observations of flux ropes in the magnetotail of the Earth. The maximum magnitude of the core field can be larger than the magnitude of the lobe field, B-L; the scale length of the individual flux ropes equals the scale length of the current reversal region in the Harris neutral sheet; and the maximum value of the north-south component is less than B-L Magnetotail flux ropes are thought to be isolated structures. Our solution, although periodic in the down-tail direction, is interesting as it Provides a consistent description not only of the flux ropes but also of the fields in which they are embedded, a feature that is lacking in other models. We use data from the December 1990 Galileo flyby of Earth and find that the unit cells of the periodic solution are unsatisfactory for the beta approximate to 1 conditions of the tail plasma sheet. We then develop a closely related solution valid in the high beta regime that incorporates particle pressure self-consistently and find that the unit cells of this solution provide an excellent fit to the Galileo flux rope observations.