In a vacuum dipole field, this space charge is a stable equilibrium,
however, at the Earth other plasmas respond to the space charge electric
field. Plasma on neighboring flux tubes would experience a perpendicular
polarization electric field force causing an drift around
the space charged flux tube. More important is the
acceleration
given to plasma on the same field line, but earthward of this structure,
that is, inside the hot ion mirror point. The first specie to respond is
the lightest, the electrons. If the space charge were composed of ions,
then electrons would be accelerated from the ionosphere toward this
positive space charge. Their momentum, as well as the ``reverse Debye
shielding effect'' [16] in which an accelerated phase space
distribution must decrease in density, cause an ``overshoot'' of the sharp
peak in ions.
Timescales are essential in discussing any dynamic instability. The
electrons, despite their speed, require several milliseconds to travel the
several thousand kilometers from the ionosphere. Since neutral densities
are virtually negligible at these altitudes, and since the plasma
densities are also very small (/cc), thermalization and
trapping of the electrons in the vicinity of the ion spike also requires
milliseconds to seconds to occur. Therefore, one can approximate the
potential as a spike of positive potential surrounded by a distended cloud
of hot electrons that overshoot.
The addition of a spike and an overshoot, we surmise, leads to a ``Mexican
hat'' potential distribution, whose gradient gives opposing electric
fields suggestive of a ``double layer''. The double layer should be
transient and vanish on an electron collision/scattering timescale if it
were not for the differing drift speeds of the ions and the
electrons, which depend on the sign of the charge and the perpendicular
energy. Since the electrons have opposite sign and little perpendicular
energy, having been accelerated only parallel to the field, the ions drift
away from the electrons on a
second time scale, and begin the
process anew.
The electrons that have pitch angle scattered in the vicinity of the ions
are left behind as the ions drift away, and find themselves
not in the loss cone, but trapped in the magnetosphere. Now the fate of
the electrons is similar to that of the ions that began the process,
finding themselves in a space charge potential that is driving them back
into the ionosphere. For these pitch angle scattered electrons, however,
the mirror force restrains them from precipitating, which is to say, some
electrons have scattered out of the loss cone to become trapped. This
gives them sufficient time to scatter and form a neutral plasma, albeit
one with
.
The inner edge of the plasma sheet is one region of the magnetosphere that
should be susceptible to QNC. Here, hot plasma is continually injected
into the dipolar magnetosphere and drifts become important to
the dynamics of the region, perhaps leading to the formation of double
layers in the auroral acceleration region. Consequently, geomagnetic
storms might be an extreme example of QNC since, during main phase, the
separatrix between corotating and convecting plasma (the Alfvén layer)
moves Earthward to as little as 2.5 Re [17].
Simultaneous POLAR / CEPPAD observations of 40keV ionospheric field aligned
beams with convected 90 keV plasmasheet ions [8] during a
geomagnetic storm led to the proposal of QNC. Sheldon and
Spence found that the ratio of trapped ion energy to beaming ion energy
was constant over many thousands of kilometers, indicating that the
trapped ions are creating the 40kV parallel potentials required to extract
and accelerate the ionospheric species. As a check on the mechanism,
we note that their trapped ion pitch-angle distribution show a
distinct cliff between 40 and 50 degrees, which would correspond to the
maximum for this population. Using
as a best estimated
pitchangle,
this predicts that exactly half the trapped ion energy is available
to produce parallel potential and accelerate cold ionospheric ions toward
the equator, which is consistent with the 40 keV ions actually measured.
(A better calculation would require integration of the measured equatorial
pitch-angle distribution to estimate the total potential drop, which would
likely be smaller than our upper limit estimate above.)
This QNC instability, then provides a
simple explanation for many features of geomagnetic storms seen during
main phase including duskside Pc1 waves [18], localized X-rays
[19], ring current filling [20], the rapid Dst
enhancement [21], the drop in average energy of ring current
ions [22], the the enrichment
[22,23], its proportionality to Dst [24],
and the two time-constant recovery of Dst [22].