The stability properties of cylindrical force-free fields: effect of an external potential field

Abstract

A large-scale potential field with an embedded smaller-scale force-free structure (∇ × B = αB) is studied in cylindrical geometry. We consider cases in which α goes continuously from a constant value α0 on the axis to zero at large r. Such a choice of α(r) produces fields which are realistic (few field reversals) but not completely stable. The MHD-unstable wavenumber regime is found. Since the considered equilibrium field exhibits a certain amount of magnetic shear, resistive instabilities can arise. The growth rates of the tearing mode in the limited MHD-stable region of º space are calculated, showing time-scales much shorter than the resistive decay time.