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

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 = qB. A corresponding profile, q_J, can be defined for the current density field lines. Ampère’s law relates any mode of current perturbation δJ_m,n with a mode of magnetic perturbation δB_m,n. It is shown that the knowledge of the pair (q_B, q_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_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_B, q_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_B and qJ 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.