No Pinching: Topological Constraints on Polar Cap Patch Formation

The creation of topologically separated patches requires a physical mechanism to tear the electron density contours. This paper begins with common assumptions about the F-region ionospheric plasma, including the electrostatic condition, and examines which sorts of topological reconfigurations of plasma density contours are possible given those assumptions. This paper shows that a particular vector field called the contour tracing field evolves in a manner that is analogous to magnetic fields in ideal or resistive magnetohydrodynamics (MHD). In the case with no net production or loss of plasma, the contour tracing field is flux preserving, line preserving, and conserves its topology exactly like magnetic field lines in ideal MHD. When a net sink of plasma is present, it creates the possibility of contour reconnection at certain singular points. The concept of contour reconnection is analogous to reconnection at an X-point in resistive MHD. The results of this paper imply that spatiotemporal variability in the plasma drifts alone can never tear electron density contours into topologically separated patches, and any contour tearing mechanism must necessarily involve net production or loss of plasma. Any theory of polar cap patch formation that only involves variable electric fields imposed from the magnetosphere onto the ionosphere is incomplete. There is no pinching mechanism by which variable electric fields can pinch off topologically separated islands of plasma. Descriptions of polar cap patch formation must consider the coupled physical and chemical dynamics of the magnetosphere-ionosphere-thermosphere system to explain topological changes of electron density contours.