Magnetic helicity injection for configurations with field errors

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Abstract
The relative magnetic helicity and its rate of injection are computed for several examples of configurations representing magnetic fusion experiments, specifically reversed field pinches (RFP’s) with field errors. Field errors, here defined to be normal components of magnetic field at the wall, are believed to have a significant effect on the loop voltage, and therefore the volt-second consumption, in RFP’s. The perturbations producing these errors can arise from imbalance of the vertical field, leakage of Ohmic transformer flux, or toroidal field ripple. In the examples given, the relative helicity is the difference between two terms, which are called, respectively, the plasma linkage and the vacuum linkage. The latter quantity, which is zero for the simplified configurations studied previously, represents the linkage between vacuum fluxes occurring within the region of interest. On the other hand, the plasma linkage is the part of the relative helicity directly related to the instantaneous state of the plasma. It is found that the rate of change of the plasma linkage in the presence of poloidal field errors contains a new term proportional to the time rate of change of toroidal flux.