Unlike the neutral air, the ionised particles are not free to move horizontally, as they are confined by the earth's magnetic field. As a result, any movement of the neutral air in the north-south direction will blow ionisation along the magnetic field. To the north, the increased southerly wind will blow ionisation up the field line, to higher altitudes where the lifetime of ionisation is longer. To the south the increased northerly wind will blow ionisation down the magnetic field line to lower altitudes where the ionisation is more quickly destroyed.
If this phenomenon is observed with two ionosondes, we would expect to see a higher, more dense F-layer to the north of the eclipsed region, while to the south, the F-layer would be expected to be lower in both altitude and density.
Under the path of the eclipse itself, the behaviour of the F peak is highly dependent on the resulting wind. Indeed, previous ionospheric observations during eclipses have observed the peak layer density to increase, decrease or remain unchanged. Not one of the previous campaigns however had the capability to measure the winds causing these effects, and the behaviour of the peak remains the subject of theory.
The following image links to an animation of the predicted changes in ionospheric density at the height of peak ionisation.