Magnet Aspect Ratio

All magnets look dipolar at distances greater than the largest dimension of the magnet, but for regions where the plasma is trapped, the aspect ratio strongly determines the curvature of the field lines. One would expect a pancake or oblate magnet to exhibit greater than dipolar curvature at the equator, and a cigar or prolate magnet to exhibit less than dipolar curvature at the equator. Likewise, an oblate magnet should have a radial gradient less than dipolar with a stronger near field, whereas a prolate magnet would have a larger gradient and a weaker near field. These two competing effects determine the thickness of the trapped ions (stronger curvature produces thinner trapped layers) as well as the radial distance of the plasma annulus (weaker fields and stronger gradients lead to smaller annuli). Thus we might expect that the oblate magnet provided the best trapping of the plasma.

In figure we show the vacuum magnetostatic field lines for these magnets.