Response of a magnetically diverted tokamak plasma to a resonant magnetic perturbation

TL;DR

This work addresses how a magnetically diverted tokamak plasma responds to a static resonant magnetic perturbation (RMP) near the magnetic separatrix. By constructing both a simple filament-based model and a more realistic flux-surface model, the authors formulate an asymptotic matching problem where the bulk plasma obeys ideal-MHD except in resistive layers centered on rational surfaces. They show that, due to strong magnetic shear near the separatrix, the rational-surface spacing and resistive-layer thickness shrink to zero, causing an overlap region where the response becomes vacuum-like, while the interior remains in the ideal regime. Practically, the analysis justifies treating the region beyond a small inner boundary $\mit\Psi=1-\epsilon_c$ as vacuum and solving only for a finite set of rational surfaces within $0<\mit\Psi<1-\epsilon_c$, with ${\epsilon_c}$ calculable from edge parameters (e.g., ${\epsilon_c}\approx1.5\times10^{-3}$ for $n=1$ and ${\epsilon_c}\approx4.8\times10^{-3}$ for $n=4$ in a typical JET H-mode plasma). This yields a physically consistent and computationally efficient framework for predicting RMP-plasma interactions and shielding current formation near the separatrix. The results have direct implications for the design and interpretation of RMP-based control strategies in diverted tokamaks.

Abstract

The safety-factor profile of a magnetically diverted tokamak plasma diverges logarithmically as the magnetic separatrix (a.k.a. the last closed magnetic flux-surface) is approached. At first sight, this suggests that, when determining the response of such a plasma to a static, externally generated, resonant magnetic perturbation (RMP), it is necessary to include an infinite number of rational magnetic flux-surfaces in the calculation, the majority of which lie very close to the separatrix. In fact, when finite plasma resistivity is taken into account, this turns out not to be the case. Instead, it is only necessary to include rational surfaces that lie in the region 0<Psi<Psi_c, where Psi is the normalized poloidal magnetic flux, and Psi_c<1 can be calculated from the edge plasma parameters. It is estimated that Psi_c= 0.9985 for an n=1 RMP, and Psi_c=0.9952 for an n=4 RMP, in a typical JET H-mode plasma.

Figures (10)

• Figure 1: The magnetic flux-surfaces ${\mit\Psi}=0.9$ (red), ${\mit\Psi}=1.0$ (green), and ${\mit\Psi}=1.1$ (blue) in the absence of a divertor plate. The black dots shows the locations of the two current filaments. Here, $q_\ast=12$ and $\zeta=0.2$.
• Figure 2: The safety-factor profile, $q({\mit\Psi})$. The red curve shows the safety-factor inside the magnetic separatrix. The blue and green curves show the safety-factor outside the separatrix in the absence and in the presence of a divertor plate, respectively. Here, $q_\ast=12$ and $\zeta=0.2$.
• Figure 3: The straight-field-line coordinate system inside the magnetic separatrix. The red curves are surfaces of constant $\hat{\psi}$, whereas the blue curves are surfaces of constant $\theta$. The black dot shows the location of the plasma current filament. Here, $q_\ast=12$ and $\zeta=0.2$.
• Figure 4: The straight-field-line coordinate system outside the magnetic separatrix in the absence of a divertor plate. The red curves are surfaces of constant $\hat{\psi}$, whereas the blue curves are surfaces of constant $\theta$. The black dots shows the locations of the two current filaments. Here, $q_\ast=12$ and $\zeta=0.2$.
• Figure 5: The magnetic flux-surfaces ${\mit\Psi}=0.9$ (red), ${\mit\Psi}=1.0$ (green), and ${\mit\Psi}=1.1$ (blue) in the presence of a divertor plate located halfway between the X-point and the divertor coil filament. The black dot shows the location of plasma current filament, and the horizontal black line shows the location of the divertor plate. Here, $q_\ast=12$ amd $\zeta=0.2$.