7.2 Storm-time ring current

The increased solar wind electric field imposed on the magnetosphere increases the ring current, as described by the dynamic evolution equation of the ground-based Dst index (see Section 4). For many purposes, the particle motion in the magnetosphere can be described in terms of the guiding center motion, which gives an average over the gyromotion around the magnetic field lines and bouncing between the mirror points. In that approximation, the particles drift under the electric and magnetic fields with a total drift velocity (Roederer, 1970)
B [ ] E × B V = ---× 2W ∥(B ⋅ ∇ )B + μ ∇B + ----2-- (9 ) eB B
where the first adiabatic invariant
μ = W--⊥ (10 ) B
is conserved. When this approximation is valid, particles convecting toward the increasing magnetic field in the quasi-dipolar inner magnetosphere are adiabatically energized.

The Burton et al. (1975) equation described earlier assumes that when the magnetopause is opened by reconnection, the solar wind electric field penetrates into the magnetosphere and drives convection that transports particles into the inner magnetosphere. Furthermore, it is often assumed that the magnetic field lines are equipotentials. This means that it is sufficient to know the electric field in one plane only, and the electric field measured in the ionosphere can be mapped to the magnetosphere. A simple but robust description of the inner tail electric field in the equatorial plane of the magnetosphere is given by the Volland–Stern electric potential Φconv in the form

Φ = AL γ sin(ϕ − ϕ ), (11 ) conv 0
where A determines the intensity of the convection electric field, γ is a shielding factor, ϕ is the magnetic local time, ϕ0 is the offset angle from the dawn-dusk meridian, and often used values are γ = 2 and ϕ0 = 0 (Volland, 1973Stern, 1975). The intensity of the electric field can then be related to magnetic activity indices such as Kp (Maynard and Chen, 1975) by writing
0.045 2 A = (1-−-0.159K---+-0.0093K2-)3kV ∕R E. (12 ) p p
On the other hand, the convection electric field can also be given as a function of the solar wind and IMF values by using the Boyle et al. (1997Jump To The Next Citation Point) function for the polar cap potential Φ in the form
[ ( 𝜃) ] sin ϕIMF ( R )2 Φpc = 1.1 ⋅ 10−4Vs2w + 11.1 ⋅ BIMF sin3-- -------- ---- , (13 ) 2 2 RB
where 𝜃IMF = tan 1(B z∕By) is the IMF clock angle, R is the radial distance, and RB = 10.47 RE. Both of these electric potential models yield a large-scale potential structure in the magnetosphere, where the electric field in the magnetotail is predominantly in the dawn-dusk direction and thus lead to transport from the tail toward the inner magnetosphere.
View Image

Figure 20: Magnetic storm on May 2 – 4, 1998. Ring current energy content as a function of time. Total energy content is shown in black, red shows the energy contribution from high-energy particles (80 – 200 keV), green shows the energy content in the medium energy particles (20 – 80 keV) and blue shows the contribution of the low-energy particles (1 – 20 keV). The left panels show observations from the Polar spacecraft. The observations indicate strong enhancement of the high-energy component during the later part of the storm (lowest panel shown in red). The three panels on the right show results from drift computations using different magnetic and electric field models, from top to bottom: dipole magnetic field and Volland–Stern convection electric field, T96 magnetic field model and Boyle et al. (1997Jump To The Next Citation Point) convection electric field, T96 magnetic field, Boyle et al. (1997Jump To The Next Citation Point) convection electric field, and substorm-associated electric field pulses. The bottom panel shows the Dst index during the storm. Only the model including the pulsed small-scale electric fields is able to reproduce the strong increase the high-energy component (after Ganushkina et al., 2005Jump To The Next Citation Point).

The drift approximation has been quite successfully applied to model inner magnetosphere plasma transport and energization during magnetic storms (Liemohn et al., 2001Jordanova et al., 2001). However, it has become clear that simplified assumptions about the electric field (assuming large-scale convection only) and magnetic field configuration (assuming time-invariant dipole field) are not sufficient to account for many of the phenomena observed during storms. Replacing the magnetic field with a more realistic (time stationary) model allows plasma transport closer to the Earth in the magnetotail region, as the E × B drift dominates in the taillike magnetic field. On the other hand, a realistic representation of the magnetopause leads to significant particle losses from the dayside magnetosphere. Thus, the effect of a realistic magnetic field model is to decrease the total ring current energy content and make it more asymmetric as the dayside losses decrease the morning-sector fluxes (Ganushkina et al., 2005Jump To The Next Citation Point). Adding localized, time-varying electric field pulses to the model causes significant changes in the energy spectrum: while steady convection creates an intense but rather low-energy ring current, the electric field pulses are effective in accelerating particles to energies of 100 keV and above.

Figure 20View Image based on results in Ganushkina et al. (2005Jump To The Next Citation Point) shows a composite of calculations of the ring current energy content under a variety of magnetic and electric field models. The black curves show the time evolution of the total ring current energy content during a double storm on May 2 – 4, 1998. The colored curves show contributions from low (blue), medium (green) and high (red) energy particles. The left column shows observations made by the CAMMICE energetic particle instrument onboard the Polar spacecraft. In the right column, the top panel shows a computation using a large-scale convection electric field to drive the particle motion under a dipole magnetic field. The second panel illustrates the energy density development using a more realistic magnetic and electric field models, the T96 (Tsyganenko, 1995) magnetic field and Boyle et al. (1997) electric field. The third panel shows the same calculation, but now in addition to the convection electric field, traveling electric field pulses representing substorms have been added to the model. The bottom panel shows the Dst index during the storm. It is evident that after the second storm peak, only the third panel shows a large increase of the energy in the highest-energy particles (red curves) consistent with the observations shown in the left panels. Ganushkina et al. (2005) conclude that the localized, pulsed electric fields are necessary for the formation of the high-energy ring current and that any enhancement of the large-scale convection electric field cannot produce the observed energy spectrum. This result highlights the fact that in order to understand the ring current intensification and energization processes we need to gain knowledge of the detailed evolution of the electromagnetic fields and their time variations.

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