No Pinching: Topological Constraints on Polar Cap Patch Formation

Abstract The creation of disconnected patches requires a physical mechanism to pinch 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 and are not 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. In the case with no net production or loss of plasma, the contour tracing field is flux preserving, line preserving, and conserves its number of connected components 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 pinch electron density contours into disconnected patches, and any contour pinching 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 disconnected 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.