F.R. Fenrich, J.G. Luhmann
Space Sciences Laboratory, University of California, Berkeley

J.A. Fedder
Institute for Computational Sciences and Informatics, George Mason University

S. Slinker
Plasma Physics Division, Naval Research Laboratory

N.A. Tsyganenko
HSTX, Goddard Space Flight Center

C.T. Russell
Institute of Geophysics and Planetary Physics
University of California, Los Angeles

Abstract

Two global magnetic field models of the Earth's magnetosphere: the Tsyganenko T96_01 model and a high resolution MHD global numerical simulation are used to examine the magnetic field configuration in the magnetosphere along the POLAR spacecraft orbit near apogee. Several sets of Polar Magnetic Field Experiment (MFE) data, taken during periods with fairly steady IMF conditions, are compared with the model outputs. It is found that both models do at times show excellent agreement with the MFE data. However, there are periods of disagreement for each model. To aid in determining the reasons for model disagreement, comparisons of the model magnetic field components along simulated POLAR trajectories are made. It is found that the MHD model lacks a ring current while the T96_01 model has difficulty reproducing the magnetospheric cusp fields. By comparing the external current systems of each of the two models we hope to be able to provide suggestions for improvement to both models. For example, a merger of a Tsyganenko type ring current and the MHD model, or the addition of the MHD currents near the cusp to the T96_01 model would both yield almost ideal models with respect to fields along a Polar type orbit.

Model Descriptions

The MHD global simulation model is a three-dimensional numerical solution of the ideal MHD equations. The simulations are a self-consistent, time-dependent model of the solar wind-magnetosphere-ionosphere system. The time resolution is about 1 second and the numerical mesh is an irregular computer-generated grid with outer boundaries at x=30 RE and -300 RE, and sqrt(y^2 + z^2)=60 RE. The inner boundary is at sqrt(x^2+y^2+z^2)=3.5 RE. For this study the raw simulation results have been interpolated to a regular grid with a resolution of 0.5 RE in each direction and boundaries at x=-10 RE and 15 RE, and |y|=|z|=20 RE. In the simulations presented here the following steady solar wind conditions were used: plasma number density, n~6.5/cc; solar wind velocity, v=400 km/s; and IMF magnetic field strength, |B|=5 nT for the North and South IMF cases and |B|=10 nT for the East IMF case.

The T96_01 model is a data-based global model of the magnetospheric magnetic field with an explicitly defined realistic magnetopause controlled by the solar wind pressure. It incorporates large scale Region 1 and 2 Birkeland current systems, and IMF penetration across the boundary. The model requires the following input parameters: solar wind pressure, DST-index, By and Bz-components of the interplanetary magnetic field, and the geodipole tilt angle. For this study the required parameters were chosen to be consistent with the parameter values in the MHD simulation model. For the North IMF case Pdyn=1.7 nPa, Dst=0, By=0, Bz=+5 nT. For the South IMF case Pdyn=1.7 nPa, Dst=-50 nT, By=0, Bz=-5 nT. For the East IMF case Pdyn=1.7 nPa, Dst=0 nT, By=+10 nT, Bz=0. In all cases the dipole tilt angle was taken to be zero. The total T96 model includes the T96 external field plus an internal dipole field consistent with the dipole field strength used in the MHD simulations.

POLAR - MFE Comparisons with MHD and T96 Models

Comparisons of external field components for three different events are shown in Figures 1 , 2 and 3 . In all events the T96 model solution is determined using the time-varying solar wind parameters and Dst index whereas the MHD model solution is that corresponding to fixed solar wind inputs. However, for the 19 May 96 event the complete MHD simulation corresponding to dynamic solar wind inputs has been determined and is shown in Figure 4 (not available on webpage).

Figure 1 (a) Plot of field components for POLAR MFE-IGRF residuals (solid), external T96 (dot-dash), and external MHD for 10 Jan 97. (b) Plot of 5 min averaged solar wind parameters and Dst (solid) together with solar wind input parameters to the T96 model (dot-dash) and the MHD model (dotted). (c) Plot of POLAR satellite trajectory as viewed in x-z plane and y-z plane. Note all coordinates are GSM.

Figure 2 (a) Plot of field components for POLAR MFE-IGRF residuals (solid), external T96 (dot-dash), and external MHD for 28 May 96. (b) Plot of 5 min averaged solar wind parameters and Dst (solid) together with solar wind input parameters to the T96 model (dot-dash) and the MHD model (dotted). (c) Plot of POLAR satellite trajectory as viewed in x-z plane and y-z plane. Note all coordinates are GSM.

Figure 3 (a) Plot of field components for POLAR MFE-IGRF residuals (solid), external T96 (dot-dash), and external MHD for 19 May 96. (b) Plot of 1 min averaged solar wind parameters and Dst (solid) together with solar wind input parameters to the T96 model (dot-dash) and the MHD model (dotted). (c) Plot of POLAR satellite trajectory as viewed in x-z plane and y-z plane. Note all coordinates are GSM.

The agreement between the MFE residual fields and the T96_01 model is excellent except during periods of large solar wind dynamic pressure, for example Figure 1 at ~11 UT, and during periods when the Polar satellite is in the dayside cusp region, for example Figure 2 at ~10 UT and Figure 3 at ~15 UT.

Considering the differences in initial solar wind conditions the MHD solutions agree reasonably well with MFE. The full MHD solution for 19 May 96 shows that the MHD model is able to reproduce the fields at Polar orbit very well particularly in the cusp region. However, in Figure 1 the MHD Bz is found to be considerably more positive than MFE Bz by as much as 50 nT. This is due to the lack of a ring current as will be discussed in the next section.

Ring Current Comparison

Figure 5 Contour plots in the X-Z plane of the Y-component current density, Jy, for the T96_01 model and the MHD model. For both models the IMF is southward at -5 nT. A Dst of -50 nT and a dynamic pressure of 1.75 nPa was input to the T96 model.

In order to improve the MHD model we consider the possibility of adding T96 type ring current fields to the MHD model. Figure 6 is a plot of field line tracings which correspond to the T96 ring current for a Dst of -50 nT and a solar wind dynamic pressure of 2 nPa. Note that the fields have been shielded from the solar wind.

Figure 6 Tracings of magnetic field lines resulting from just the shielded ring current as determined by the T96_01 model using Dst=-50 nT and dynamic pressure = 2 nPa.

It may be possible to add similar ring current fields to the Earth's internal dipole field and use that as an initial starting point for the MHD simulation. However any fields added must be curl free in order to keep the MHD solution self-consistent. This may be achieved by adding internal multipole fields to the dipole field.

Cusp External Field and Current Density Comparisons

Figure 7(a)	Figure 7(b)	Figure 7(c)

Figure 8(a)	Figure 8(b)	Figure 8(c)

Figures 7 and 8 show a comparison of external magnetic fields and current densities, respectively, for the MHD and T96 models along a noon-midnight simulated Polar orbit. It can be seen in these figures that the external fields and current densities in the cusp region are significantly different for the two models.

Referring back to the comparisons with Polar MFE data, recall that the MHD model provided a better fit to the data in the cusp region. Thus the MHD fields and currents in the cusp are more representative of the real magnetosphere and can be used to better understand the cusp current systems.

By studying the MHD current systems threading the cusp region we can learn how to better model these systems for input into current empirical models such as the T96 model.

Please send comments to Frances Fenrich at ffenrich@ssl.berkeley.edu.