Gerd-Hannes Voigt

A mathematical magnetospheric field model with independent physical parameters

Abstract A quantitative magnetospheric magnetic field model has been calculated in three dimensions. The model is based on an analytical solution of the Chapman-Ferraro problem. For this solution, the magnetopause was assumed to be an infinitesimally thin discontinuity with given geometry. The shape of the dayside magnetopause is in agreement with measurements derived from spacecraft boundary crossings. The magnetic field of the magnetopause currents can be derived from scalar potentials. The scalar potentials result from solutions of Laplaces equation with Neumanns boundary conditions. The boundary values and the magnetic flux through the magnetopause are determined by all magnetic sources which are located inside and outside the magnetospheric cavity. They include the Earths dipole field, the fields of the equatorial ring current and tail current systems, and the homogeneous interplanetary magnetic field. In addition, the flux through the magnetopause depends on two constants of interconnection which provide the possibility of calculating static interconnection between magnetospheric and interplanetary field lines. Realistic numerical values for both constants have been derived empirically from observed displacements of the polar cusps which are due to changes in the orientation of the interplanetary field. The transition from a closed to an open magnetosphere and vice versa can be computed in terms of a change of the magnetic boundary conditions on the magnetopause. The magnetic field configuration of the closed magnetosphere is independent of the amount and orientation of the interplanetary field. In contrast, the configuration of the open magnetosphere confirms the observational finding that field line interconnection occurs primarily in the polar cusp and high latitude tail regions. The tail current system reflects explicitly the effect of dayside magnetospheric compression which is caused by the solar wind. In addition, the position of the plasma sheet relative to the ecliptic plane depends explicitly on the tilt angle of the Earths dipole. Near the tail axis, the tail field is approximately in a self-consistent equilibrium with the tail currents and the isotropic thermal plasma. The models for the equatorial ring current depend on the Dst-parameter. They are self-consistent with respect to measured energy distributions of ring current protons and the axially symmetric part of the magnetospheric field.

A magnetospheric magnetic field model with flexible current systems driven by independent physical parameters

A tilt-dependent magnetic field model of the Earths 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 ΔB 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 models 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.

Solution of the Chapman‐Ferraro problem with an arbitrary magnetopause

We present a global model of the magnetic field of the magnetosphere that includes the effects of the Chapman-Ferraro currents at the magnetopause. In contrast to earlier models, the magnetopause shape is arbitrary, thus allowing the use of more realistic geometries. The internal magnetospheric field model of Hilmer and Voigt [1993], is completely shielded within the magnetopause by solving the Laplace equation with Neumann boundary conditions using a finite difference method on a non-orthogonal, curvilinear grid. The resulting model magnetosphere is perfectly closed although the method can also be applied with more general boundary conditions, to generate a set of open models based on the approach of Toffoletto and Hill [1989, 1993]. The purpose of this paper is to demonstrate the feasibility of a purely numerical approach to solving the Chapman-Ferraro problem with arbitrary magnetopause shape and boundary conditions.

A study of weak anisotropy in electron pressure in the tail current sheet

The authors adopt a magnetotail model with stretched field lines where ion motions are generally nonadiabatic and where it is assumed that the pressure anisotropy resides only in the electron pressure tensor. They show that the magnetic field lines with p{sub {perpendicular}}>p{sub {parallel}} are less stretched than the corresponding field lines in the isotropic model. For p{sub {parallel}}> p{sub {perpendicular}}, the magnetic field lines become more and more stretched as the anisotropy approaches the marginal firehose limit, p{sub {parallel}}=p{sub {perpendicular}}+B{sup 2}/{mu}{sub 0}. The authors also show that the tail current density is highly enhanced at the firehose limit, a situation that might be subject to a microscopic instability. However, they emphasize that the enhancement in the current density is notable only near the center of the tail current sheet (z=0). Thus it remains unclear whether any microscopic instability can significantly alter the global magnetic field configuration of the tail. By comparing the radius of the field-line curvature at z=0 with the particle`s gyroradius, the authors suspect that even the conventional adiabatic description of electrons may become questionable very close to the marginal firehose limit. 22 refs., 9 figs.

Quasi-static MHD processes in Earth's magnetosphere †

An attempt is made to use the MHD equilibrium theory to describe the global magnetic field configuration of earths magnetosphere and its time evolution under the influence of magnetospheric convection. To circumvent the difficulties inherent in todays MHD codes, use is made of a restriction to slowly time-dependent convection processes with convective velocities well below the typical Alfven speed. This restriction leads to a quasi-static MHD theory. The two-dimensional theory is outlined, and it is shown how sequences of two-dimensional equilibria evolve into a steady state configuration that is likely to become tearing mode unstable. It is then concluded that magnetospheric substorms occur periodically in earths magnetosphere, thus being an integral part of the entire convection cycle.