Firstly the introductory explanation of theories on the helical axis torus is given briefly. The Pfirsch Schluter current is obtained from the solution of Grad-Shafranov equation. The net axial current in such a so called currentless plasma is shown to be given by the formula q=n/β (n=toroidal period number). Secondly some examples of the technical methods to obtain such a helical axis field configuration are shown. The helical axis torsatron is one of the most interesting devices.
Confinement of toroidal plasmas is studied in the view point of the MHD global instabilities. The instabilities described are the ballooning instability, the disruptive instability and the positional instability. The cause of the instabilities and the methods of the stability control are described by using the result of numerical simulations and experiments mainly of tokamaks.
Recent theoretical contributions to magnetohydrodynamics (MHD) have been reviewed from a view-point of mathematical sciences. Analytical structures of the convective nonlinearity in the incompressible dissipative MHD have been discussed stressing on their relevance to the fundamental theory of dynamical systems.