Magnetohydrodynamic and double adiabatic stability of compact toroid plasmas

The linear stability of compact toroids is examined in the magnetohydrodynamic and double adiabatic models. The long-thin approximation in ideal magnetohydrodynamics is used to investigate tilting and shifting modes in field reversed configurations without toroidal fields. A necessary and sufficient condition is obtained and used to show that the combination of flux surface shaping and profile flatness results in stability to a class of transverse modes in a region about the O point. The double adiabatic model yields for general confined plasmas a sufficient condition for stability in the form of six ordinary differential equations along each field line. Further reduction of the condition to a single second-order equation depends on the sign of ∂S/ ∂B, where S(ψ,B)=p_∥B⁵/ p⊥³ is a combination of the two entropies. Strong stabilizing effects of pressure anisotropy are shown.