N. A. Tsyganenko

A magnetospheric magnetic field model with a warped tail current sheet

Abstract An improved quantitative representation of the magnetic field in the geomagnetosphere is developed. The model takes into account the effect of warping the tail current sheet in two dimensions due to the geodipole tilt, as well as spatial variations of the current sheet thickness along the Sun-Earth and dawn-dusk directions. The corresponding analytic forms for the magnetic field components have been obtained using an indirect approach in a two-stage procedure. First of all, a simple axially symmetric infinitely thin current disc model with different rates of the current density decreasing in the radial direction are derived. The next step consists in a formal modification of the obtained expressions for the vector potential, which results in a transverse broadening of the initially thin current sheet and incorporates an account for the sheet warping. A truncation factor is also introduced, with the aim to simulate the finite extension of the current system in the dawn-dusk direction, as well as its day-night asymmetry. Based on the proposed representation and the IMP and HEOS spacecraft data pool, a series of magnetospheric models are generated, giving a quantitative description of the average magnetic field configuration for different disturbance levels. A comparison of the magnetic field distributions predicted by the model and those measured at geosynchronous orbit has been carried out.

Modeling the Earth's magnetospheric magnetic field confined within a realistic magnetopause

Empirical data-based models of the magnetospheric magnetic field have been widely used during recent years. However, the existing models (Tsyganenko, 1987, 1989a) have three serious deficiencies: (1) an unstable “de facto” magnetopause, (2) a crude parametrization by the Kp index, and (3) inaccuracies in the equatorial magnetotail Bz values. This paper describes a new approach to the problem; the essential new features are (1) a realistic shape and size of the magnetopause, based on fits to a large number of observed crossings (allowing a parametrization by the solar wind pressure), (2) fully controlled shielding of the magnetic field produced by all magnetospheric current systems, (3) new flexible representations for the tail and ring currents, and (4) a new “directional” criterion for fitting the model field to spacecraft data, providing improved accuracy for field line mapping. Results are presented from initial efforts to create models assembled from these modules and calibrated against spacecraft data sets.

Modeling the global magnetic field of the large‐scale Birkeland current systems

Quantitative models are developed for representing the global distribution of the average magnetic field produced by the region 1 and 2 Birkeland current systems. The problem is solved in four following steps: (1) constructing a realistic tilt-dependent model of the Birkeland current sheets, based on the formalism of Euler potentials, (2) numerically computing their field at a large number of points within the modeling region, (3) finding a best-fit analytical approximation for that field, and (4) adding a current-free shielding field which confines the Birkeland field within the model magnetopause. At low altitudes, the model field-aligned currents reach the ionosphere along eccentric ovals, which fit the observed region 1 and 2 zones of Iijima and Potemra, and they continue there as horizontal currents. At larger distances, the nightside region 1 currents map to the plasma sheet boundary layer and are then diverted toward the tail flanks, while currents in the dawn-dusk and dayside sectors connect directly to the higher-latitude magnetopause. The region 2 current closes azimuthally near the equator, forming a spread-out partial ring current system. The described approach allows a great flexibility in the geometry of the Birkeland currents, making it feasible to infer their properties from spacecraft data.

Global quantitative models of the geomagnetic field in the cislunar magnetosphere for different disturbance levels

Abstract A previously proposed model (Tsyganenko and Usmanov, 1982, Planet. Space Sci . 30 , 985) is further developed, using IMP -A, C, D, E, F, G, H, I, J and HEOS -1, -2 spacecraft measurements made during 1966–1980. The main improvement consists of a considerable extension of the modeling region by adding to the original data set a large number of magnetotail field measurements. Data points used in the present study cover a vast range of distances 4≲ R ≲70 R E and comprise an unprecedentedly large number of measurements (a total of 36682 vector averages, almost twice as many as in our earlier data set). The data have been divided into groups corresponding to a sequence of K p -index intervals, as well as different conditions in the solar wind. Mathematical representation of the magnetic field follows in its general features the approach developed in our earlier work, with some modifications. Two versions of the model are proposed, namely, (i) a “long” one with 26 parameters, valid up to distances ∼70 R E , and (ii) a “truncated” one with 20 parameters and an applicability limit of ∼30 R E .

Pitch-angle scattering of energetic protons in the magnetotail current sheet as the dominant source of their isotropic precipitation into the nightside ionosphere

Abstract Characteristics of the nightside isotropic precipitation of energetic protons during a period of 4 quiet days has been studied using data from the ESRO 1A satellite. The observed features of the equatorward precipitation boundary (its thickness, energy dependence, dynamics, dependence of its latitudinal position on the magnetic field at the geosynchronous orbit, etc.) were found to be in good agreement with calculations based on recent magnetospheric magnetic field models. We argue that the mechanism of non-adiabatic pitchangle scattering in the equatorial current sheet is a dominant source of isotropic precipitation of energetic protons observed in the nightside auroral zone. Observations of the isotropic precipitation boundary can be used for monitoring the changes in the magnetotail current intensity.

