Abstract: An apparatus and method for controlling charged particles. The charged particles comprise electrons and positive ions. A magnetic field having only point cusps is used to confine energetic injected electrons and so to generate a negative potential well. Positive ions injected into or created within the negative potential well are trapped therein. The magnetic field is generated by current-carrying elements arranged at positions spaced from but closely adjacent and parallel to edges of a polyhedron which has an even number of faces surrounding each vertex or corner. The current-carrying elements are spaced apart at their corners (the vertices of the polyhedron) so as not to touch, and the containing structures for the current-carrying coils of the magnetic-field-providing system are conformal to the fields so produced. Preferably, the coils are placed on the outboard side of the confining coils so as to increases electron confinement.