Why can we not see auroras at lower latitudes?

[MozAngeles]

So I've been thinking about how the magnetic fields from the Earth create a magnetic mirror which accelerates the the particles in the atmosphere causing them to ionize and thus produce the auroras we see. But it is curious to me that they can only be seen in the upper most northern and southern hemisphere. I would think that the concentration of the accelerated particles would be towards the center of magnetic bottle because the field is pushing the particle away at each end.
So then my question is why can we not see the auroras at lower latitudes? My think was that the bottle juts out so far here that there is not as much interaction with the particles in the atmosphere.
Furthermore, why did this recent geomagnetic storm that produced such a strong solar flare make it such that the auroras were seen at lower latitudes?

 

[rootone]

The magnetic field of the Earth causes solar wind particles to be deflected towards the Earth's magnetic poles.
So this is where the particles become more concentrated, and so are more likely to react with gases in the atmosphere, causing auroras.
In the event of a exceptional solar flare there simply are more particles.
So they can be concentrated enough somewhat further away than usual from the poles to give rise to aurora.
I am in Europe and auroras are only usually seen in the Scandinavia, the most northern part, but they have been recorded as far south as Italy, although rarely.