Stability of a class of bifurcated, magnetohydrodynamic free boundary equilibria

The ideal magnetohydrodynamic free boundary model is employed to study the bifurcation of a family of helically symmetric equilibria. The equilibria are intended to approximate the Stellarator experiment with low plasma pressure and L = 2 helical symmetry. The study is carried out in a plasma column of finite length, surrounded by a vacuum region, all enclosed within an outer conducting wall. The straight helical equilibria are obtained by expansion in two parameters, c and epsilon, the ratio of the helical magnetic field to the theta pinch field, and the product of the helical wavenumber times the plasma column radius, respectively. The distortion of the plasma column from a true cylinder is taken to be small of order c. The column length is chosen to avoid ''kink instabilities'' for some range of azimuthal wavenumbers, n, for which the theory applies, and the critical beta is obtained. At this beta, a marginally stable state of principally n = 1 long wavelength mode is determined and serves as the starting point for bifurcation. The stability analysis is based on a determination of the sign of the second variation of the potential energy. Neighboring bifurcated equilibria are found by expanding the fields in another small parameter. The bifurcated equilibria are found to be stable when the conducting wall is within 1.15 plasma column radii of the plasma vacuum interface. This position was not sufficient to stabilize the original equilibrium. (U.S.)