Institute of Geophysics and Planetary Physics,
University of California
Los Angeles, CA 900951567
Originally Published In: J. Geophys. Res., 103, 17, 345350, 1998.
Abstract. The equatorial ring current and the magnetopause current both contribute to the magnetic field at low altitudes over the polar cap. In this region the magnetic field is dominated by the Earth's internal field and is well described by empirical models. The average change in the magnetic field strength due to external sources (the residual of the observed magnetic field strength upon subtracting the International Geomagnetic Reference Field (IGRF) 95 internal field model) is typically a few tens of nanotesla, or a few tenths of 1% of the total magnetic field over the polar cap at the altitude of the POLAR spacecraft. It is easier to measure such small differences in the total field than in the vector components because the accuracy of the residuals in the vector magnetic field depends on the accuracy of the knowledge of spacecraft pointing which is generally less well known than the position of the spacecraft. In order to isolate the ring current effects on the total field we adjust the Dst index for the contributions of the magnetopause current using the solar wind dynamic pressure, and we adjust the observed field values for the same effect using the Tsyganenko 1996 model. After these adjustments the ring current strength as measured by the adjusted Dst index is well correlated with the residual of the field strength observed in the lowaltitude polar region over a wide range of local times except when the spacecraft track is near the noonmidnight meridian. These comparisons, using more than a full year of Polar data, demonstrate that the Tsyganenko 1996 model together with the IGRF 1995 internal field model provides a good baseline for the magnetic field at the altitude of the Polar perigee passes (~5000 km above the Earth's surface). Further they demonstrate that total field measurements from lowaltitude polar orbiting spacecraft are potentially useful as monitors of the ring current when they cross the polar cap.
The magnetic field disturbances caused by the major magnetospheric current systems can be seen everywhere on the Earth's surface. Geomagnetic indices are widely used to characterize these disturbances and thus the state of the solar wind interaction with the Earth's magnetic field. One of the most important indices is the disturbance storm time indexDst that provides information on the occurrence of worldwide magnetic storms through its dependence on the strength of the ring current. The index is derived from the average deviation of the horizontal component of the geomagnetic field from that of a quiet day at middle and low latitudes at a variety of longitudes around the globe. Such deviations are caused mainly by the combined effect of the magnetopause current and the ring current. Since the Earth's main field is northward at mid latitudes and in the equatorial region, an enhanced magnetopause current increases the Dst index and an enhanced ring current decreases it. On a quiet day the ring current effect on the surface magnetic field is roughly equal and opposite to that of the magnetopause currents, ~20 nT (Araki et al. 1993). The contribution to Dst due to the magnetopause current is proportional to the square root of solar wind dynamic pressure [Siscoe et al., 1968; Ogilvie et al., 1968]. The Dst index contributed by the ring current is proportional to the total energy of the ring current particle [Dessler and Parker, 1959; Sckopke, 1966]. By correcting the Dst index for the dynamic pressure, the equatorial Dst index provides information on how much energy is contained in the trapped particles in the inner magnetosphere [Burton et al., 1975]. Thus the corrected Dst index has a straightforward physical interpretation, albeit other current systems such as the tail current do also contribute to Dst [e.g., Campbell, 1996].
The effects of the various magnetospheric current systems can also be detected at high latitudes as well as at low. However, at high latitudes the enhanced ring strengthens the magnetic field in contrast to its effects at low latitudes. For measurements from a fixed location on the surface of the Earth, quiet day values can be used to determine baselines for calculating the residual magnetic fields, but for spacecraft well above the surface of the Earth, moving rapidly through a varying magnetic field, we need to use a model of the internal magnetic field such as the International Geomagnetic Reference Field (IGRF) 1995 model. Since the magnetic field strength due to external sources is typically a few tens of nanotesla, the internal model and the magnetic field measurements need to be accurate. Since the measurement of vector magnetic field residuals requires accurate knowledge of the pointing of the spacecraft axes, it is desirable to be able to make such comparisons with the total magnetic field that has fewer sources of possible error. The Polar spacecraft passes over the southern polar cap at ~5000 km from the Earth’s surface near its perigee. In this paper we present initial observations of the effects of the ring current and the magnetopause current in the lowaltitude polar magnetosphere by the Polar Magnetic Field Experiment (MFE). We examine the magnetic field residuals due to external sources in the lowaltitude polar region using magnetic field models and study the residuals of the magnetic field strength and how they depend on the Dst index and the solar wind dynamic pressure.
