Numerical studies on the stability of kink and resistive tearing modes in a current-carrying linear stellarator are presented for various current profiles and helical fields. In the case of an ℓ = 2 helical field, the magnetic shear vanishes and the stability diagram is given by the straight lines with ισ + ιδ = const., where ισ is the rotational transform due to the plasma current and ιδ is that due to the helical field. For the ℓ = 2 stellarator with , the magnetohydrodynamic stability against kink and tearing modes is improved compared to that in tokamaks. When an ℓ = 3 helical component exists, magnetic shear plays an important role in the stability properties. The stability diagrams become fairly complex; they are, however, understandable from properties of the Euler equation. It should be noted that the internal kink modes are made more unstable than in a tokamak, because of the ℓ = 3 helical field.
Bifurcated helical core equilibrium states in tokamaks