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[1] The distribution of current-driven electrostatic potentials along auroral magnetospheric flux tubes is studied analytically, based on the principles of quasi-neutrality and kinetic orbital motion of electrons and ions governed by inertia, electric forces, and magnetic mirror forces. When certain particle accessibility conditions are fulfilled, the kinetics determines the electron and ion number densities as unique functions of position along the flux tube and local potential. These functions are used to define potential profiles for which electron and ion number densities everywhere match, or alternatively positions where potential jumps (double layers) may occur. Magnetospheric and ionospheric particle sources in the form of Maxwellians with loss cones depending on the total voltage drop are considered, as well as trapped particles. The potential profile generally comprises a potential jump that accounts for a sizeable fraction of the total voltage drop (only by assuming unrealistic velocity distributions of the magnetospheric electron source can solutions without a jump be found). The jump may typically occur around an altitude of 1 RE, an altitude that increases with density of the ionospheric source and that decreases with increasing density of trapped, secondary, and backscattered particles and total voltage drop along the flux tube. Below the potential jump, only small potential variations occur. Above the potential jump, the potential falls off gradually, asymptotically linear in magnetic field intensity. Only a small percentage of the potential drop occurs above an altitude of a few RE, but the weak field extending to higher altitudes is essential for quasi-neutrality and for the current-voltage relationship (discussed in a previous paper). Above the potential jump, the number density of particles is reduced as compared to regions without current flow and potential drops. Depending on the density of the ionospheric source, solutions are possible for total potential drops much larger than the temperature of the magnetospheric electron source. While full accessibility for the mirroring electrons tends to be locally violated, accessibility for all particles within the source cone is fulfilled in these solutions, so the current-voltage relationship does not depend on the shape of the potential profile. Some comments are also made on transient conditions when there is no time for transport of neutralizing ions from the ionosphere.

[1] The current–voltage characteristic of magnetospheric magnetic flux tubes is studied under rather general conditions, assuming the current to be carried by collision-free particles experiencing inertia, electric forces, and magnetic mirror forces. The approach is that of the powerful kinetic “orbital motion” theory of current collectors in plasma as developed by H. M. Mott-Smith and I. Langmuir in 1926. When C. Davisson's 1925 condition on particle access is fulfilled, the total voltage drop is uniquely determined from the current by kinetic/geometric considerations only, without considerations of the actual space charge and electrostatic potential distribution. For any velocity distribution that is isotropic within the source cone, the current–voltage characteristic is linear for sufficiently small currents. The nature of the corresponding global flux tube electric resistance is discussed. The current–voltage characteristic is given for a variety of distribution functions (where the Maxwellian case corresponds to that studied by S. Knight in 1973) including distributions with a reduced (nonisotropic) flux in the source cone. The current–voltage characteristic is also discussed for cases where the Davisson condition is not fulfilled, when the solution method provides a lower bound on the voltage for a given current. Making assumptions on the altitude extent of the voltage drop, we can also define an upper bound on the voltage for a particular current. The magnetospheric source of particles should be taken to be located at the top of the acceleration region in order to fulfill the Davisson condition. This may limit the effective magnetic mirror ratio, such that the applicability of the linear approximation to the current–voltage characteristic is more restricted, and the saturation current is moderately small, which may lead to overvoltages, a redistribution of the current, or an increased extent of the acceleration region. Joining solutions that piecewise fulfill the Davisson condition, we can derive the current flow for a rather wide range of prescribed potential distributions. Earlier works on the Knight mechanism and related theories for determining the voltage drop along a flux tube are discussed. Determination of the electrostatic potential distribution, and verification of the Davisson condition, requires considerations of the space charge (Poisson equation), to be discussed in a second paper.

The authors present an analysis using statistical methods of a large number of observations of weak double layers and solitary waves in auroral regions, made from Viking spacecraft. Such structures, supporting non-neutral plasma regions, exhibit voltage drops along field lines, and are a possible explanation for ion acceleration mechanisms in the auroral region. The authors show that these events are found in conjunction with beams of upward flowing ions. They are primarily seen in the altitude range 7 to 11,000 km. They are seen in groups which may have perpendicular extents of a few km.

