Abstract. Two years of Geotail data in the (-30 < x < -8, lyl < 15) R E region first were sorted into (x, y, [3) boxes. Direct measurements of the average electron and ion current densities, symmetry assumptions, and the momentum equation were used to get three different estimates of the electric current in each box. The momentum equation method gave the most consistent results, while the other two methods provided complementary information about particle drifts. The average common drift of electrons and ions was found to be comparable to the average differential drift of ions with respect to electrons. These two components of the ion drift velocity tended to cancel on the dawnside, resulting in currents that were primarily carried by electrons moving at the common drift speed. The two ion drifts added on the duskside where ions carried most of the cross-tail current.The particle and magnetic field measurements were used to estimate the z thickness of each [3 box.A concentration of the long-term-averaged cross-tail current was seen near the neutral sheet. The region of nonadiabatic orbital motion had an average characteristic length scale of-•0.4 RE.The principal plasma sheet extended to -2.5 R E from the neutral sheet at midnight and to -5 R E in the .flanks. The final result is a method to create models in (x, y, z) coordinates of the long-term-averaged values of any of the measured fluid parameters or fields. The isotropic portion of the pressure tensor was used as an example of one parameter that can be modeled. These pressure plots showed that the x component of the long-term-averaged magnetic field line tension force is important everywhere, that the z component is small everywhere, and that the y component is significant in the flanks. IntroductionThis paper develops methods needed to make three-dimensional (3-D) measurement-based long-term-averaged models of particles and fields in the plasma sheet. The goal is to use these 3-D models to study the average current sheet structure and the transport of quantities such as energy, momentum, and magnetic flux. The hardest step is estimating how far a satellite is from the neutral sheet, which is defined as the sheet on which B x = O. Trajectory information in GSM or GSE coordinates gives an adequate measure of the satellite x and y locations because typical scale lengths in these directions are of the order of 10 R E . In contrast, the characteristic z-scale length is near 1 R E . In addition,

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An example of Galactic cosmic-ray modulation in a fully three-dimensional heliosphere is presented here. We use a stochastic particle method to solve for modulation without requiring symmetric boundaries or fields. We include all typical modulation terms, including full three-dimensional drift. We have applied this to an MHD heliosphere appropriate for solar minimum conditions. This field includes nonradial solar wind velocity components, as well as a built-in nonspherical termination shock. Parameters that are of interest in modulation can be analyzed in detail, particularly the momentum change of cosmic rays during their transport through the heliosphere. We show radial profiles of modulation at different energies, latitude, and longitude, as well as the more traditional modulated spectra at various locations. Finally, we are able to show in detail where particles at a particular energy and location gain and lose energy. We are able to conclude that the radial profiles of modulation are strongly dependent on the latitudinal angle with respect to the stagnation point. We see that modulation of GCRs near the stagnation point takes place mostly upstream of the shock but that modulation continues far outside the shock as the stochastic particles will random walk across the shock several times before entering our observation region. The modulation profiles remain similar with differing longitude, although the exact shape of the radial profile and spectra are strongly dependent on the termination shock location. Cosmic-ray intensity at high energies can be higher than the ISM intensity, while at low energies cosmic rays still experience solar modulation. The termination shock and heliosheath regions were important to modulation in the outer heliosphere. Finally, the sign of the latitudinal gradient is not a simple function of the qA direction, in general.

Abstract. Thick and thin models of the middle magnetotail were developed using a consistent orbit tracing technique. It was found that currents carried near the equator by groups of ions with anisotropic distribution functions are not well approximated by the guiding center expressions. The guiding center equations fail primarily because the calculated pressure tensor is not magnetic field aligned. The pressure tensor becomes field aligned as one moves away from the equator, but here there is a small region in which the guiding center equations remain inadequate because the two perpendicular components of the pressure tensor are unequal. The significance of nonguiding center motion to substorm processes then was examined. One mechanism that may disrupt a thin cross-tail current sheet involves field changes that cause ions to begin following chaotic orbits. The lowest-altitude chaotic region, characterized by an adiabaticity parameter • = 0.8, is especially important. The average cross-tail particle drift is slow, and we were unable to generate a thin current sheet using such ions. Therefore any process that tends to create a thin current sheet in a region with • approaching 0.8 may cause the cross-tail current to get so low that it becomes insufficient to support the lobes. A different limit may be important in resonant orbit regions of a thin current sheet because particles reach a maximum cross-tail drift velocity. If the number of ions per unit length decreases as the tail is stretched, this part of the plasma sheet also may become unable to carry the cross-tail current needed to support the lobes. Thin sheets are needed for both resonant and chaotic orbit mechanisms because the distribution function must be highly structured. A description of current continuity is included to show how field aligned currents can evolve during the transition from a two-dimensional (2-D) to a 3-D configuration.

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