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The solution of Grad-Shafranov equation in field-reversed configuration (FRC) is a basic problem. The solution of Grad-Shafranov equation can help to understand most of physical processes in FRC plasma, such as magnetohydrodynamic (MHD) instabilities and plasma transport. In the present paper, based on the FRC asymptotic theory by Barnes D C, the code for solving the two-dimensional Grad-Shafranov equation in FRC is developed. By using the code, the equilibriums of FRC with different elongations and separatrix radii are investigated in the present paper. The one-dimensional numerical results show that the plasma density gradient increases linearly with magnetic flux increasing in the FRC center, while, it steepens due to the high magnetic field distribution at the separatrix. The results also show that the plasma density in the closed field region increases with the density at the separatrix increasing, which implies that FRC embodies the strong confinement ability. It is a key problem to choose equations determining the shape of the separatrix in a two-dimensional numerical investigation. In the present paper, the shape equation is described as rs = rs max (1 - z2a), in which a is the shaping parameter. When a=1, the separatrix shape is elliptical, and when a1, the separatrix shape is like a racetrack. The geometry character of the separatrix appears in the one-order equations (in one-order equations: (0)/(z) = (0)/(rs)(rs)/(z), where (0)/(rs) is determined by lead equations and (rs)/(z) is given by separatrix equation). The two-dimensional numerical results show that O-point moves outward as the sparatrix radius increases. The curvature radius of magnetic flux surface increases with the separatrix radius increasing. The O-point of magnetic flux surface is just at the curvature center. Thus O-point moves outward as the sparatrix radius increases.
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Keywords:
- field-reversed configuration /
- Grad-Shafranov equation /
- separatrix /
- elongation
[1] Steinhauer L C 2011 Phys. Plasmas 18 070501
[2] Shafranov V D 1966 Reviews of Plasma Physics 2 103
[3] Schwarzmeier J L, Barnes D C, Hewett D W, Seyler C E, Shestakov A I, Spencer R L 1983 Phys. Fluids 26 1295
[4] Schwarzmeier J L, Seyler C E 1984 Phys. Fluids 27 2151
[5] Iwasawa N, Ishida A, Steinhauer L C 2001 Phys. Plasmas 8 1240
[6] Ohtsuka T, Okubo M, Okada S, Goto S 1998 Phys. Plasmas 5 3649
[7] Steinhauer L C 1990 Phys. Fluids B 2 2679
[8] Werley K A 1987 Phys. Fluids 30 2129
[9] Herbert L B, James H H, Harold W 1981 Phys. Fluids 24 1758
[10] Morse R L 1969 Equilibria of Collisionless Plasma Part II (N. Mex.: Los Alamos Scientific Lab.) p5
[11] Hewett D W, Spencer R L 1983 Phys. Fluids 26 1299
[12] Spencer R L, Tuszewski M 1985 Phys. Fluids 28 1810
[13] Spencer R L, Hewett D W 1982 Phys. Fluids 25 1365
[14] Webster R B, Schwarzmeier J L, Lewis H R, Choi C K, Terry W K 1991 Phys. Fluids B 3 1026
[15] Steinhauer L C 2011 Phys. Plasmas 18 110509
[16] Armstrong W T, Linford R K, Lipson J 1981 Phys. Fluids 24 2068
[17] Okada S, Kiso Y, Goto S, Ishimura T 1989 J. Appl. Phys. 65 4625
[18] Barnes D C 2001 Phys. Plasmas 8 4865
[19] Barnes D C 2001 Phys. Plasmas 8 4864
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[1] Steinhauer L C 2011 Phys. Plasmas 18 070501
[2] Shafranov V D 1966 Reviews of Plasma Physics 2 103
[3] Schwarzmeier J L, Barnes D C, Hewett D W, Seyler C E, Shestakov A I, Spencer R L 1983 Phys. Fluids 26 1295
[4] Schwarzmeier J L, Seyler C E 1984 Phys. Fluids 27 2151
[5] Iwasawa N, Ishida A, Steinhauer L C 2001 Phys. Plasmas 8 1240
[6] Ohtsuka T, Okubo M, Okada S, Goto S 1998 Phys. Plasmas 5 3649
[7] Steinhauer L C 1990 Phys. Fluids B 2 2679
[8] Werley K A 1987 Phys. Fluids 30 2129
[9] Herbert L B, James H H, Harold W 1981 Phys. Fluids 24 1758
[10] Morse R L 1969 Equilibria of Collisionless Plasma Part II (N. Mex.: Los Alamos Scientific Lab.) p5
[11] Hewett D W, Spencer R L 1983 Phys. Fluids 26 1299
[12] Spencer R L, Tuszewski M 1985 Phys. Fluids 28 1810
[13] Spencer R L, Hewett D W 1982 Phys. Fluids 25 1365
[14] Webster R B, Schwarzmeier J L, Lewis H R, Choi C K, Terry W K 1991 Phys. Fluids B 3 1026
[15] Steinhauer L C 2011 Phys. Plasmas 18 110509
[16] Armstrong W T, Linford R K, Lipson J 1981 Phys. Fluids 24 2068
[17] Okada S, Kiso Y, Goto S, Ishimura T 1989 J. Appl. Phys. 65 4625
[18] Barnes D C 2001 Phys. Plasmas 8 4865
[19] Barnes D C 2001 Phys. Plasmas 8 4864
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