Mars does not have a bipolar magnetosphere
Unlike Earth, Venus, and the Gas giants, Mars does not have an active and dominantly bipolar magnetosphere as a result of an internal geodynamo.
Instead it has a patchy magnetic field, as measured by recent spacecraft.
There is NO polar concentration of charged particles.
Therefore your model fails.
As I often say, Mars is NOT Earthlike, it is Mars-like. You have to understand the physics of the planet before you try to use it to explain observations. Transplanting what works on Earth to Mars simply does not work...