The ideal magnetohydrodynamic equilibrium of a diffuse high-β stellarator is investigated by an asymptotic expansion in the inverse aspect ratio. The basic new feature of the calculation is that the lowest order flux surfaces are assumed noncircular and nonconcentric. Equilibria are found for a wide range of experimentally interesting parameters. Finally, the connection of the high-β expansion with the low-β stellarator expansion is discussed in detail.

The investigation of the spectrum of the simplified differential equation describing the variation of the amplitude of the ideal MHD ballooning instability along magnetic field lines constitutes a multiparameter Schrödinger eigenvalue problem. An exact eigenvalue relation for the discrete part of the spectrum is obtained in terms of the oblate spheroidal functions. The dependence of the eigenvalues λ on the two free parameters γ2 and μ2 of the equation is discussed, together with certain analytical approximations in the limits of small and large γ2. A brief review of the principal properties of the spheroidal functions is given in an appendix.

A magnetic plasma confinement configuration aimed at sustaining high-current densities is proposed. It involves a small triangular and elliptic deformation imposed over a circular cross section of the plasma column by a surrounding conducting shell at close distance. The stability against kink modes is analyzed and shown to be the same as that of an equivalent plasma column with equal area, but circular cross section. An assessment of the over-all stability of this configuration points to a significant improvement, in terms of the Ohmic heating resulting from the induced current, over the known configurations with circular cross section.

A plane slab of current-carrying plasma is generally shown to be stable against ideal magnetohydrodynamical modes. It is shown that some of the stability criteria appearing in the literature and contradicting this fact can be brought to bear on the stability of the tearing mode. In this connection, simple stability diagrams are shown for the tearing mode in plane and cylindrically symmetric force-free magnetic fields.