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Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states. (English) Zbl 1391.76324
Summary: M3D-\(C^{1}\) is an implicit, high-order finite element code for the solution of the time-dependent nonlinear two-fluid magnetohydrodynamic equations [S.C. Jardin et al., J. Comput. Phys. 226, No. 2, 2146–2174 (2007; Zbl 1388.76442)]. This code has now been extended to allow computations in toroidal geometry. Improvements to the spatial integration and time-stepping algorithms are discussed. Steady-states of a resistive two-fluid model, self-consistently including flows, anisotropic viscosity (including gyroviscosity) and heat flux, are calculated for diverted plasmas in geometries typical of the National Spherical Torus Experiment (NSTX) [M. Ono et al., Exploration of spherical torus physics in the NSTX device, Nucl. Fusion 40, No. 3Y, 557–561 (2000; /10.1088/0029-5515/40/3Y/316)]. These states are found by time-integrating the dynamical equations until the steady-state is reached, and are therefore stationary or statistically steady on both magnetohydrodynamic and transport time-scales. Resistively driven cross-surface flows are found to be in close agreement with Pfirsch-Schlüter theory. Poloidally varying toroidal flows are in agreement with comparable calculations [A. Y. Aydemir, Shear flows at the tokamak edge and their interaction with edge-localized modes, Phys. Plasmas 14, 056118 (2007; doi:10.1063/1.2727330)]. New effects on core toroidal rotation due to gyroviscosity and a local particle source are observed.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
82D10 Statistical mechanics of plasmas
Software:
NIMROD; FINESSE; M3D-C
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References:
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