“The earth’s magnetic field then accelerates these electrons to near-relativistic speeds”
This alone tells me you don’t know what you are talking about. I don’t mean this as criticism of you. You read this someplace and believed it. It just isn’t true...
A magnetic field will bend (deflect) the path of an electron. It will not accelerate it. It takes an electric field to accelerate an electron.
Velocity is a vector, remember?