Abstract
High-beta tokamak equilibria with flow comparable to the poloidal Alfvén velocity in the reduced magnetohydrodynamics (MHD) model with two-fluid and ion finite Larmor radius (FLR) effects are investigated. The reduced form of Grad-Shafranov equation for equilibrium with flow, two-fluid and FLR effects is analytically solved for simple profiles. The dependence of the Shafranov shift for the magnetic axis and the equilibrium limits on the poloidal beta and the poloidal Alfvén Mach number are modified by the two-fluid and FLR effects. In the presence of the diamagnetic drift due to the two-fluid effect, the equilibrium depends on the sign of the E × B drift velocity. The FLR effect suppresses the large modification due to the two-fluid effect. By constructing magnetic flux coordinates and a local equilibrium model from the analytic solution, the effects of the non-circular property of the magnetic flux surfaces in the poloidal cross-section on the components of the curvature vector is examined in detail. The analytic solution is also used for the benchmark of the numerical code. The numerical solutions with non-uniform pressure, density and temperature profiles show similar behavior to analytic solution.
Highlights
Macroscopic equilibrium and stability of plasmas are described by magnetohydrodynamics (MHD)
The reduced Grad-Shafranov (GS) equation with flow, two-fluid and ion finite Larmor radius (FLR) effects is obtained from the radial component of the force balance equation (28) as μ 2
We have solved the equations for high-beta tokamak equilibria with flow comparable to the poloidal Alfvén velocity in the reduced MHD model with two-fluid and FLR
Summary
Macroscopic equilibrium and stability of plasmas are described by magnetohydrodynamics (MHD). The reduced MHD equilibrium equations for high-beta tokamaks with flow comparable to the poloidal Alfvén velocity, two-fluid, and FLR effects were derived [13]. We solve analytically and numerically the reduced MHD equilibrium equations for high-beta tokamaks with flow comparable to the poloidal Alfvén velocity, two-fluid, and FLR effects. 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. Analytic representations of flux coordinates and the components of the magnetic curvature enables detailed parameter study of non-circular property of the poloidal cross-sections of the magnetic flux surfaces due to high-beta, flow and diamagnetic effects.
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