PRIMARY ELECTRON TRAJECTORIES IN A MULTIPOLAR DISCHARGE

In a two-dimensional magnetic field (x,y), there exist two invariants of the motion: the velocity vector modulus (v//o) and the canonical z momentum (P//z). If vertical P//z vertical mv//o is greater than one, the motion is limited to a region near the magnets (the particles are trapped). If it is smaller than one, the particles can reach zero magnetic field regions. Numerical integration of the equations of motion shows that if vertical P//z vertical mv//o is sufficiently great, guiding center theory describes fairly well the main features of trapped trajectories, even in regions where the validity conditions are not completely fulfilled. The trapping of a previously free charged particle by a multipolar field results from a variation of vertical P//z vertical /mv//o due to external causes. After considering the effect of collisions, we show that a small electric field, E//z, can lead to large populations of trapped particles.