中国物理B ›› 2005, Vol. 14 ›› Issue (12): 2552-2559.doi: 10.1088/1009-1963/14/12/029

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Topology of toroidal helical fields in non-circular cross-sectional tokamaks

王燕1, 朱思铮2, 虞清泉2, 查学军3   

  1. (1)Department of Physics, Shanghai University, Shanghai 200436, China; (2)Institute of Plasma Physics, Chinese Academy of Sciences,Hefei 230031, China; (3)State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China;Institute of Plasma Physics, Chinese Academy of Sciences,Hefei 230031, China
  • 收稿日期:2005-01-25 修回日期:2005-05-26 出版日期:2005-12-20 发布日期:2005-12-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10405030 and 10135020).

Topology of toroidal helical fields in non-circular cross-sectional tokamaks

Zha Xue-Jun (查学军)ab, Zhu Si-Zheng (朱思铮)b, Yu Qing-Quanb, Wang Yan (王燕)c    

  1. a State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China; b Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China; c Department of Physics, Shanghai University, Shanghai 200436, China
  • Received:2005-01-25 Revised:2005-05-26 Online:2005-12-20 Published:2005-12-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10405030 and 10135020).

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摘要： The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade (HT-7U) when the equilibrium field with a monotonic $q$-profile is perturbed by a helical magnetic field. We find that a single mode ($m,n$) helical perturbation can cause the formation of islands on rational surfaces with $q=m/n$ and $q=(m\pm 1, \pm 2, \pm 3,\ldots) /n$ due to the toroidicity and plasma shape (i.e. elongation and triangularity), while there are many undestroyed magnetic surfaces called Kolmogorov--Arnold--Moser (KAM) barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field $\tilde {B}_r (r)$ and the toroidal magnetic field amplitude $B_{\phi 0} $ is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.

关键词: plasma equilibrium, magnetic island, stochasticity

Abstract: The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade (HT-7U) when the equilibrium field with a monotonic $q$-profile is perturbed by a helical magnetic field. We find that a single mode ($m,n$) helical perturbation can cause the formation of islands on rational surfaces with $q=m/n$ and $q=(m\pm 1, \pm 2, \pm 3,\ldots) /n$ due to the toroidicity and plasma shape (i.e. elongation and triangularity), while there are many undestroyed magnetic surfaces called Kolmogorov--Arnold--Moser (KAM) barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field $\tilde {B}_r (r)$ and the toroidal magnetic field amplitude $B_{\phi 0} $ is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.

Key words: plasma equilibrium, magnetic island, stochasticity

中图分类号:  (Tokamaks, spherical tokamaks)

  • 52.55.Fa
52.55.Hc (Stellarators, torsatrons, heliacs, bumpy tori, and other toroidal confinement devices) 52.65.-y (Plasma simulation)