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)
where the first adiabatic invariant
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
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, 1973; Stern, 1975). The intensity of the electric field can
then be related to magnetic activity indices such as Kp (Maynard and Chen, 1975) by writing
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. (1997
) function for the polar cap potential Φ in the form
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.
The drift approximation has been quite successfully applied to model inner magnetosphere plasma
transport and energization during magnetic storms (Liemohn et al., 2001; Jordanova 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., 2005).
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 20 based on results in Ganushkina et al. (2005) 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.
based on results in Ganushkina et al. (2005
![B [ ] E × B V = ---× 2W ∥(B ⋅ ∇ )B + μ ∇B + ----2-- (9 ) eB B](article27x.gif){kind=small}
![[ ( θ) ] sin φIMF ( R )2 Φpc = 1.1 ⋅ 10−4Vs2w + 11.1 ⋅ BIMF sin3-- -------- ---- , (13 ) 2 2 RB](article31x.gif){kind=small}