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

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.

Counter differential rigid-rotation equilibrium of electrically non-neutral two-fluid plasma with finite pressure

“…In modern plasma physics research, the two-fluid plasma model (Shumlak et al 2011) is popular for analysing phenomena for which conventional hydorodynamic models, for example single-fluid equations and magnetohydrodynamics (generally abbreviated as MHD), are unsuitable. The two-fluid plasma equations permit a high degree of freedom in determining not only the spatiotemporal evolutions (Zhu, Francisquez & Rogers 2017;Morel et al 2021) but also the equilibrium profiles (Ishida, Steinhauer & Peng 2010;Kanki & Nagata 2019;Ito & Nakajima 2021) of the density n σ , pressure p σ and mean velocity v σ of the ion and electron fluids (hereafter, called plasma); subscript σ denotes either i or e because the equations comprise two sets of Euler equations as well as Maxwell's equations. However, a fundamental question arises on the assumption (De Jonghe & Keppens 2020;Mironov 2021;Zhang et al 2021) that the ion and electron plasmas are electrically neutral, although it is not required by the two-fluid plasma model.…”