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| Titel |
On the current-voltage relationship in fluid theory |
| VerfasserIn |
P. Janhunen  |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
0992-7689
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| Digitales Dokument |
URL |
| Erschienen |
In: Annales Geophysicae ; 17, no. 1 ; Nr. 17, no. 1, S.11-26 |
| Datensatznummer |
250013641
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| Publikation (Nr.) |
 copernicus.org/angeo-17-11-1999.pdf |
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| Zusammenfassung |
The kinetic theory of precipitating electrons
with Maxwellian source plasma yields the well-known current-voltage relationship
(CV-relationship; Knight formula), which can in most cases be accurately
approximated by a reduced linear formula. Our question is whether it is possible
to obtain this CV-relationship from fluid theory, and if so, to what extent it
is physically equivalent with the more accurate kinetic counterpart. An answer
to this question is necessary before trying to understand how one could combine
time-dependent and transient phenomena such as Alfvénic waves with a slowly
evolving background described by the CV-relationship. We first compute the fluid
quantity profiles (density, pressure etc.) along a flux tube based on kinetic
theory solution. A parallel potential drop accumulates plasma (and pressure)
below it, which explains why the current is linearly proportional to the
potential drop in the kinetic theory even though the velocity of the accelerated
particles is only proportional to the square root of the accelerating voltage.
Electron fluid theory reveals that the kinetic theory results can be reproduced,
except for different numerical constants, if and only if the polytropic index
γ is equal to three, corresponding to one-dimensional motion. The
convective derivative term v·∇v provides the
equivalent of the "mirror force" and is therefore important to include
in a fluid theory trying to describe a CV-relationship. In one-fluid equations
the parallel electric field, at least in its functional form, emerges
self-consistently. We find that the electron density enhancement below the
potential drop disappears because the magnetospheric ions would be unable to
neutralize it, and a square root CV-relationship results, in disagreement with
kinetic theory and observations. Also, the potential drop concentrates just
above the ionosphere, which is at odds with observations as well. To resolve
this puzzle, we show that considering outflowing ionospheric ions restores the
possibility of having the acceleration region well above the ionosphere, and
thus the electron kinetic (and fluid, if γ=3) theory results are
reproduced in a self-consistent manner. Thus the inclusion of ionospheric ions
is crucial for a feasible CV-relationship in fluid theory. Constructing a
quantitative fluid model (possibly one-fluid) which reproduces this property
would be an interesting task for a future study.
Key words. Ionosphere (ionosphere-magnetosphere
interactions; particle precipitation) · Magnetospheric physics
(magnetosphere-ionosphere interactions) |
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