On arc-polarized structures in the solar wind
A theoretical model is proposed to account for some of the behavior of arc-polarized magnetic structures seen in the solar wind. To this end, an exact analytical solution is developed that describes infinite plane wave trains of arbitrary amplitude in a plasma governed by ideal Hall MHD. The main focus is on intermediate-mode wave trains, which display double-branched magnetic hodogram signatures similar to those seen in the solar wind. The theoretically derived hodograms have field rotation in the ion-polarized sense at a slightly depressed field magnitude on one branch and an electron-polarized rotation at a slightly enhanced field magnitude on the other branch. The two branches are joined at the two "turning points", at which the normal flow is exactly Alfvénic. The behavior is accounted for in terms of the opposite dispersive properties of ion and electron whistlers. The hodograms derived from the theory are shown to compare favorably with those of one event, observed by the Cluster spacecraft near the ecliptic plane, and one event at high heliographic latitude observed by the Ulysses spacecraft. However, these two observed structures comprise only a single full wave period, approximately from one turning point to the other and then back again. The theory can be used to predict propagation direction (away from, or towards, the sun) from magnetic data alone, provided the sign of the magnetic field component along the wave normal can be reliably determined. Under the same condition, it also predicts whether the ion-polarized branch should precede or follow the electron-polarized branch. Both behaviors are seen in the solar wind. The major shortcoming of the theory is that it fails to reproduce the observed saw-tooth like time series for the magnetic field, in which the field rotation is rapid in the ion sense and slow in the electron sense. Instead, the theory gives about the same rotation rates. Possible explanations for this discrepancy are discussed. Also discussed is the fact that the magnetic field measurements by Cluster, while giving high quality determinations of normal direction and normal field component for each of the four spacecraft, indicate a reversal of the normal field component and the predicted propagation sense during the event, as well as a wide spread in the four normal vector orientations.