Hydromagnetic Instability in a Stellarator

When there is a uniform externally imposed longitudinal magnetic field much larger than the field of a discharge current in a cylindrical plasma, one should expect instabilities in the form of a lateral displacement of the plasma column into a helix of large pitch. This problem is examined under the conditions which might occur in the stellarator during ohmic heating. It is shown that the presence of external conductors is unimportant. When effects of the finite length of the machine are considered, a critical current is obtained below which the system is stable to this displacement. Consideration of current distributions other than uniform shows that instabilities which vary as ei(mθ+kz) can occur for values of m greater than one, so that instabilities can be found for any finite length machine. Experimental results are in agreement with the theory for the m = 1 mode. There is no experimental indication of the higher m modes, for which several possible explanations are suggested.