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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.

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
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[1] Jardin, S.C.; Breslau, J.; Ferraro, N., A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions, J. comp. phys., 226, 2, 2146-2174, (2007) · Zbl 1388.76442
[2] Ono, M.; Kaye, S.M.; Peng, Y.-K.M.; Barnes, G.; Blanchard, W.; Carter, M.D.; Chrzanowski, J.; Dudek, L.; Ewig, R.; Gates, D.; Hatcher, R.E.; Jarboe, T.; Jardin, S.C.; Johnson, D.; Kaita, R.; Kalish, M.; Kessel, C.E.; Kugel, H.W.; Maingi, R.; Majeski, R.; Manickam, J.; McCormack, B.; Menard, J.; Mueller, D.; Nelson, B.A.; Nelson, B.E.; Neumeyer, C.; Oliaro, G.; Paoletti, F.; Parsells, R.; Perry, E.; Pomphrey, N.; Ramakrishnan, S.; Raman, R.; Rewoldt, G.; Robinson, J.; Roquemore, A.L.; Ryan, P.; Sabbagh, S.; Swain, D.; Synakowski, E.J.; Viola, M.; Willians, M.; Wilson, J.R.; Team, N., Exploration of spherical torus physics in the NSTX device, Nucl. fusion, 40, 3Y, 557-561, (2000)
[3] A.Y. Aydemir, Shear flows at the tokamak edge and their interaction with edge-localized modes, Phys. Plasmas 14.
[4] Stringer, T.E., Diffusion in toroidal plasmas with radial electric field, Phys. rev. lett, 22, 15, 770-774, (1969)
[5] Rosenbluth, M.N.; Taylor, J.B., Plasma diffusion and stability in toroidal systems, Phys. rev. lett., 23, 7, 367-370, (1969)
[6] Galeev, A.A., Influence of termperature perturbation on plasma diffusion in toroidal systems, Zhetf pis. red., 10, 7, 353-357, (1969)
[7] Pogutse, O.P., Classical diffusion of a plasma in toroidal systems, Nucl. fusion, 10, 399-403, (1970)
[8] Bondeson, A.; Ward, D.J., Stabilization of external modes in tokamaks by resistive walls and plasma rotation, Phys. rev. lett., 72, 17, 2709-2712, (1994)
[9] Garofalo, A.M.; Strait, E.J.; Johnson, L.C.; Haye, R.J.L.; Lazarus, E.A.; Navratil, G.A.; Okabayashi, M.; Scoville, J.T.; Taylor, T.S.; Turnbull, A.D., Sustained stabilization of resistive-wall mode by plasma rotation in the DIII-D tokamak, Phys. rev. lett., 89, 23, 235001, (2002)
[10] LaBombard, B.; Rice, J.E.; Hubbard, A.E.; Hughes, J.W.; Greenwald, M.; Irby, J.; Lin, Y.; Lipschultz, B.; Marmar, E.S.; Pitcher, C.S.; Smick, N.; Wolfe, S.M.; Wukitch, S.J., Transport-driven scrape-off-layer flows and the boundary conditions imposed at the magnetic separatrix in a tokamak plasma, Nucl. fusion, 44, 1047-1066, (2004)
[11] Biglari, H.; Diamond, P.H.; Terry, P.W., Influence of sheared poloidal rotation on edge turbulence, Phys. fluids B, 2, 1, 1-3, (2001)
[12] Burrell, K.H., Effects of \(E \times B\) velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices, Phys. plasmas, 4, 1499, (1997)
[13] Taylor, J.B., Relaxation of toroidal plasma and generation of reverse magnetic fields, Phys. rev. lett., 33, 19, 1139-1141, (1974)
[14] Steinhauer, L.C.; Ashida, A., Nearby-fluids equilibria. I. formalism and transition to single-fluid magnetohydrodynamics, Phys. plasmas, 13, 052513, (2006)
[15] Throumoulopoulos, G.N.; Tasso, H., On Hall magnetohydrodynamics equilibria, Phys. plasmas, 13, 102504, (2006)
[16] Semenzato, S.; Gruber, R.; Zehrfeld, H.P., Commputation of symmetric ideal MHD flow equilibria, Comp. phys. rep., 1, 389, (1984)
