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 iotasub(h)+iotasub(sigma)=1 surface shift and deform non-circularly, whereas magnetic surfaces outside this surface are not disturbed. The rotational transform iotasub(h) is due to the stellarator fields and iotasub(sigma) 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 iotasub(h)+iotasub(sigma)=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. (author)