Magnetohydrodynamic equilibrium and stability of rotating field-reversed configurations with excluded multipole fields

Abstract

The rotational instability in field-reversed configurations (FRC’s) is observed experimentally to be suppressed by the application of multipole fields. In this paper the equilibrium and stability of a FRC with multipole fields that do not penetrate into the plasma are studied. It is shown that two rotating magnetohydrodynamic (MHD) equilibria are possible for a long FRC in a multipole field. One is nearly circular while the other is cusp shaped. Experiments and hybrid simulations indicate that cusp-like equilibria are usually obtained. The effect of helical multipole fields on the equilibrium is also discussed. The stability of such a configuration has been previously studied by using the MHD model on a circular plasma and by using a hybrid simulation code. In the important quadrupole case, the two calculations disagree: the simulation shows that the mode is stabilized while the circular MHD calculation predicts that it remains unstable. A close look at the MHD calculation shows that stability is strongly influenced by the shape of the equilibrium. Simple estimates indicate that the cusp-like equilibrium should be more stable than the circular one.