The variation of the self‐consistent electrostatic potential along the magnetic field is calculated by application of the principle of quasi‐neutrality to the plasma components distributed along an auroral field line. The equilibrium plasma consists of hot anisotropic magnetospheric plasma, ionospheric plasma evaporated or extracted upward by the parallel electrostatic field, and backscattered electrons. It is shown that the above charged particle populations can support a potential difference of up to several Kilovolts between the equator and the ionosphere along an auroral field line. Moreover, the corresponding parallel electric field has the proper signature to account for electron precipitation characteristics. Comparisons between theoretical and observed electron precipitation fluxes lead to estimates for the various physical parameters in the model.

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Given auroral electron and ion distribution functions as observed with satellites in inverted V events, we construct a self-consistent electrostatic field distribution (both parallel and perpendicular to the earth's magnetic field). This field distribution is determined by (1) magnetic mirror forces which cause charge separation for species w•tn different pitch angle distributions; (2) Poisson's equation, which gives the electric field in terms of the charge separation; (3) the ionospheric physics of charge and current conservation, coupled with precipitation sources and recombination losses; and (4) particle distribution functions specified at the equator (and for thermal and backscattered plasma, at the ionosphere). We assume that equatorial particle distribution functions depend on L only through the dependence of the electrostatic potential on L; an assumed factorized form for the potential allows this L dependence to be simply parameterized. These ingredients combine to yield a self-consistent latitudinal scale length of some tens of kilometers, typical for quiet arcs. A variety of particle and field data at and below S3-3 altitude are fit semiquantitatively with the model. We do not consider in this paper physical processes which act in the equatorial magnetosphere, although they could well be connected to the processes we do consider through some sort of feedback. ! Permanent address:In this work we take into account both mechanisms discussed above, as well as some standard simple ionospheric physics of the type usually incorporated into the MHD models. The result is a fairly accurate representation of the particle and field data taken by the auroral satellite S3-3 at some thousands of kilometer altitude. A major new feature is the selfconsistent prediction of latitudinal spatial structure in an auroral arc (indeed, that is what the term 'arc' refers to) near and above the ionosphere; the scale length depends on ionospheric properties as well as properties of the equatorial particle distribution functions. The predicted scale length for the perpendicular electric field is tens to perhaps 100 or 200 kin, more or less in agreement with observations of the largest-sized feature of discrete auroral arcs. (We are not trying to explain the small-scale spatial variations, which are undoubtedly connected to rapid cross-field variations in energetic particle fluxes at very high altitudes.)The reader may recall that the other works referred to earlier either were silent on the question of latitudinal spatial scales [e.g., Swift, 1975Swift, , 1976Kan, 1975] or (for the MHD models) required time-dependent (feedback current) mechanisms to establish the scale [e.g., Sato, 1978; •ltkinson, 1970]. We do not dispute the existence or possible importance of feedback mechanisms, but it seems worthwhile to establish that there is a self-consistent scale length under the static conditions invoked by us.Actually, it is well known that such a scale length is determined by the ionospheric physics if, in addition, the relation betw...

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