A magnetic bottle is an arrangement that permits to confine charged particles. Here you can find a review for charged particle rotating in a magnetic field and at the bottom of the page a description of the magnetic bottle:
Let's use this image since it's more clear
What results from this picture is that a particle inside a magnetic bottle makes a circular motion following magnetic field lines which have a sort of cylindrical symmetry as it's expressed by this simulation:
So you can imagine to put the earth in the middle of the picture: in this way the two rings are to the two magnetic poles.
In the case of a Van Allen's radiation belt motion simulation (Radiation Belt as a Magnetic Bottle), particles move around a magnetic field lines instead of moving around the earth.
But from this simulation:
you can see that a motion around a magnetic line is possible but i can't understand heuristically why.
So the questions are:
- how a particle can move around a magnetic line if there is closed to it another one? so how can a particle choose around which line move (losing in this way the cylindrical symmetry)?
- why the two type of motions are in disagreement?
Is the motion in the first picture just an approximation perhaps?