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arXiv 1404.3897astro-ph.SRphysics.flu-dynphysics.plasm-phphysics.space-ph
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关于开放磁场的螺旋度

On the Helicity of Open Magnetic Fields

C. Prior, A. R. Yeates

备注：
31 pages, 8 figures, accepted in ApJ
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摘要：

我们重新考虑了开域中磁场的磁螺旋度的拓扑解释，并将其与相对螺旋度联系起来。具体来说，我们的域在两个平行平面之间伸展，并且这些末端中的每一个都可以是磁性开放的。它表明，虽然磁螺旋度是规范相关的，它的值在任何规范可以被物理解释为平均绕组数之间的所有对场线相对于一些正交框架场。实际上，规范的选择等同于相对螺旋度中参考场的选择，这意味着磁螺旋度在物理意义上并不逊色。我们证明，一个特定的衡量总是衡量绕组相对于一个固定的框架，并建议，这通常是最好的选择。对于周期性场，这种选择相当于测量相对于潜在参考场的相对螺旋度。但对于非周期场，我们证明了位场是可以扭曲的。我们通过构造证明了总是存在一个可能的无扭参考场。

英文摘要：

We reconsider the topological interpretation of magnetic helicity for magnetic fields in open domains, and relate this to the relative helicity. Specifically, our domains stretch between two parallel planes, and each of these ends may be magnetically open. It is demonstrated that, while the magnetic helicity is gauge-dependent, its value in any gauge may be physically interpreted as the average winding number among all pairs of field lines with respect to some orthonormal frame field. In fact, the choice of gauge is equivalent to the choice of reference field in the relative helicity, meaning that the magnetic helicity is no less physically meaningful. We prove that a particular gauge always measures the winding with respect to a fixed frame, and propose that this is normally the best choice. For periodic fields, this choice is equivalent to measuring relative helicity with respect to a potential reference field. But for aperiodic fields, we show that the potential field can be twisted. We prove by construction that there always exists a possible untwisted reference field.

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