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 $q=q_{\mathbf{B}}$. A corresponding profile, $q_{\mathbf{J}}$, can be defined for the current density field lines. Amp\`{e}re's law relates any mode of current perturbation $\delta \mathbf{J}_{m,n}$ with a mode of magnetic perturbation $\delta \mathbf{B}_{m,n}$. It is shown that the knowledge of the pair $(q_{\mathbf{B}},q_{\mathbf{J}})$ allows then to characterize the resonant, or non-resonant, nature of the modes for both the magnetic and current density field lines. The expression of $q_{\mathbf{J}}$ in flux coordinate is derived. Including this calculation in the real-time Grad-Shafranov equilibrium reconstruction codes would yield a comprehensive view of the magnetics. The monitoring of the pair $(q_{\mathbf{B}},q_{\mathbf{J}})$ would then allow investigating 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 $q_{\mathbf{B}}$ and $q_{\mathbf{J}}$ are disjoint, these filamentary modes would not impact the magnetic field topology, being not associated to magnetic islands but to non-resonant magnetic modes. It remains to be explored to which 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.
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