[17] Beliën, A.J.; Botchev, M.A.; Goedbloed, J.P.; van der Holst, B.; Keppens, R., FINESSE: axisymmetric MHD equilibria with flow, J. comp. phys., 182, 1, 91-117, (2002) · Zbl 1021.76026
[18] Guazzotto, L.; Betti, R.; Manikam, J.; Kaye, S., Numerical study of tokamak equilibria with arbitrary flow, Phys. plasmas, 11, 2, 604-614, (2004)
[19] Guazzotto, L.; Betti, R., Magnetohydrodynamics equilibria with toroidal and poloidal flow, Phys. plasmas, 12, 056107, (2005)
[20] Breslau, J.A.; Sovinec, C.R.; Jardin, S.C., An improved tokamak sawtooth benchmark for 3D nonlinear MHD, Comm. comp. phys., 4, 3, 647-658, (2008) · Zbl 1364.76235
[21] Aydemir, A.Y.; Barnes, D.C., Three-dimensional nonlinear incompressible MHD calculations, J. comp. phys., 53, 1, 100-123, (1984) · Zbl 0527.76122
[22] Ferraro, N.M.; Jardin, S.C., Finite element implementation of braginskii’s gyroviscous stress with application to the gravitational instability, Phys. plasmas, 13, 9, 092101, (2006)
[23] Sovinec, C.; Glasser, A.; Gianakon, T.; Barnes, D.; Nebel, R.; Kruger, S.; Plimpton, S.; Tarditi, A.; Chu, M., Nonlinear magnetohydrodynamics with high-order finite elements, J. comp. phys., 195, 355, (2004) · Zbl 1087.76070
[24] Jardin, S.C., A triangular finite element with first-derivative continuity applied to fusion MHD applications, J. comp. phys., 200, 133-152, (2004) · Zbl 1288.76043
[25] Braginskii, S.I., Transport processes in a plasma, (), 205-311
[26] Rosen, M.D.; Greene, J.M., Radial boundary layers in diffusing toroidal equilibria, Phys. fluids, 20, 9, 1466-1475, (1977) · Zbl 0369.76098
[27] Dunavant, D.A., High degree efficient symmetrical Gaussian quadrature rules for the triangle, Int. J. numer. methods eng., 21, 1129-1148, (1985) · Zbl 0589.65021
[28] Harned, D.S.; Schnack, D.D., Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions, J. comp. phys., 65, 1, 57-70, (1986) · Zbl 0591.76187
[29] Chacón, L.; Knoll, D.A., A 2D high-\(\beta\) Hall MHD implicit nonlinear solver, J. comp. phys., 188, 2, 573-592, (2003) · Zbl 1127.76375
[30] Caramana, E.J., Derivation of implicit difference schemes by the method of differential approximation, J. comp. phys., 96, 484-493, (1991) · Zbl 0732.65082
[31] Fitzpatrick, R., Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamic Taylor problem, Phys. plasmas, 11, 3, 937-946, (2004)
[32] D. Pfirsch, A. Schlüter, Tech. Rep. MPI/PA/7/62, Max-Planck-Institut für Plasmaphysik, 1962.
[33] N.M. Ferraro, Non-ideal effects on the stability and transport of magnetized plasmas, Ph.D. thesis, Princeton University, Nov. 2008.
[34] Mikhailovskii, A.B.; Tsypin, V.S., Transport equations and the gradient instabilities in a high pressure collisional plasma, Plasma phys., 13, 785-798, (1971)
[35] Maingi, R.; Shaing, C.S.; Ku, S.; Biewer, T.; Maqueda, R.; Bell, M.; Bush, C.; Gates, D.; Kaye, S.; Kugel, H.; LeBlanc, B.; Menard, J.; Mueller, D.; Raman, R.; Sabbagh, S.; Soukhanovskii, V., Effect of gas fuelling location on h-mode access in nstx, Plasma phys. control. fusion, 46, A305-A313, (2004)
[36] Hassam, A.B.; Kulsrud, R.M., Time evolution of mass flows in a collisional tokamak, Phys. fluids, 21, 12, 2271-2279, (1978)
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