The Polar spacecraft moves around the Earth in a highly elliptical 1.8 x 9 R_{E} polar orbit with a period of 17.5 hours. The magnetic field is measured by MFE [Russell et al., 1995]. In this study we will examine the MFE data in the lowaltitude polar region (around Polar perigee). At perigee the Polar spacecraft is ~5000 km above the southern polar cap, and the magnetic field strength increases to up to ~10,000 nT. For these intervals the inboard magnetometer is used at its highgain setting with a digital window of 1.2 nT. The data used in this study are despun vectors obtained once per spacecraft spin (6 s) that are computed immediately after the sun sensor detects the sun direction. These data have been corrected to an angular accuracy of 0.06^{o}limited by the 1ms timing accuracy of the magnetic vectors. The solar wind dynamic pressure used in this study is calculated from the solar wind proton density, and the bulk velocity is calculated from the Wind Solar Wind Experiment (courtesy of K. Ogilvie) by assuming a 4% alpha particle content.
To examine the magnetic field caused by the external current systems, we use the Tsyganenko 1996 empirical magnetosphere model [Tsyganenko and Peredo, 1994; Tsyganenko, 1995, 1996], combined with the 1995 IGRF model for the internal field as the average magnetosphere configuration. The amplitude of the magnetic field from external sources depends on input parameters such as the square root of the solar wind dynamic pressure (Pdyn), the Dst index, and the interplanetary magnetic field (IMF) By and Bzrelated parameter. In the Tsyganenko 1996 (T96) model the magnetosphere is best modeled when the input parameters are within the range of Pdyn between 0.5 and 10 nPa, Dst between 100 and +20, IMF By and Bz: between 10 and +10 nT. Under these conditions, there are data from 477 perigee passes with solar wind data available in the 15 month period from March 20, 1996 to May 31, 1997.
Fig. 1. Polar orbit segments projected on noonmidnight meridian in the solar magnetic (SM) coordinates for the three perigee passes in Figure 2: (a) March 25, 1996, (b) May 1, 1996, and (c) April 8, 1996. Tick marks on the orbit correspond to 20 min intervals, and the circle denoted by P indicates the perigee time. 
Three examples of magnetic field residuals near Polar perigee passes on March 25, 1996 in Figure 2a, May 1, 1996 in Figure 2b, and April 8, 1996 in Figure 2c. From top to bottom in Figures 2a, 2b and 2c are the magnetic latitude of the Polar spacecraft, the eastward magnetic field residuals in fieldaligned coordinates, and the residuals in the magnetic field strength, respectively. The thin traces are the residuals with the International Geomagnetic Reference Field (IGRF) internal field removed. The thick traces are residuals with the IGRF+T96 model removed. In the T96 model, the observed Dst index, the solar wind dynamic pressure, and the interplanetary magnetic field (IMF) data from Wind are used as inputs: (a) Dst = 39, Pdyn = 3.0 nPa, IMF By = 2.4 nT and IMF Bz = 3.2 nT; (b) Dst = 4 nT, Pdyn = 3.4 nPa, IMF By = 2.6 nT and IMF Bz = 2.6 nT; and (c) Dst = +18 nT, Pdyn = 2.9 nPa, IMF By = 4.6 nT, and IMF Bz = 0.2 nT. 
We first show three examples of observed magnetic field data and model predictions in the lowaltitude polar region for different Dst levels. Figure 1 shows the Polar orbit segments projected on the noonmidnight meridian in solar magnetic (SM) coordinates for the three perigee passes: (Figure 1a,) March 25, 1996 (Dst = 39, Pdyn = 3.0 nPa, IMF By = 2.4 nT and IMF Bz = 3.2 nT); (Figure 1b,) May 1, 1996 (Dst = 4 nT, Pdyn = 3.4 nPa, IMF By = 2.6 nT and IMF Bz = 2.6 nT); and (Figure 1c) April 8, 1996 (Dst = +18 nT, Pdyn = 2.9 nPa, IMF By = 4.6 nT and IMF Bz = 0.2 nT), respectively. In the SM coordinates, Z is along the north dipole axis, Y is perpendicular to the Earthsun line toward dusk, and X is perpendicular to Z and in the plane containing the dipole axis and the Earthsun line. In Figure 1, tick marks on the orbit correspond to 20 min intervals and the circle denoted by P indicates the perigee time. Figure 2 shows the magnetic field residuals for the three examples. From top to bottom in Figures 2a2c, the magnetic latitude of the Polar spacecraft, the eastward magnetic field residuals in fieldaligned coordinates, which are caused mainly by the fieldaligned currents, and the residuals in the magnetic field strength are shown, respectively. The thin traces are the residuals with the IGRF internal field removed. The thick traces are residuals with the IGRF+T96 model removed. In the T96 model, observed Dst index and solar wind dynamic pressure and IMF data from Wind are used as inputs.
