Abstract
General conditions for adiabatic instability of weak axisymmetric toroidal magnetic fields are obtained. In particular all fields which haveHϕ=0 and ∂Hϕ2/∂δ>0 simultaneously are unstable. This includes all fields which exist near to the axis of symmetry and, indeed, any without an infinite current density anywhere. A detailed discussion is given of fields with an angular dependenceHϕ2∼|Pl (cos θ)|. These fields are dynamically unstable with respect to both axisymmetric and non-axisymmetric perturbations for all values of the azimuthal wave number |m|. The maximum growth rates are independent ofm and they are largest for the fields that are defined in the regions closest to the polar axis.
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