Toroidal High-β Equilibria

To contain a toroidal high-β plasma (e.g., the proposed Scyllac device) requires rather complex fields. In the MHD (scalar pressure) and guiding-centre theories it has been found that under many circumstances static equilibrium solutions do not exist. This difficulty is not resolved with finite resistivity. It is possible that finite Larmor radius could yield solutions, but for the complex geometries which are necessary such a theory does not appear to be feasible. In the past, high-β equilibria have usually been calculated from the β = 1 plasma model with field excluded from the plasma at a sharp boundary. But all such equilibria are automatically unstable (dynamic stabilization has been suggested to remedy this). The problem of non-existence of equilibrium solutions does not arise in this model. The same is true of any model with piece-wise constant pressure layers or piece-wise constant distributions f(ϵ, μ). Under certain circumstances the plasma fluctuations which would arise from the lack of equilibrium with a continuous pressure profile can be estimated to be small. In such cases the mathematically expedient step-function equilibrium could be expected to give a fairly accurate representation of the plasma both with regard to equilibrium and stability. The mathematical problem is that of a number of free boundaries separating vacuum field regions (scalar pressure) or f(ϵ, μ) regions (satisfying elliptic equations similar to the vacuum field). We have obtained an equilibrium in scalar pressure MHD for arbitrary β as an expansion for a torus of large aspect ratio with a simple helical winding. This equilibrium exists under a wide range of parametric values. There are many different indications of MHD stability of the device and none to the contrary. (author)