Near the Polar perigee the dominant magnetic field is the main field produced by internal currents within the Earth's core. The average field model agrees very well with the measurements. In Figure 2 it is apparent that the magnitude of the residual in the magnetic field strength depends on the Dst index. The residual in the field strength from external sources (thin traces) is ~70 nT for Dst = 39 nT, is ~40 nT for Dst = 4 nT, and is ~20 nT for Dst = 18 nT over the polar cap. With the observed parameters of the Dst index, the solar wind dynamic pressure, and the IMF as inputs to the T96 model to model the magnetospheric currents, residuals of the field strength are greatly reduced over the polar cap (thick traces). It shows that the T96 model predicts very well the magnetic field strength over the lowaltitude polar cap. However, the T96 model does not predict well the fieldaligned current since it does not reduce the residual of the eastward magnetic field component.
The relationship between the residual of the field strength and the Dst index over the polar cap is due to the combined effect of the ring current and the magnetopause current. The residual of the field strength varies with latitude since the Earth's magnetic field changes direction along the Polar orbit from northward in the equatorial region to southward in the polar region. Only in the polar and equatorial regions are the magnetic fields associated with the ring current and the magnetopause current in the general direction of Earth’s internal field. In these regions the residual in the magnetic field strength reflects the magnitude of the magnetic field perturbation associated with these current systems. Below we show the statistical relationship between the residual of the field strength over the polar cap and the Dst index from 477 Polar perigee passes. To calculate the residual of the magnetic field strength over the polar cap, we subtract the model predictions from the Polar MFE data and then average the residual of the field strength over a time period around the perigee when the overall magnetic field direction is within 25^{o} of the dipole axis.
Fig. 3.
Residuals of magnetic field strength over the polar cap as a function of the Dst index. The residuals are calculated using the IGRF internal field model.

Fig. 4.
Residuals of magnetic field strength over the polar cap as a function of the Dst index. The residuals are calculated using the IGRF+T96 model with fixed average input parameters (Dst = 0 nT, Pdyn = 2 nPa, IMF By = 0, and IMF Bz = 0 nT).

The dependence of the residual of the magnetic field strength on the Dst index is confirmed statistically in Figures 3 and 4. In Figure 3 the residuals of the field strength averaged over the polar cap are calculated by subtracting the IGRF magnetic field model from the data. Figure 3 shows that the contribution of external sources to the field strength varies as a function of the equatorial Dst index. A correlation between the residual in the field strength and the Dst index is clearly shown. The residual increases as the Dst index decreases. This is also true in Figure 4 when using the IGRF+T96 model with fixed average input parameters (Dst = 0 nT, Pdyn = 2 nPa, IMF By = 0 nT, and IMF Bz=0 nT) that include contributions from the average magnetopause current and quiet time ring current. Figures 3 and 4 clearly demonstrate that the residuals of the field strength observed in the lowaltitude polar magnetosphere are caused by the combined effects of the ring current and the magnetopause current. The amplitude of the residual is ordered by the Dst index. It decreases from positive to negative values as the Dst index increases from negative to positive values.
