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arXiv 1001.4480physics.plasm-phcond-mat.stat-mechmath-phmath.MPphysics.gen-ph
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磁化等离子体密度极限的第一性原理解释

A first principles explanation for the density limit in magnetized plasmas

M. Zuin, A. Carati, M. Marino, E. Martines, L. Galgani

摘要:

磁约束核聚变研究面临着一个严峻的问题,即核聚变装置所需的电子密度。事实上,高密度是获得高效率的必要条件,而经验发现,灾难性的破坏性事件发生在密度超过最大值n^M_e时。另一方面,尽管有大量的理论工作,但没有广泛接受的密度极限的第一原理模型(见[1],摘要)。在这里,我们提出了一个简单的微观模型的磁化等离子体适用于托卡马克,密度极限的存在被证明。这种性质被证明是点电荷电动力学的一个普遍的集体特征,而在连续近似中却失去了这种特征。我们发现的定律是n^M_e = 1.74 1/(me c^2)B^2/ μ_0,(1),其中μ_0是真空磁导率,c是光速,me是电子质量,B是磁场。如图1所示,理论极限(大圆圈)与经验数据相当吻合,实际上对于基于第一原理的模型来说,这是一个令人惊讶的好结果,没有可调参数。

英文摘要:

Fusion research on magnetic confinement is confronted with a severe problem concerning the electron densities ne to be used in fusion devices. Indeed, high densities are mandatory for obtaining large efficiencies, whereas it is empirically found that catastrophic disruptive events occur for densities exceeding a maximal one n^M_e. On the other hand, despite the large theoretical work there is no widely accepted, first principles model for the density limit (see [1], abstract). Here, we propose a simple microscopic model of a magnetized plasma suited for a tokamak, for which the existence of a density limit is proven. This property turns out to be a general collective feature of electrodynamics of point charges, which is lost in the continuum approximation. The law we find is n^M_e = 1.74 1/(me c^2) B^2/ μ_0, (1), where μ_0 is the vacuum permeability, c the speed of light, me the electron mass, and B the magnetic field. As shown in Fig. 1, the theoretical limit (big circles) is in rather good agreement with the empirical data, actually a surprisingly good one for a model based on first principles, with no adjustable parameter.

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