Interplay of the magnetic and current density field topologies in axisymmetric devices for magnetic confinement fusion

Abstract

In magnetic confinement fusion devices close to axisymmetry, such as tokamaks, a key element is the winding profile of the magnetic field lines, or its inverse, the safety profile $q=q_{\boldsymbol {B}}$ . A corresponding profile, $q_{\boldsymbol {J}}$ , can be defined for the current density field lines. Ampère's law relates any mode of current perturbation $\delta \boldsymbol {J}_{m,n}$ with a mode of magnetic perturbation $\delta \boldsymbol {B}_{m,n}$ . It is shown that the knowledge of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ allows us then to characterize the resonant, or non-resonant, nature of the modes for both the magnetic and current density field lines. The expression of $q_{\boldsymbol {J}}$ in the flux coordinate is derived. Including this calculation in real-time Grad–Shafranov equilibrium reconstruction codes would yield a comprehensive view of the magnetics. The monitoring of the pair $(q_{\boldsymbol {B}},q_{\boldsymbol {J}})$ would then allow us to investigate the role played by the resonant modes for the current density, that are current filamentary modes, in the plasma small-scale turbulence. By driving the magnetic and current density profiles apart so that the images of $q_{\boldsymbol {B}}$ and $q_{\boldsymbol {J}}$ are disjoint, these filamentary modes would not impact the magnetic field topology, being not associated with magnetic islands but with non-resonant magnetic modes. It remains to be explored to what extent such a configuration, where the spectrum of tiny current density filaments produces a spectrum of magnetic modes that has practically no effect on heat transport, is beneficial.