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

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

Abstract

In conjunction with a Polar MFE study of the cusp, a high resolution MHD global numerical simulation is used to examine the cusp region of the northern magnetosphere. The cusp is generally identified by a decrease in the total magnetic field strength together with enhancements in plasma density and temperature. Such signatures are being used by the Polar MFE team to study various characteristics of the cusp such as its latitude, width and maximum decrease in total B field. The advantage of MHD simulation models over data-based models is that they include plasma density and temperature information in addition to magnetic field information and therefore can be used to study the cusp in a similar manner to the Polar MFE study. In this paper we will present measurements of cusp width, latitude and decrease in total B as a function of local time and three IMF orientations (+By, -Bz, +Bz). By comparing these measurements to those of the Polar MFE study we will determine how well the MHD model is able reproduce both magnetic fields and plasma parameters in the cusp region.

MHD Model Description

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.

Discussion

Since the MHD model solutions include measurements of plasma density and temperature as well as magnetic fields, it provides a useful tool for studying the cusp region of the magnetosphere. The cusp is generally characterized by weak magnetic field strengths together with enhanced plasma densities and temperatures. The plasma densities and temperatures are enhanced because the weak magnetic field allows penetration of magnetosheath plasma into the cusp. Figure 1 shows the MHD model magnetic field and plasma parameters along a noon-midnight simulated POLAR satellite trajectory for the southward IMF case. In this study the cusp region along the simulated POLAR orbit is defined by the criteria n > 5 cm-3 and dBtot < -20 nT. Note that we are investigating the MHD cusp along simulated POLAR satellite orbits in order to compare with an observational study of the cusp using field and plasma measurments from the POLAR satellite.

Figure 1 Magnetic field residuals from dipole and plasma parameters corresponding to the MHD model along a simulated noon-midnight plane POLAR orbit for the South IMF case. The enhancements in number density, pressure and temperature which occurs simultaneously with the depression in total B field are signatures of the cusp region. The criteria n > 5 cm-3 and dBtot < -20 nT has been used to identify the cusp. The dashed lines designate the cusp boundaries according to this criteria.

The cusp minimum in the total magnetic field residual, dBtot, and the cusp maximum in plasma density, n, were measured as a function of the local time plane of the simulated Polar orbit. Plots of these measurements for each of the three different IMF clock angles are shown in Figure 2 . This figure shows that in the North and South IMF cases the cusp is centered around noon whereas in the East IMF case the cusp is shifted towards dusk by approximately 1.5 hrs in local time. It is interesting that the northward IMF case exhibits significant cusp signatures with minimum dBtot values similar to those in the southward case and maximum number densities as large as ~60% of those seen in the southward IMF case. It will be interesting to see if similar cusp fields and densities are seen with the Polar satellite.

Figure 2 (a) MHD model minimum total B field values along simulated POLAR satellite trajectories as a function of local time plane of orbit for three different IMF conditions: North (solid), South (dotted), East (dashed). (b) MHD maximum number density along simulated POLAR satellite trajectories as a function of the local time plane of orbit for the same three different IMF conditions.

Plots of cusp boundary and cusp local time width are shown in Figure 3 and Figure 4 . These plots show the northward IMF cusp significantly poleward and narrower in local time than the southward and northward IMF cases. The shift of the cusp towards dusk in the east IMF case is also seen. Note that when mapped to the Earth along the MHD model field lines the cusp is significantly shifted towards dusk. This would be expected for the East IMF case but not for the North and South cases.

Figure 3 (a) Plot of MHD cusp location at Polar orbit as a function of magnetic latitude and local time for North (solid), South (dotted), and East (dashed) IMF. (b) Plot of MHD cusp width at Polar orbit as a function of local time for the three different IMF cases.

Figure 4 (a) Plot of the MHD cusp location when mapped to the Earth along the MHD field lines. (b) Plot of the MHD cusp width when mapped to Earth as a function of local time.

Figure 5(a)	Figure 5(b)	Figure 5(c)

Figure 5 (a) , (b) , (c) summarize very well the differences in number density, temperature and magnetic field topology particularly in the cusp region for the three different IMF inputs to the MHD solution. Some of the interesting features seen in this figure include:

• 1. In the North IMF case the region of enhanced densities, which were used to identify the cusp, fall on closed field lines threading the dayside magetosphere. This is different from the South and East IMF cases where the regions of enhanced plasma density inside the magnetosphere correspond to open field lines resulting from dayside magnetic merging.
• 2. The enhancements in plasma temperature occur slightly equatorward of the maximum in number density for both the East and South IMF cases but occurs significantly poleward of the maximum in number density for the North IMF case.
• 3. In the South and East IMF cases regions of greatest plasma density are seen at Z values of ~10 RE or greater while in the North IMF case the region of greatest plasma density remains at the subsolar point.

In the North IMF case, the presence of magnetosheath-like plasma on closed field lines is a very interesting result. It suggests that magnetic merging is occurring at the poles which heats the magnetosheath plasma and traps it in the magnetosphere. In both the South and East IMF cases the regions of highest plasma temperature on the dayside corresponds to the most recently reconnected field lines with the maximum enhancements in cusp plasma density occurring slightly poleward. Thus by analogy, the regions of enhanced plasma temperature poleward of the density enhancements in the North IMF case should also indicate the regions of recently reconnected field lines.

By comparing the MHD cusp signatures as measured along simulated POLAR orbits to actual POLAR spacecraft measurement we will be able to determine just how accurately the MHD model represents the true magnetosphere.

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