We present preliminary results of a magnetospheric substorm that occurred on applying the Rice convection model to the early September 19, 1976 [Harel et al., 1981a,b; Spiro main phase of the magnetic storm of July 29, et al., 1981; Karty et al., 1982; Chen et al., 1977. The computer model self-consistently com-1982]. The relationship of the Rice convection putes electric fields and currents, as well as model to other related theoretical formulations, plasma distributions and velocities, in the and our model's basis in earlier research, were inner-magnetosphere/ionosphere system. In the described in Harel et al. [1981a]. For the sake 1present address is Mail Code 144-218, Jet Pro-B. Formulation

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We present a two‐dimensional, force‐balanced magnetic field model in which flux tubes have constant pVγ throughout an extended region of the nightside plasma sheet, between approximately 36 RE geocentric distance and the region of the inner edge of the plasma sheet. We have thus demonstrated the theoretical existence of a steady state magnetic field configuration that is force‐balanced and also consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD (isotropic pressure, perfect conductivity). The numerical solution was constructed for a two‐dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The primary characteristics of our steady state convection solution are (1) a pressure maximum just tailward of the inner edge of the plasma sheet and (2) a deep, broad minimum in equatorial magnetic field strength Bze, also just tailward of the inner edge. Our results are consistent with Erickson's (1985) convection time sequences, which exhibited analogous pressure peaks and Bze minima. Observations do not indicate the existence of a Bze minimum, on the average. We suggest that the configurations with such deep minima in Bze may be tearing‐mode unstable, thus leading to substorm onset in the inner plasma sheet.

A tilt-dependent magnetic field model of the Earth's magnetosphere with variable magnetopause standoff distance is presented. Flexible analytic representations for the ring and cross-tail currents, each composed of elements derived from the Tsyganenko and Usmanov (1982) model, are combined with the fully shielded vacuum dipole configurations of Voigt (1981). The ring current, consisting of axially symmetric eastward and westward currents fixed about the dipole axis, resembles that inferred from magnetic field observations yet permits easy control of inner magnetospheric inflation. The cross-tail current contains a series of linked current sheet segments which allow for the tilt-dependent flexing of the current sheet in the x-z plane and arbitrary variations in current sheet position and intensity along the length of the magnetotail. Although the current sheet does not warp in the y-z plane, changes in the shape and position of the neutral sheet with dipole tilt are consistent with both MHD equilibrium theory and observations. In addition, there is good agreement with observed AB profiles and the average equatorial contours of magnetic field magnitude. While the dipole field is rigorously shielded within the defined magnetopause, the ring and cross-tail currents are not similarly confined, consequently, the moders region of validity is limited to the inner magnetosphere. The model depends on four independent external parameters, namely, (1) the dipole tilt angle, (2) the magnetopause standoff distance, (3) the midnight equatorward boundary of the diffuse aurora, and (4) the geomagnetic index Dst. In addition, we present a simple but limited method of simulating several substorm related magnetic field changes associated with the disruption of the near-Earth cross-tail current sheet and collapse of the midnight magnetotail field region. These include the classic dipolarization of the near-Earth field and the reduction of the far-tail equatorial field accompanying current sheet thinning. This feature further facilitates the generation of magnetic field configuration time sequences useful in plasma convection simulations of real magnetospheric events. IntroductionA wide variety of currents are required to support the magnetospheric magnetic field structure in the presence of flowing solar wind plasma and the interplanetary magnetic field. In addition to the magnetic field generated in the Earth's interior, the major contributors to this structure include magnetopause currents, the ring and cross-tail currents, and a variety of field-aligned currents. The intensities of these currents fluctuate constantly as they feed into each other to form the global circuit. For this reason, a model of magnetic fields and currents must represent a diverse array of magnetospheric configurations as well as the "average" configurations. It must rely on physical magnetospheric and solar wind parameters and reproduce appropriate configuration changes. These changes include the distortion of magnetic field and its mapping characteristics ...

