Magnetic helical fields in a Tokamak

Three sets of helical windings have been installed around the vacuum chamber of the tokamak at the Atomic Energy Corporation of South Africa Limited (AEC) at Pelindaba. A current through these windings creates magnetic fields inside the torus. The magnetic fields and magnetic surfaces due to this type of winding are discussed. The results have immediate relevance to the experiment which is currently running at the AEC. The experiment running at the AEC is described. A literature review is given which describes the publications on the coordinate system which is used and those published on the theory of helical toroidal fields. A detailed description of the coordinate system is given. The analysis is done in the so called hyperbolic toroidal non-coordinate system. Its definition is given, the toroidal parameters are discussed and the relevant line element is given. The literature which uses this coordinate system is discussed. The theory describing the magnetic field of a line current on the surface of a torus is elaborated on. The exposition and developement of the theory is presented. Working in the hyperbolic toroidal coordinate system, the Laplace equation is solved with appropriate boundary conditions. Finally, the theoretical expressions derived for the magnetic field are computed numerically and these results are compared with the experimental measurements. An excellent agreement is observed. 39 figs., 24 refs