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基于反场构型(field-reversed configuration)渐近理论,编写了反场构型等离子体中二维Grad-Shafranov方程的数值模拟代码,研究了不同拉长形状的反场构型剖面. 通过模拟,得到了磁面坐标系中反场构型等离子体压强及梯度分布,同时求解了大拉长比、不同分界面(separatrix)类型的磁通量分布. 研究结果表明,等离子体压强梯度随着磁通量呈线性增长,在分界面处发生突变;分界面处的等离子体压强越高,分界面内部的压强会更高,即具有更高的等离子体值,反映了反场构型较好的约束效果.
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关键词:
- 反场构型 /
- Grad-Shafranov方程 /
- 分界面 /
- 拉长比
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.-
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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