Profile consistency of an elongated field-reversed configuration. I. Asymptotic theory

Abstract

An asymptotic theory of field-reversed configuration (FRC) equilibrium is developed, where the small expansion parameter is the square of the inverse elongation of the separatrix. It is shown that equilibrium alone completely determines the closed-field pressure profile of an elongated FRC in terms of the open-field profile. Examples show that the closed profile is insensitive to details of the open profile. A surprising result is that the open outflow plasma (axially beyond closed region) is always totally diamagnetic on the axis (β=1, where β is measured in the θ-pinch sense). The separatrix shape (axial variation) depends uniquely on the first-order pressure profile, and any separatrix shape may be realized within the limitations of the asymptotic theory. This sensitive dependence of shape on pressure profile explains extreme stiffness of the FRC equilibrium problem which was reported earlier. These results are compared favorably with experimental observations.