Magnetic flux coordinates for analytic high-beta tokamak equilibria with flow

Abstract

Magnetic flux coordinates are constructed from an analytic solution (Ito A and Nakajima N 2009 Plasma Phys. Control. Fusion 51 035007) for the reduced magnetohydrodynamics (MHD) equilibrium equations for high-beta tokamaks in the presence of poloidal and toroidal flows comparable to the poloidal sound velocity. The analytic solution indicates non-circular magnetic flux surfaces and transition between sub-and super-sonic poloidal flows. The magnetic flux coordinates for such noncircular magnetic flux surfaces are obtained for stability analysis. The flux coordinates are numerically obtained from the high order polynomial equations for the relation with the geometrical coordinates. As applications, pressure profiles in the poloidal direction on each flux surface, which become non-constant due to flow, and the flux average of the pressure are obtained. The transitions of the pressure profiles and the flux average of the pressure between sub-and super-sonic poloidal flows are discussed in relation with the radial force balance. The flux coordinates are also obtained analytically by expanding the coordinate relations with respect to the inverse aspect ratio.

Two-fluid and finite Larmor radius effects on high-beta tokamak equilibria with flow in reduced magnetohydrodynamics

“…The magnetic flux coordinates ( ) x Q , in the poloidal cross-section are obtained from the analytic solution of ψ 1 , (47), by the relations, the same as those for the static MHD equilibrium [27,28],…”

“…The analytic solution is easily obtained as an extension of the static MHD case [18,19,20] and the case of MHD with flow [21] when the density is constant. This is different from the case of flow comparable to the poloidal sound velocity, which is slower than the poloidal Alfvén velocity, where the reduced equilibrium equations have those effects in the next order [22,23,24,25,26,27]. Since the GS equation in that order couples with other equations such as pressure equation, those equations with two-fluid and FLR effects are studied numerically [22,24].…”

“…From the radial profile of the magnetic flux function, the Shafranov shift for the magnetic axis and the equilibrium limits due to the effects of high-beta and flow are obtained. By constructing magnetic flux coordinates from the analytic solution such those for the static MHD equilibrium [27,28], the components of the magnetic curvature are analytically obtained. These are expected to be applied to the analysis of the kink, interchange and ballooning instabilities.…”

Stability of a tokamak plasma with diffuse toroidal rotation

“…In this work, is regarded as an expansion parameter. In recognition of the non-circular nature of magnetic flux surfaces in high- configurations (characterized here by ), other works ( Ito & Nakajima (2019), and references therein) have constructed magnetic flux coordinates in the presence of flows as the basis for stability analysis.…”