Stability theory of plasma current multipole

The plasma current multipole has a deep average well and strong shear due to a characteristic separatrix and stagnation point produced by moderately strong plasma currents and special shaping of the flux surfaces by a conducting wall to include, for example, quadrupole terms. The stability of a toroidal device with a large aspect ratio κ −1 and relatively strong toroidal field component B 0 is discussed with respect to helical modes localized about flux surfaces, driven by gradients in both pressure and current, and to axi-symmetric modes. Stability considerations lead to a torus whose minor cross-section is a particular configuration utilizing only one petal of the 'figure-of-eight', with its stagnation line on the side nearest the axis of symmetry and coplanar with the magnetic axis. This wall shape produces toroidal-volume effects and shear satisfying the necessary conditions for stability of localized modes at relatively large values of current density j 0 and pressure P 0 so that (j K-S /j 0 ) 2 ∼κ, ∼ κ ½ where j K-S is the Kruskal-Shafranov current. Comparison is made with a standard Tokamak.