Next we demonstrate the effect of the ring current alone by removing the effect of the magnetopause current. Since the magnetopause current responds to the solar wind dynamic pressure nearly instantaneously, the Dst index can be corrected through knowledge of the solar wind dynamic pressure to include only the contribution of the ring current. The contribution to the Dst index by the magnetopause current is proportional to the square root of the solar wind dynamic pressure. In studies of sudden impulses using lowlatitude groundbased magnetometer data, Russell et al. [1994a] found that the effect of the magnetopause current is 18.4 nT/(Pdyn)^{1/2} at noon and 12.4 nT/(Pdyn)^{1/2} at midnight for northward IMF on the Earth’s surface. The effect is 25% smaller when the IMF is southward [Russell et al, 1994b]. We used the average value to correct the Dst index; that is, the corrected Dst index is equal to Dst minus 13.5 (Pdyn)^{1/2 }. To calculate the residual of field strength due to the ring current alone, we used the T96 model with real time WIND observations of the solar wind dynamic pressure to model the magnetopuase current and to set the ring current strength to zero in the model. Figure 5 shows the residual of magnetic field strength over the polar cap as a function of Dst due to the ring current and demonstrates that the magnetic field associated with the ring current accounts completely for the residual of magnetic field strength seen in the lowaltitude polar region. The solid line in Figure 5 is the ideal case; that is, its slope is equal to 1.0. For a least square fit of the data that is forced to go through the origin the slope is 1.02, which is very close to the ideal case. This result provides a simple means to estimate the ring current strength by measurements from lowaltitude polar orbiting spacecraft. It also demonstrates that the IGRF+T96 model provides a good baseline for the magnetic field. In Figure 5 we also see that the corrected residual field strength over the polar cap is always slightly positive and that the corrected Dst index is always slightly negative. This is an indication of the continuous presence of a quiet time ring current whose strength on a typical quiet day creates a surface magnetic field of ~20 nT [Araki et al., 1993]. Finally, we note that the three data points corresponding to the most disturbed Dst values are among the furthest from the expected slope. These passes all occurred near the equinoxes and also when the polar orbit plane was most nearly aligned with the noonmidnight plane.
Fig. 5.
Residuals of magnetic field strength over the polar cap as a function of the corrected Dst index. The residuals are calculated using the IGRF+T96 model with real solar wind dynamic pressure as inputs and without contribution from the ring current. The Dst is corrected by its solar wind dynamic pressure component using Dst* = Dst13.5(Pdyn)^{1/2}.

In this paper we have examined the effects of the equatorial ring current and the magnetopause current on the magnetic field observations in the lowaltitude polar magnetosphere obtained by the Polar magnetometer. The magnetic field in the lowaltitude magnetosphere is dominated by the Earth's internal field and is well described by empirical magnetic field models. External sources contribute, on average, a few tens of nanotesla to the magnetic field strength, in the lowaltitude polar region. We demonstrate that the residuals of the observed magnetic field strength minus the IGRF field model or the T96+IGRF model with fixed average input parameters are well correlated with the equatorial Dst index. By correcting the Dst index for its solar wind dynamic pressure component and by comparing it with the Tsyganenko 1996 model with and without the magnetopause and ring current contribution to the model, we demonstrate that the magnetic field associated with the ring current can account for the residual of the field strength observed in the lowaltitude polar region. Thus the Tsyganenko 1996 model together with the IGRF 95 internal field model provides a good baseline for the magnetic field at the altitude of the Polar perigee passes (~5000 km above the Earth's surface).
Conversely, the study shows that we can use the measurements obtained over the polar cap to provide a quick estimate of the strength of the ring current. Thus these data allow us to monitor one of the principal energy reservoirs in the magnetosphere. The Polar data were obtained at ~5000 km altitude in a background field strength of ~10,000 nT, whereas most lowaltitude polar orbiters are at lower altitudes, obtaining data in background field strengths of ~40,000 nT. Thus it is somewhat more difficult to obtain the same accuracy with these spacecraft but not impossible. Thus we recommend that our study be repeated with such data sets. If this measurement is indeed feasible at these lower altitudes, then it should be possible to obtain a nearly real time ring current measure for nowcasting the state of the magnetosphere from these data.
We would like to thank N. Tsyganenko for providing his 1996 field model in advance of publication and for his useful comments on this paper. We also wish to thank K. Ogilvie for providing data from the WIND Solar Wind Experiment, R. Lepping for providing data from the WIND Magnetic Fields Investigation, and NGDC for providing the Dst index data. The work at UCLA was supported by the National Aeronautics and Space Administration under research grant NAG53171.
The Editor thanks N. A. Tsyganenko and another referee for their assistance in evaluating this paper.
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