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Ann. Geophys., 24, 325-338, 2006
www.ann-geophys.net/24/325/2006/
© European Geosciences Union 2006
Current-voltage and kinetic energy flux relations for relativistic field-aligned acceleration of auroral electrons
S. W. H. Cowley
Department of Physics & Astronomy, University of Leicester, Leicester LE1 7RH, UK
Abstract. Recent spectroscopic observations of Jupiter's "main
oval" auroras indicate that the primary auroral electron beam is routinely
accelerated to energies of ~100 keV, and sometimes to several hundred
keV, thus approaching the relativistic regime. This suggests the need to
re-examine the classic non-relativistic theory of auroral electron
acceleration by field-aligned electric fields first derived by Knight
(1973), and to extend it to cover relativistic
situations. In this paper we examine this problem for the case in which the
source population is an isotropic Maxwellian, as also assumed by Knight, and
derive exact analytic expressions for the field-aligned current density
(number flux) and kinetic energy flux of the accelerated population, for
arbitrary initial electron temperature, acceleration potential, and field
strength beneath the acceleration region. We examine the limiting behaviours
of these expressions, their regimes of validity, and their implications for
auroral acceleration in planetary magnetospheres (and like astrophysical
systems). In particular, we show that for relativistic accelerating
potentials, the current density increases as the square of the minimum
potential, rather than linearly as in the non-relativistic regime, while the
kinetic energy flux then increases as the cube of the potential, rather than
as the square.
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