Magnetohydrodynamic equilibrium and stability of centrifugally confined plasmas

Abstract

Centrifugal confinement is an alternative approach to magnetic fusion, employing a magnetic field with an open field line configuration. In this scheme, a plasma with magnetic mirror geometry is made to rotate azimuthally at supersonic speeds. The resulting centrifugal forces, given the field line curvature, prevent the plasma from escaping along the field lines. This dissertation addresses the equilibrium and stability of this configuration within the framework of magnetohydrodynamics (MHD). Well confined equilibrium with desirable profiles is demonstrated by numerical simulation. As far as stability is concerned, four types of magnetohydrodynamic modes determine the overall stability of centrifugally confined plasmas: flute interchanges and the Kelvin--Helmholtz instability, in a low $\beta$ system, and the magnetorotational instability (MRI) and the Parker instability, in a high $\beta$ system. One of the underpinnings of the centrifugal confinement is that flute interchanges could be stabilized by the strong velocity shear accompanying the rotation. Numerical simulations show strong evidence of stabilization, provided that the shear flow is not unstable to Kelvin--Helmholtz (KH) modes. The KH modes are ideally stable if the generalized Rayleigh's Inflexion criterion is satisfied. Particle sources and shown to be important to both equilibrium and stability. In the absence of particle sources, density profiles relax under resistive diffusion to pile up to the outboard side of the confining vessel. Tailoring the density profiles by appropriately placing the particle sources could be used to achieve control over MHD stability, for both interchanges and KH modes. Analytic analysis of interchanges based on an extension of MHD which applicable for low density plasmas with $V_A \sim c$ is presented. The interchange growth rates are reduced by a factor of $\sqrt{1+V_A^2/c^2}$ compared to the usual MHD prediction. The physical mechanisms of both the MRI and the Parker instability are examined and an explanation of why the MRI mechanism is insufficient to destabilize the system while the Parker instability could occur is given. Numerical simulations of the nonlinear behavior of the Parker instability are presented. It is shown that clumping from the Parker instability could reinforce centrifugal confinement.