The configuration of the tail All these semiempirical models are more or less plasma sheet in earth's magnetotail has been cal-in good agreement with quiet time magnetic field culated in connection with a three-dimensional measurements in the near-earth and tail regions; magnetospheric B field model. This model is they are very useful for practical purposes. based on the i-•ea that thermal plasma, tail Considering them from a theoretical point of currents, and magnetic field be in magnetohydro-view, though, they reveal a major disadvantage: static equilibrium during time periods of mag-their magnetic configurations are not in equinetically quiet conditions. The tail configura-librium with the magnetospheric currents and tion is generated by a separation method assuming the thermal plasma [Walker and Southwood, 1982; a cylindrical magnetotail boundary with constant Walker et al., 1983]. radius.The separation method restricts self-The second line of theoretical work is based consistency to planes perpendicular to the tail on the idea that the quiet magnetosphere reaches axis.The computed tail plasma sheet is flexible the state of magnetohydrostatic equilibrium. and reacts to changes of the earth's dipole tiltOwing to the immense complexity of the equiangle and changes of the solar wind pressure. librium problem, most models are restricted to Consequences for the plasma sheet configuration the far tail region, where the magnetic field with respect to the assumed tail magnetopause lines are stretched out and the inf]uence of the shape and the separation method are the fo]low-earth's dipole field can be ignored. Schindler ing: (1) the plasma sheet thickness increases [1972] and Bird and Beard [1972a, b] can be The next step, namely, the development of a Copyright 1984 by the American Geophysical Union. three-dimensional model for the whole magnetosphere, is the purpose of this paper. As in the Paper number 4A0037. Fuchs and Voigt [1979] approach, we impose a 0148-0227/84/004A-0037505.00 constraint on the pressure function in that we 2169

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The geomagnetic field is part of the shield prohibiting energetic particles of solar and cosmic origin directly hitting the Earth surface. During geomagnetic polarity transitions the geomagnetic field strength significantly decreases with energetic particles having a much better access to the atmosphere and surface. To study in more detail the flux of energetic particles into the paleomagnetosphere we use a potential field approach to model the paleomagnetosphere which generalizes the parametric model of Voigt (1981) by taking into account a non-zero quadrupole moment of the core field. We study in particular the quadrupolar situation as a geomagnetic polarity transition is also characterized by a significant increase of non-dipolar contributions. Our model is used as a tool for tracing particle trajectories in such paleomagnetospheres and to assess variations of high-energy particle fluxes into the atmosphere. As a first application of the particle tracing scheme we determine cutoff latitudes and impact areas for different paleomagnetospheric configurations. For configurations with equivalent magnetic field strength or magnetic energy the impact area is very similar.

We compare Voyager 2 magnetic field and plasma data with theoretical model calculations for the magnetosphere of Uranus in order to derive a global picture from the quite limited set of measurements. In two dimensions we use a tilt-dependent linear MHD equilibrium model for the entire magnetosphere to calculate the plasma parameter /• = 8r•P/B 2 and the resulting B field in the tail plasma sheet. The three-dimensional model satisfies the MHD equilibrium equations in an approximate fashion; it is used to calculate the large-scale magnetic field structure, the tilt-dependent shape and position of the Uranian magnetotail plasma sheet, and the influence of the interplanetary magnetic field (IMF). The main results of the model calculations are the following: (1) The actual solar wind pressure at Uranus was found to be about a factor of 5 higher than a calculated solar wind pressure derived from an adiabatically expanding quiet solar wind. This means that the Uranian magnetosphere must have experienced a major magnetic storm prior to the Voyager encounter. (2) The previous conjecture is supported by the fact that the asymptotic plasma beta parameter in the neutral sheet,/•o =/•(Ixl >> 1), relaxes from/•o = 37 to/•o -14 between the first and second neutral sheet crossings. (3) The excellent agreement between measured and modeled tail lobe magnetic field values suggests that during the time period of the Voyager encounter the Uranian tail plasma sheet, measured in units of planetary radii, was thicker and less stretched than the average Earth's tail plasma sheet. (4) Despite sizable temporal variations suggested by the data and the model, the Uranian magnetosphere seems to reach the state of quasi-static, i.e., slowly time-dependent, MHD equilibrium. (5) In relation to a given IMF orientation the magnetosphere changes periodically every 8.62 hours (the Uranian day is 17.24 hours) from an "open" to a "closed" configuration and back. Thus the convection process, driven by the direct influence of the IMF, is periodically interrupted by the planet's rotation, such that the plasma sheet might not experience its full stretching. Consequently, the Uranian magnetosphere might not experience convectively driven, Earth-type substorms. On the other hand, the possibility of substorms cannot be ruled out either. 1. 1986]. This scenario is sketched in Figure 1 from a fixed observer's point of view. Figure 1 also depicts the two extreme orientations of the dipole axis with respect to the solar wind direction. Magnetospheric rotation causes magnetotail flux tubes to twist. A small helical twist (5.5 ø __+ 3 ø) has been discovered by Voyager 2 [Behannon et al., this issue].The purpose of this study is to interpret these and related signatures in the light of the quasi-static MHD equilibrium theory. This theory enables us to construct large-scale mathematical models of the Uranian magnetosphere. In particular, models of this type help us answer the following question: can we understand the Uranian magnetosphere as a system that reaches a ...