Interchange, rotational, and ballooning stability of long-thin axisymmetric systems with finite-orbit effects

The stability of axisymmetric tandem mirror plasmas with respect to interchange, rotational, and ballooning modes is investigated in the paraxial approximation. The stabilizing effects of finite orbits, rigid energetic fast-drifting electrons, nearby conducting walls, and line-tying by a cold plasma halo are incorporated. Numerical calculations are performed to construct equilibria with finite plasma pressure and to determine linear stability by integrating a two-dimensional, initial-value equation. These numerical calculations support and extend analytical results. Analytical and numerical stability criteria are obtained.