There's a LOT you don't understand.
A good physics course would help you, IF you made the effort to understand the meaning of the equations and concepts.
The earth's magnetotail contains trapped solar wind electrons and protons and these are then accellerated by the constant buffeting of the magnetic field - buffeted by fluctuations in the solar wind. It's like being at the end of a bullwhip. The charged particles are flicked around by waves that ripple down the magnetotail...