Magnetic relaxation and hyper-resistivity during helicity injection

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.

Simple Model of the (alpha)(omega) Dynamo: Self-Excited Spheromaks

“…Magnetic relaxation by turbulence has not always been useful in fusion research [4], and MHD turbulence might kill the dynamo [9]. The mechanism of Ref.…”

“…The extent of relaxation in the region of helicity generation is in part controlled by the momentum source [4], and the expanding radiolobe is only a little bit relaxed, giving a magnetic energy and helicity dominated by the lobe vacuum field due to the jet current deep inside the lobe (hence the factor lnR/a above) [11].…”

“…The second term represents electrostatic generation of helicity, while the term with R represents resistive losses, and also turbulent transport of helicity, which however, conserves helicity for most processes [3,4]. Eq.…”

“…(2) can describe an αω dynamo driven by momentum follows from the coupling of helicity to momentum injection, as follows. Since most of the helicity is in the mean field B o [3,4], Eq. (2) is equivalent to the mean field energy equation obtained from the symmetric average of B dotted into Faraday's Law, giving:…”

“…(2) as it usually appears in spheromak literature describing electrostatic helicity injection [4,5]:…”