Abstract
Transport theory is applied to magnetic helicity injection into plasmas with toroidal geometry. Magnetic relaxation during helicity injection can be described as hyper-resistive diffusion of the current. By using the generalized Balescu–Lenard extension of quasi-linear transport theory, it is shown that hyper-resistive diffusion is generally slow compared with heat transport. It follows that magnetic relaxation due to such turbulence tends to flatten the temperature profile, as observed in reversed-field pinches. Given flattened temperature profiles, Taylor's minimum principle for magnetic relaxation is usefully reformulated as minimum dissipation, yielding circuit equations for electrostatic helicity injection in laboratory devices such as spheromaks and tokamaks. A favorable heat pinch could benefit helicity injection into tokamaks. These results are also relevant to natural phenomena involving the generation of fields by magnetic relaxation.
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