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

An asymptotic theory of field-reversed configuration (FRC) equilibrium is d eveloped, 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 insensi tive to details of the open profile. A surprising result is that the open o utflow plasma (axially beyond closed region) is always totally diamagnetic on the axis (beta =1, where beta is measured in the theta -pinch sense). Th e separatrix shape (axial variation) depends uniquely on the first-order pr essure profile, and any separatrix shape may be realized within the limitat ions of the asymptotic theory. This sensitive dependence of shape on pressu re profile explains extreme stiffness of the FRC equilibrium problem which was reported earlier. These results are compared favorably with experimenta l observations. (C) 2001 American Institute of Physics.