Determination of the magnetospheric current system parameters and development of experimental geomagnetic field models based on data from IMP and HEOS satellites

Abstract An elaborate analytical model representation of the magnetospheric magnetic field has been developed based on the merged IMP-HEOS experimental data set. As distinct from the approach of Mead and Fairfield (1975), our model incorporates separate mathematical description of the ring current, the magnetotail current sheet and the magnetopause contributions to the total magnetic field. Model formulae for the magnetic field components contain in total 28 input parameters (21 linear coefficients and 7 non-linear parameters) obtained by means of an iterative minimization procedure, which fits the model to the experimental data sets corresponding to different levels of geomagnetic activity, as well as to different conditions in the solar wind.

Magnetospheric configurations from a high-resolution data-based magnetic field model

[1] We present first results of the magnetospheric magnetic field modeling, based on large sets of spacecraft data and a high-resolution expansion for the field of equatorial currents. In this approach, the field is expanded into a sum of orthogonal basis functions of different scales, capable to reproduce arbitrary radial and azimuthal variations of the geomagnetic field, including its noon-midnight and dawn-dusk asymmetries. Combined with the existing method to model the global field of Birkeland currents, the new approach offers a natural way to consistently represent the field of both the tail and symmetrical/partial ring currents. The proposed technique is particularly effective in the modeling of the inner magnetosphere, a stumbling block for the first-principle approaches. The new model has been fitted to various subsets of data from Geotail, Polar, Cluster, IMP-8, and GOES-8, GOES-9, GOES-10, and GOES-12 spacecraft, corresponding to different activity levels, solar wind IMF conditions, and storm phases. The obtained maps of the magnetic field reproduce most basic features of the magnetospheric structure, their dependence on the geomagnetic activity and interplanetary conditions, as well as characteristic changes associated with the main and recovery phases of magnetic storms.

Quantitative models of the magnetospheric magnetic field: methods and results

The paper reviews various approaches to the problem of evaluation and numerical representation of the magnetic field distributions produced within the magnetosphere by the main electric current systems including internal Earths sources, the magnetopause surface current, the tail plasma sheet, the large-scale systems of Birkeland current, the currents due to radiation belt particles, and the partial ring current circuit. Some basic physical principles as well as mathematical background for development of magnetospheric magnetic field models are discussed.A special emphasis is placed on empirical modeling based on datasets created from large bodies of spacecraft measurements. A review of model results on the average magnetospheric configurations and their dependence on the geomagnetic disturbance level and the state of interplanetary medium is given. Possibilities and perspectives for elaborating the ‘instantaneous’ models capable of evaluating a current distribution of magnetic field and force line configuration based on a synoptic monitoring the intensity of the main magnetospheric electric current systems are also discussed. Some areas of practical use of magnetospheric models are reviewed in short. Magnetospheric plasma and energetic particle measurements are considered in the context of their use as an independent tool for testing and correcting the magnetic field models.

Disturbances in Mercury's magnetosphere: Are the Mariner 10 “substorms” simply driven?

In addition to providing the first in situ evidence of a magnetosphere at Mercury, the first flyby by Mariner 10 inspired reports of Earth-like substorms. While the small scales at Mercury should make the substorm timescale there much shorter than it is at the Earth, these early interpretations may have too readily assumed that the substorm requirement of an energy storage and release phase occurs. Instead, its size should make Mercurys magnetosphere especially prone to disturbances that are purely “driven” by the changing external boundary conditions on the magnetosphere imposed by the solar wind. These result simply from the magnetospheres relatively unhindered reconfiguration in response to the varying interplanetary parameters, including the IMF southward component. In this paper we demonstrate that the “disturbed” structure observed outbound from closest approach during the first Mariner 10 flyby can alternately be explained as a consequence of a typical period of rotating IMF. We use an appropriately modified IMF-dependent terrestrial magnetosphere model scaled for Mercury, together with an assumed, reasonable IMF time series, to reproduce the magnetic field signature during the disturbed outbound pass segment. This result suggests that rapid restructuring of the small magnetosphere in response to changing local interplanetary conditions may dominate the magnetospheric dynamics at Mercury. Future Mercury magnetosphere missions should be instrumented to distinguish between this driven magnetospheric dynamism and any internal Earth-like substorm processes. These results also remind us that driven reconfigurations must always be considered in studies of transients in the terrestrial magnetosphere.

Hybrid state of the tail magnetic configuration during steady convection events

Previous observations have shown that during periods of steady magnetospheric convection (SMC) a large amount of magnetic flux crosses the plasma sheet (corresponding to ∼10° wide auroral oval at the nightside) and that the magnetic configuration in the midtail is relaxed (the current sheet is thick and contains enhanced BZ). These signatures are typical for the substorm recovery phase. Using near-geostationary magnetic field data, magnetic field modeling, and a novel diagnostic technique (isotropic boundary algorithm), we show that in the near-Earth tail the magnetic configuration is very stretched during the SMC events. This stretching is caused by an intense, thin westward current. Because of the strongly depressed BZ, there is a large radial gradient in the near-tail magnetic field. These signatures have been previously associated only with the substorm growth phase. Our results indicate that during the SMC periods the magnetic configuration is very peculiar, with co-existing thin near-Earth current sheet and thick midtail plasma sheet. The deep local minimum of the equatorial Bz that develops at R ∼ 12 RE is consistent with steady, adiabatic, Earthward convection in the midtail. These results impose constraints on the existing substorm theories, and call for an explanation of how such a stressed configuration can persist for such a long time without tail current disruptions that occur at the end of a substorm growth phase.