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On the conditions for up-down asymmetry in the core of tokamak equilibria: a matter of simple geometry

机译：关于托卡马克平衡核心中上下不对称的条件：一个简单的几何问题

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摘要

Drawing from decades-long-established results on tokamak equilibria (showing that flux surfaces closely surrounding the magnetic axis are ellipses), and using basic geometry and back-of-the-envelope calculations, recent theoretical results are revisited which have revealed that, for an externally imposed tilting, the elongation and hence the up-down asymmetry (UDA) of flux surfaces in the core of a tokamak plasma are inversely proportional to the toroidal current density flowing on axis. A figure of merit is also proposed to measure on-axis UDA, which stems from a simple geometrical analysis of elliptical flux surfaces and lies between zero and one. Moreover, it is shown that the current density on axis is bounded from below by the asymmetry-controlling coefficients themselves (which are essentially set by external shaping coils), meaning there is no way around it: enforcing stronger ellipticity from the outside can only result in increasing the minimum current density allowed in the core, whereas trying to make the latter go down is only possible with milder shaping coefficients. Such a severe structural constraint is simply the manifestation of a topological necessary condition to have closed flux surfaces nested around a tokamak magnetic axis and suggests that experimental attempts to push UDA from a strongly shaped plasma boundary into the core will remain mostly elusive.
机译：根据数十年来关于托卡马克平衡的确定性结果（表明紧密围绕磁轴的磁通表面是椭圆形），并使用基本几何形状和包络线计算，重新审视了最近的理论结果，这些发现表明，对于如果外部施加倾斜，则托卡马克等离子体核心中的通量表面的伸长率以及因此而产生的上下不对称性（UDA）与在轴上流动的环形电流密度成反比。还提出了品质因数用于测量轴向UDA，该品质因数源自对椭圆通量表面的简单几何分析，并且介于零和一之间。此外，还显示出轴上的电流密度由不对称控制系数本身（基本上由外部整形线圈设置）从下方限制，这意味着无法绕开它：只能从外部强制增强椭圆率增加芯子中允许的最小电流密度，而只有降低成形系数时，才可能使芯子下降。如此严格的结构约束只是拓扑必须条件的表现，即具有围绕托卡马克磁轴嵌套的封闭通量表面的拓扑必要条件，并暗示了将UDA从强形等离子体边界推入铁芯的实验尝试仍将是遥不可及的。

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  • 来源
    《Nuclear fusion》 |2014年第8期|083015.1-083015.6|共6页
  • 作者

    Joao P.S. Bizarro;

  • 作者单位

    Instituto de Plasmas e Fusao Nuclear, Instituto Superior Tecnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    up-down asymmetry; tokamak equilibria; flux-surface geometry; intrinsic rotation;

    机译：上下不对称托卡马克平衡通量表面几何内在旋转;

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