An analytic stability criterion is derived for the vertical mode in a large aspect ratio stellarator with uniform current density profile. The effects of vacuum magnetic field generated by helical coils are shown to be stabilizing due to enhancement of field line bending energy. For a wall at infinite distance from the plasma, the amount of external poloidal flux needed for stabilization is given by f=(κ2−κ)/(κ2+1), where κ is the axisymmetric elongation and f is the ratio of vacuum rotational transform to the total transform.
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G. Y. Fu (2000) studied this question.
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