Quantifying resonant drive in resistive perturbed tokamak equilibria

Abstract

Resonant drive in tokamaks is routinely quantified using a variety of different metrics that target different aspects of a resonant response to an external perturbation. Two of the most direct metrics, $Δ_{mn}$ and $b_{pen}$, are widely used but their relative behavior was previously uncharacterized. This work examines how these metrics representing the shielding current and penetrated field relate in resistive perturbed tokamak equilibria using asymptotically matched solutions with a resistive MHD inner layer model in GPEC. $b_{pen}$ scales with Lundquist number as $S^{-2/3}$ until saturation at low $S$, and $Δ_{mn}$ remains consistent with its ideal definition but is affected by global kink structure. Both metrics are shown to yield closely similar dominant coupling modes within the same resistive model. However, the resistive physics shifts this dominant mode spectrum to lower poloidal mode numbers $m$ in a low-rotation ITER equilibrium. This alteration is predicted to be observable in experiment in the form of optimal relative phasings of resonant magnetic perturbation coils.

Figures (11)

• Figure 1: A schematic showing the preservation of magnetic field topology in an ideal plasma (a) compared to the opening of an island as magnetic field lines reconnect (b) in the presence of a 2/1 radial field perturbation. Vertical direction in the lower island schematics is increasing poloidal coordinate and horizontal direction is radial, the same as the upper plots.
• Figure 2: Ideal (left) and resistive (right) total perturbed fields in ITER when applying a 1 kA perturbation via the middle EFC coil, including the plasma response. The resistive plasma response, using a neoclassical resistivity $\eta_{NC}$ from Jardin jardinTSCSimulationOhmic1993, is stronger and has noticeably different structure compared to the ideal response.
• Figure 3: Inner and outer layer structures shown from LAR case (a) in Table \ref{['tab:equilibria']} at the $q=2$ surface, (a) $\xi^{m=2}_\psi$ and (b) $b^{m=2}_\psi$.
• Figure 4: The structure of resistive GPEC solutions varies with $\eta$ --- for small perturbations from ideal MHD, $b_{pen}^{res} \sim S^{-2/3} \sim \eta^{2/3}$. The ideal solution is shown as a black dashed line. $k_\eta$ is a constant multiplier that scales resistivity on all surfaces, with $k_\eta=1$ signifying neoclassical resistivity. Solutions shown are in a DIII-D-like equilibrium, detailed in Table \ref{['tab:equilibria']} and Fig. \ref{['fig:equilibria']}.
• Figure 5: Different discrete jump widths for different resistivities calculated using Eq. \ref{['eq:dpsi']} are shown. The top panel shows these points on $b_\psi$ curves for $m=2$ in a scan of resistivity in a DIII-D-like scenario with $k_\eta=1$ representing the neoclassical resistivity. The dotted line is the same $b_\psi$ curve for $\eta=0$. The bottom panel shows for each resistivity value the $\Delta_{2,1}$ value that would be obtained by using a jump width at the given point, showing that until resistivity is relatively high, $\Delta_{2,1}$ remains relatively consistent in value. Note the small ($\sim 20\%$) range of the y-axis.