Construction of three-dimensional equilibria of a magnetically confined plasma with closed and nested toroidal magnetic surfaces

Abstract

We construct fully three-dimensional (3D) equilibria with pressure anisotropy and closed, nested toroidal magnetic surfaces that are strongly asymmetric in the toroidal direction by applying a sinusoidal perturbation to the axisymmetric Solov'ev equilibrium. They also have distinct closed and nested current-density surfaces. For certain values of the free parameters involved, the perturbations lead to the formation of magnetic islands and stochastic areas in the outer plasma region, while well-defined magnetic surfaces persist in the inner region. In addition, it is demonstrated that the existence of closed and nested surfaces within the plasma region on which the magnetic field modulus is uniform (isomagnetic surfaces), related to quasisymmetry, is neither necessary nor sufficient for the existence of respective closed and nested magnetic surfaces.

Figures (11)

• Figure 1: The axisymmetric diamagnetic Solov'ev configuration for $\delta=\epsilon=0.4$.
• Figure 2: Variation of the axial position of the isomagnetic axis, $r^B_{ax}$, of the Solov'ev equilibrium of Fig. \ref{['SolF']} through the parameters $\delta$, $\epsilon$ and $F_0$ related, respectively, to the elongation, aspect ratio, and vacuum toroidal magnetic field.
• Figure 3: Isomagnetic contours on the poloidal plane (red-continuous curves) for the equilibrium of Fig. \ref{['SolF']}, with the outer curve touching the separatrix. The blue-dashed curves represent the respective intersections of the magnetic surfaces with the poloidal plane.
• Figure 4: Left panel: Poincaré plot of magnetic-field lines on the poloidal plane $\phi=0$ for an equilibrium with $\delta=0.4$, $\epsilon=0.3$, $F_0=3.5$, $c_s=d_s=0\ (s=g,w)$, $c_h=0.4$, $m_h=5$ and $d_h=0$. Right panel: Respective 3D magnetic surfaces.
• Figure 5: Left panel: Poincaré plot for the current-density lines of the equilibrium of Fig. \ref{['ex1B']} on the poloidal plane $\phi=0$. Right panel: Respective 3D current-density surfaces.