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The ideal magnetohydrodynamic stability of the diffuse linear pinch is studied in the special case when the poloidal magnetic field component is small compared with the axial field component. A two‐term approximation for growth rates is derived by straightforward asymptotic expansion in terms of a small parameter that is proportional to (Bϑ/rBz). Evaluation of the second term in the expansion requires only a trivial amount of additional computation after the leading‐order eigenvalue and eigenfunction are determined. For small, but finite, values of the expansion parameter the second term is found to be non‐negligible compared with the leading term. The approximate solution is compared with exact solutions and the range of validity of the approximation is investigated. Implications of these results to a wide class of problems involving weakly unstable near ϑ‐pinch configurations are discussed.

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 guiding center plasma description of an isotropic, collisionless plasma is used to study the linear stability of the diffuse screw pinch in the special case when the poloidal magnetic field component is small compared with the axial magnetic field component. A two‐term approximation for growth rates is derived from the linearized guiding center plasma equations by straightforward asymptotic expansion in terms of a small parameter that is proportional to (Bϑ/rBz)‖r=0. The two‐term approximate solution is compared with exact solutions and the range of validity of the approximations is examined. The result obtained from the guiding center plasma model is compared and contrasted with that from ideal magnetohydrodynamics. It is shown that the isotropic guiding center plasma may be more unstable or less unstable than ideal magnetohydrodynamics for the same configuration, depending on the parameters.