(DOI: will be inserted by hand later) The stability of toroidal elds in stars

the date of receipt and acceptance should be inserted later Abstract. We present numerical models of hydromagnetic instabilities under the conditions prevailing in a stably stratied, non-convective stellar interior, and compare them with previous results of analytic work on instabilities in purely toroidal elds. We conrm that an m = 1 mode (`kink') is the dominant instability in a toroidal eld in which the eld strength is proportional to distance from the axis, such as the eld formed by the winding up of a weak eld by differential rotation. We measure the growth rate of the instability as a function of eld strength and rotation rate, and investigate the effects of a stabilising thermal stratication as well as magnetic and thermal diffusion on the stability. Where comparison is computationally feasible, the results agree with analytic predictions. Key words. instabilities magnetohydrodynamics (MHD) stars: magnetic elds 1