Abstract
Endless lines of force confined in toroidal plasma containing geometries are subject to periodic perturbations by field errors which can produce integral, half-integral, third-integral, and quarter-integral, etc. resonant-like disturbances on the spiralling line of force. A formal analogy exists between the topology of a trace of a line of force in the co-ordinate space of a plasma-confining region and the trace of a phase point in the phase space for a particle orbit in an accelerator. The methods used for determining stability limits for particles in periodic accelerators are thus applicable to the problem of confining lines of force in stellarators and pinches. Examples are given and computer methods are described for typical stellarator configurations subject to a variety of field errors.