Propagation via an aurora is a lesson in geometry, and specifically ray tracing.
First, let’s take the vertical plane.
A station A to the south of the aurora will naturally have to point northwards to have its signals returned. It should have a low launch angle. Ideally this station, as with all stations, should have little foreground or mid-path obstructions that would add diffraction loss that would eat into the path budget.
Maths allows a quick calculation to suggest that the distance in a normal troposphere to the reflection point in the aurora is about 600km. This assumes a 10-degree angle to the horizon.
Stations around Station A would of course be able to likewise point north and hold a QSO with Station A. For a northern station to hear Station A, it would need to be able to elevate its antenna otherwise the antenna vertical plane loss will reduce the received signal below that usable. Few stations have antennas that can be elevated.
Both theory and practice suggest that for some states of the troposphere, the wave launched from Station A on its way to the ionosphere will be refracted towards the Earth, thereby travelling further to the reflection point at the aurora. Maximum distances of 1,000km are suggested. This is shown suggesting communication possible with more northern stations such as Station C. Alternatively, of course, this means that more southerly stations can participate and, in the diagram, the auroral columns would move right to bring Station C into play. The horizontal plan is equally interesting.
We see in the above diagram Station A to the south of the UK pointing north.
For every station, there is a locus of points where reflection from the auroral columns is possible. The strongest returns will be due south, but communication will also be possible, for example, with a station in northern Norway. To do this, the UK station would need to beam east of north. For communications, this station would need to recognise that there’s an aurora in progress and point its antennas somewhat west of north.
This then illustrates how a radio amateur would approach communications via an aurora. An estimate of the strength of the aurora and hence how far south the radio auroral oval has sunk leads speculation about likely beam angles. If it’s a strong aurora, beaming east from the UK will enable QSOs with northern European stations. Likewise, beaming west will enable QSOs with Greenland and Canada.
Past experiences with auroras suggest maximum path lengths under strong auroras of around 3,000km.
On the other hand, a weak aurora will enable QSOs up and down the UK.