A model of auroral arcs is presented. It is assumed that the magnetic field lines into the auroral oval are loaded with kev electrons, that precipitating auroral electrons locally constitute a net field‐aligned current, and that currents close in the outer magnetosphere by polarization currents. The model predicts that a flux tube convecting through the oval will undergo a highly nonlinear oscillation that produces standing waves, the auroral arcs. The conditions to be satisfied are (1) Ohm's law in the ionosphere, (2) electron number conservation in the ionosphere, (3) electric current continuity, (4) the tendency for electric fields to map between ionosphere and magnetosphere. The physics of condition 4 is not understood, but it is probable that arc‐like solutions exist for several models. A specific model, including perfect mapping of electric fields, is studied. The solutions to this model closely resemble the arcs. Predicted in agreement with observation are arc thickness, inter‐arc spacing, and the electric field behavior. The thickness and the spacing are functions of both the amplitude of the oscillation and the physical properties of the system. However, thickness times spacing is a function of the physical properties only, and the thickness divided by the spacing is a function of amplitude only. Presumably these and other quantitative relationships can be checked by observations.

A mechanism is presented by which X lines cause auroral arcs. The mechanism should apply to most existing steady state merging models if the fluid is an electron‐ion plasma. Hall electric fields are produced in the plane perpendicular to the X line in order to equalize the flow of electrons and ions through the diffusion region despite their differences in inertia. It is suggested that these electric fields map along magnetic field lines to the auroral acceleration region at much lower altitudes. Since mapping along field lines occurs by oblique Alfvén waves, stationary in the convective flow, there are accompanying Birkeland currents. The currents and fields provide the upper boundary condition for the auroral electron acceleration region believed to exist above discrete arcs. A solution of a flow problem, similar to the merging situation, by Sonnerup and Wang is used to show that the voltage is sufficient for auroral arcs and that momentum transfer between the diffusion and exterior regions is consistent with the production of “paired electrostatic shocks” for a rigorous solution. An integration along a path through the diffusion region for the general case shows that auroral‐sized voltages are expected in both collisional and collisionless cases. Finally it is shown that the ion‐inertial scale length is appropriate for the diffusion region in the collisionless case, and maps to the ionosphere as ∼10 km.

The electric field data in the polar cap do not display the expected mirror symmetry for positive and negative values of the solar magnetospheric y component of the interplanetary magnetic field, suggesting that an additional effect is squeezing the antisunward flow toward the dawnside of the polar cap. It is shown that a conductivity decrease toward the nightside will produce such an effect. Results are both for a model with a discontinuous decrease in density and for models with a smooth exponential decrease in conductivity with distance across the polar cap. Steeper conductivity gradients cause stronger squeezing of the flow toward the dawnside of the polar cap. Outside the polar cap the return flow towards the dayside spreads over a wider latitude range on the dawnside than on the duskside. Comments on a paper by J. P. Heppner, 'Polar cap electric field distributions related to interplanetary magnetic field direction,' J. Geophys .. Res., 78, 4001, 1973. Atkinson and Hutchison' Brief Report 729 Wolf, R. A., Effects of ionospheric conductivity on convective flow of plasma in the magnetosphere,

A recent model of polar substorms suggests they are the result of an impulsive recombination of magnetic field lines across the neutral sheet in the tail of the magnetosphere. The flow of flux tubes within the magnetosphere is shown to be dominated by the discharging action of the ionosphere on flux tubes. This fact enables an approximate flow equation for flow within the magnetosphere to be developed by integrating along flux tubes. This equation is applied to the above model of polar substorms and is shown to give reasonable agreement with the following experimental observations: (i) the velocity and flow pattern of auroral patches; (ii) the height and shape of the auroral breakup bulge; and (iii) the bay current system, including the westward electrojet under the assumption that the westward electrojet is current‐induced by the southward component of flow of flux tube feet in the high conductivity strips under auroral arcs. These strips are expected to exhibit a Cowling conductivity. The westward traveling surge is probably caused by an increasing width of the recombination slot in the tail of the magnetosphere. The current flow down field lines and through the ionosphere results in a density (and hence pressure) decrease in the neutral sheet at the west edge of the recombination slot, and thus causes a corresponding westward propagation of the west edge of the recombination slot. Application of the flow equations to the viscous bounday layer problem indicates an exponential falloff in velocity from the magnetosphere boundary with a 1/e distance of 5 × 104 m.

The result of an attempt to express the net energy input to the magnetosphere‐ionosphere system in terms of upstream solar wind parameters is presented. Seven types of electric current system within the magnetosphere are defined and discussed, and it is found that only three of these systematically transfer energy into the magnetosphere from the solar wind. One of these is the magnetotail current system, and the other two form the field‐aligned current observed at the northern edge of the auroral oval. In order to calculate energy input, reasonable models are developed for each of a number of magnetospheric processes. These include (1) flow through the shock, flow in the magnetosheath, and merging; (2) reconnection and the neutral line in the magnetotail; and (3) Alfven layer shielding of the inner magnetosphere from convective flow, nightside pressure balances, and precipitation, and hence from these the width and conductance of the nightside auroral oval. The use of these models permits the development of explicit equations for the total energy input to the magnetosphere‐ionosphere system in terms of upstream solar wind parameters. The interplanetary magnetic field strength and orientation and the solar wind velocity dominate energy input via the nightside plasma sheet. The density of the solar wind is also an important variable for the energy input by the high‐latitude current systems.