When the Viking satellite crossed the auroral acceleration region, where the electron density is supposed to be less than a few particles per cubic centimeter, a strong spin modulation of the signal of a positively biased Langmuir probe was observed. This spin modulation is better correlated with the angle of the antenna to the geomagnetic field than with the angle to the Sun. A simple model based on the photoelectron orbits in a spherically symmetric electric field, in the presence of a uniform magnetic field, gives the right phase and amplitude of the extrema. In addition, it shows that the perturbation could be negligible when the antenna is perpendicular to the magnetic field, provided that the photoelectron sources are far enough from the magnetic field lines connected to the probe (about 2 Larmor radii). As a consequence, we deduce important information for the design of experiments devoted to very low density measurements, and we show that the magnetic field may be a crucial parameter for the study of the exchange of photoelectrons between parts of a satellite. The most important result of this study is to facilitate the probe density measurements inside the acceleration structures. It is shown that in these regions the cold plasma density is depleted, with a density of thermal electrons below 5 cm−3 at altitudes between 6500 km and 8500 km. When auroral kilometric radiation (AKR) is generated inside such structures, the density of thermal electrons can be below 1 cm−3. The edges of the structures are sharply defined, and the gradient scale can be as low as 1.4 km. This is the first time that density measurements of thermal electrons have been realized inside clearly identified AKR sources, with appropriate resolution.

Birkeland (field-aligned) sheet currents flowing into and out of the auroral oval as reported by Zmuda and Armstrong (1974) are integrally associated with convective motion of plasma in the magnetotail. It is demonstrated that these currents can be driven by energy supplied by the braking of this convective motion of the plasma sheet particles as they drift toward the flanks of the magnetosphere. In the ionosphere the sheet currents close as Pedersen currents, resulting in the dissipation of power, while far from the earth the closure currents, which provide the braking force for the plasma, flow in the plasma sheet approximately normal to the neutral sheet out to radial distances of about 80 RE. During periods of moderate magnetospheric activity the Birkeland currents result in a rate of dissipation of convective energy of the order of 10 GW.

A model current system, in which magnetospheric and ionospheric sections are connected by currents flowing along the geomagnetic field lines, is proposed to represent the current system responsible for polar magnetic substorms. The magnetic perturbations from model current systems of this type are studied in terms of elementary loops, whose magnetic effects are evaluated numerically. The influence of currents induced in the ground is studied for a time-independent case, but it is found that such effects do not change the gross character of the perturbation pattern. Using a north-south chain of stations and an appropriate coordinate system, the model predictions are compared with the magnetic variations observed during some substorms. It is found that the model is capable of explaining the gross features of the magnetic perturbation pattern observed. However, at times there are minor deviations from the predictions, which suggest the presence of additional ionospheric and magnetospheric current systems.

Two different methods are discussed for taking geomagnetic effects into accourt when evaluating the counting rate of a cosmic-ray detector for a given anisotropic radiation source. The applicability of these methods is studied, and some properties of the asymptotic cone of acceptance are found by performing the transformrtion through the geomagnetic dipole field of the infinitely small solid- angle elements that constitute the acceptance cone. A solid angle at the detector is greater than the corresponding asymptotic cone for all latitudes, angles of incidence, and energies except immediately above the geomagnetic cutoff. This focusing effect is especially good for high-latitude detectors, which thus have the best resolving power. (auth)

Certain observations indicate that the auroral electrojets are confined to the auroral arcs. A model of an arc is presented in which the height variation of the auroral ionization is taken into account and vertical currents are allowed to flow. The current flow in the arc is investigated, and the electric field or wind velocity field required to drive the currents is computed for two different cases: in one, the current flow between the auroral-zone ionosphere and the outer magnetosphere is assumed to be limited and electric fields occur along the magnetic field lines in the magnetosphere; in the other, the conductivity along the field lines is assumed to be perfect. In the first case the electrojets are probably driven by a longitudinal electric field in the magnetosphere. In the second case the driving electric field must be a meridional field in order to explain the observations, and strong sheet currents must flow along the field lines that connect the auroral ionosphere to the outer magnetosphere.