Non-linear calculation of the m = 1 internal kink instability in current-carrying stellarators

Non-linear properties of the m = 1 internal kink mode are demonstrated for a low-β current carrying stellarator. The effect of the external stellarator fields is considered in terms of the rotational transform; the outermost magnetic surface is assumed to be circular. Magnetic surfaces inside the ι h + ι σ = 1 surface shift and deform non-circularly, whereas magnetic surfaces outside this surface are not disturbed. The rotational transform ι h is due to the stellarator fields and ι σ to the plasma current. Many higher harmonics are excited after the fundamental mode has saturated. – When the external stellarator fields are lowered, the m = 1 tearing mode similar to that in a low-β tokamak grows and magnetic islands appear near the ι h + ι σ = 1 surface. – For adequate stellarator fields, the current-carrying stellarator becomes stable both against the m = 1 internal kink mode and the m = 1 tearing mode, without lowering the rotational transform.