Recent Development of the Ring Current Model and Future Plan

Recently, our ring current model was extended to include a realistic, activity-dependent magnetic field model. Analytical expressions for the bounce-averaged drifts in a realistic magnetic field model no longer exist and must be calculated numerically. Since -.B = 0, B can be expressed as B = -a ¥ -b, where a and b are the Euler potentials. Northrop [1963] showed that the relativistic bounce-averaged motion of the guiding center can be expressed as,

(2a)

(2b)

where and F is the sum of the electric potential associated with convection and corotation. We have taken b = f, the magnetic local time, and a = xli, where li is the magnetic latitude of the ionospheric foot point of the field line and x is a constant such that . In other words, the ionospheric foot point is used to label a field line instead of the equatorial crossing point. As the magnetosphere is compressed or expanded in response to the solar wind and/or internal instabilities, the equatorial crossing of a particular field line is no longer a constant. However, field lines can be granted as rooted at the ionosphere, where the magnetic variation is very small. Thus it is more convenient to identify a filed line by its foot point in the ionosphere. If a dipole field is assumed in the ionosphere, x is equal to ME sin2li /ri, where ME is the earth's magnetic dipole moment; ri is the radial distance of the ionospheric foot point of a field line. Similarly to (2), the bounce-averaged drift in (li, f) coordinates is given by:

(3)

In terms of new spatial parameters, the kinetic equation (1) is rewritten as,

(4)

Particle distributions at the equator or any point on field lines can be obtained from the values at the ionosphere by mapping along field lines, which may have instantaneous configurations. Therefore, our model will be able to admit any magnetic field configuration and reflect field line stretching and collapsing during substorm activities.

We have considered the ring current response to the changing magnetic field configuration during substorms. To describe variations of the magnetic fields, the activity-dependent Tsyganenko model [Tsyganenko, 1989] is used. The magnetic field configuration is associated with 6 levels of geomagnetic disturbance, with level 1 corresponding to quiet condition and level 6 to the most disturbed situation. Therefore, the expansion phase can be modeled by rapid collapse of field lines from level 6 to lower levels. The time dependence of level is given through the observed variations of the AE index. The line plot in Plate 1 shows the simulated Tsyganenko level as a function of time during the main phase of the storm on May 2, 1986. The particle drift is continuously updated according to the instantaneous magnetic field configuration.

We calculated the differential fluxes of 1.7 keV H+ at the equator during the storm and they are plotted in Plate 1. It can be seen that the ion flux is greatly enhanced (Plate 1b) at the nightside outer region where particles are injected earthward, in response to the induced electric field during dipolarization (magnetic level drops from 6 to 1 between 1 to 2 hours). At the middle of the main phase, the stretching and collapsing of the magnetic field are in smaller amplitudes than at the early main phase. However, the injection of ions continues and an earthward propagation of injection front is seen (Plate 1d-e). A low-flux region is formed in the inner region at all local time and this region extends outward in the postnoon sector. This region represents the area of closed drift path of low energy ions. The pre-existing low energy particles are lost by charge exchange and the injected ions from the tail cannot reach this region. After ~ 10 hours, the magnetosphere is so disturbed that the magnetic field fluctuates in a very small amplitude. Near the peak of the storm (Plate 1f), the strong convection electric field pushes ions close to the earth and compresses the region of closed drift path.

Plate 1. Simulated equatorial differential flux (cm-2s-1sr-1keV-1) of 1.7 keV H+ during the storm on May 2, 1986. The simulated values of the magnetic field level, for which the ion fluxes are shown, are indicated by red dots.

Proposed Improvements

It is known that the magnetospheric convection electric field is dominantly controlled by the interplanetary conditions, i.e. intensity and direction of the interplanetary magnetic field (IMF) and solar wind plasma parameters near the Earth's orbit. Instead of the simple Volland-Stern type model, an IMF-controlled electric potential model will be employed to calculate the E¥B drifts of the ring current particles. One of the candidate model is the IZMIRAN Electrodynamic Model (IZMEM). IZMEM is derived from a large quantity of high-latitude ground-base geomagnetic data. A linear regression analysis technique is used to obtained the quantitative response of magnetic disturbances of the earth's surface to changes of IMF components. Then ionospheric electrodynamics is mapped to the polar regions using a given model of the ionospheric conductivity. The distinct feature of IZMEM from other similar models is that it does not require input of ground-based geomagnetic data.

The global plasmasphere convection model developed by one of our co-investigator, Dr. D. L. Gallagher, will replace the model of Rasmussen et al. [1993] in the study of ring current-plasmasphere coupling. To be consistent, both the plasmasphere model and the ring current model will use the same model of convection to move the plasmas. The coupling between the ring current and the plasmasphere, through wave-particle interactions, will be pursued. The subsequent effects on both the energetic and the thermal populations will be solved self-consistently.

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