An Alfvén wave approach to auroral field-aligned currents

The theoretical work presented here was stimulated by the interpretation of auroral field-aligned currents in terms of an Alfvén wave generated in the neutral sheet. Allowing for convection such a wave can be stationary relative to the Earth, and with an Alfvén Mach number of about 10^?2, hydromagnetics predict that the wave normal should be nearly perpendicular to the magnetic field. All the theory presented here is limited to the cold plasma approximation, which is the next step after hydromagnetics, but should have validity here as the wave is propagating into the cold polar wind plasma.The approach is similar to that of Kellogg (1964) except here we consider only the Alfvén mode, and only for Alfvén Mach numbers of about 10^?2. Initially a linear approach was adopted but further computation showed that non-linear effects were responsible for making the current density approximately uniform.The final section presents a plasma sheet boundary crossing selected to illustrate the theory, and is taken from ISEE 1 and 2. The data is such that it permits a first-order estimation of scale sizes to be made in the tail, which in this case was found to be about 1000 km. Subsequent mapping to ionospheric altitudes produced a scale of about a few tens of kilometers.