Abstract
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.
Highlights
The exchange of momentum between a magnetised conducting body and its outer plasma envelope via the magnetic field requires the establishment of large-scale electric current systems flowing between them
The relativistic expressions given by Eqs. (23) and (26) for the current density and kinetic energy flux of the accelerated population for arbitrary initial thermal energy kT, acceleration energy e, and field strength ratio B Bo beneath the voltage drop, constitute the principal results derived in this paper
Results are shown for the normalised current density and kinetic energy flux versus β= B Bo in the log-log plots in Figs. 2a and b, where the solid lines show values derived from the relativistic general expressions given by Eqs. (23) and (26), while the dotted lines correspond to the non-relativistic approximations given by Eqs. (24) and (27)
Summary
The exchange of momentum between a magnetised conducting body and its outer plasma envelope via the magnetic field requires the establishment of large-scale electric current systems flowing between them. On some occasions, the accelerated electron energies are deduced by these means to reach to at least a few hundred keV, approaching the relativistic regime These observations suggest the need to extend Knight’s (1973) theory to encompass relativistic situations, in which the plasma electrons are either very energetic initially, or become so due to the presence of field-aligned potentials which are comparable with or exceed the electron rest energy (∼511 keV). Such field-aligned potentials are not implausible in Jupiter’s magnetosphere, for example, since the total cross-field potential across the outer and middle magnetosphere region is of order ∼10 MV In this paper we present a relativistic formulation of Knight’s (1973) kinetic theory, and derive exact analytic expressions for the field-aligned current density (number flux) and kinetic energy flux of the accelerated particles, for arbitrary initial temperature, accelerating potential, and magnetic field strength beneath the voltage drop
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