Field line trajectories in a Skornyakov trap

Abstract

Skornyakov has proposed a magnetic trap in which a spiral conductor connects diametrally opposite points on the inside surface of a superconducting sphere. He has argued that such a system will have nested toroidal magnetic surfaces and that these surfaces will have favourable stability properties both in terms of ‘average minimum B’ and of ‘shear’. Further he has maintained that the field distribution in such a trap can be closely reproduced by substituting an outer return spiral for the superconducting sphere and traps of this technically simpler type have been constructed. In this note we discuss the results of numerical calculations of the trajectories of magnetic field lines in such a two-spiral trap. We find that there are always some field lines originating near the centre of the system which leave it after one or two transits across the machine. Other lines are contained but trace out surfaces which are not topologically toroidal. Thus traps of the two-spiral type will not contain plasma effectively.