作为扭结模阈值的加性自螺旋度
Additive Self Helicity as a Kink Mode Threshold
摘要：
在本文中，我们提出了Longcope和Malanushenko（2008）引入的加性自螺旋度在复杂平衡的扭结不稳定性中起作用，类似于薄通量管的扭曲螺旋度（Hood和Priest（1979），Berger和Field（1984））。我们通过Fan和Gibson（2003）的模拟计算扭曲通量管的加性自螺旋度来支持这一假设。随着更多的扭曲被引入，附加自螺旋度增加，并且在附加自螺旋度达到$H_A/Φ^2\approx 1.5$的值之后，管的扭结不稳定性与附加自螺旋度的下降一致（其中$Φ$是管的通量，并且$H_A$是附加自螺旋度）。我们比较了加性自螺旋度和扭曲的一个薄的子部分的管，以说明$H_A/Φ^2$是等于扭曲数，研究了伯杰和字段（1984年），当薄通量管近似是适用的。我们建议，当薄通量管近似不适用时，可以把$H_A/Φ^2$量看作是扭曲数的推广。广义扭曲数的阈值可能被证明是非常有用的研究复杂的平衡，就像扭曲数本身被证明是有用的研究理想化的薄通量管。我们明确地描述了一种计算加性自螺旋度的数值方法，其中包括用于识别磁通束所占据的域的算法和计算局限于该域的潜在磁场的方法。我们还描述了一种数值方法来计算扭曲的薄通量管，使用框架沿轴向传输的管。
英文摘要：
In this paper we propose that additive self helicity, introduced by Longcope and Malanushenko (2008), plays a role in the kink instability for complex equilibria, similar to twist helicity for thin flux tubes (Hood and Priest (1979), Berger and Field (1984)). We support this hypothesis by a calculation of additive self helicity of a twisted flux tube from the simulation of Fan and Gibson (2003). As more twist gets introduced, the additive self helicity increases, and the kink instability of the tube coincides with the drop of additive self helicity, after the latter reaches the value of $H_A/Φ^2\approx 1.5$ (where $Φ$ is the flux of the tube and $H_A$ is additive self helicity). We compare additive self helicity to twist for a thin sub-portion of the tube to illustrate that $H_A/Φ^2$ is equal to the twist number, studied by Berger and Field (1984), when the thin flux tube approximation is applicable. We suggest, that the quantity $H_A/Φ^2$ could be treated as a generalization of a twist number, when thin flux tube approximation is not applicable. A threshold on a generalized twist number might prove extremely useful studying complex equilibria, just as twist number itself has proven useful studying idealized thin flux tubes. We explicitly describe a numerical method for calculating additive self helicity, which includes an algorithm for identifying a domain occupied by a flux bundle and a method of calculating potential magnetic field confined to this domain. We also describe a numerical method to calculate twist of a thin flux tube, using a frame parallelly transported along the axis of the tube.
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