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The Earth's Magnetosphere

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 $E \times B$ drift around the space charged flux tube. More important is the $E_{\vert\vert}$ 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 ($\sim 10^4$/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 $\nabla
B$ 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 $\sim 1$ 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 $\nabla
B$ 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 $T_{\vert\vert} > T_\perp$.

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 $\nabla
B$ 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 $K_{0\vert\vert}$ for this population. Using $45^\circ$ 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 $O^+$ enrichment [22,23], its proportionality to Dst [24], and the two time-constant recovery of Dst [22].

next up previous
Next: Astrophysical Jets Up: The spinning terrella plasma Previous: Whipple's Second Equilibrium
Rob Sheldon 2001-03-09