We investigate the geometric property of a scalar position function, the so-called force-free α, to see how it quantitatively characterizes the magnetic structure of solar active regions, which is reminiscent of the electrostatic potential whose geometric property provides information on the structure of electrified objects. Scatter plots of (α, ∇2α) show characteristic shapes representing twisted magnetic field configurations in two model active regions, one of which is formed by an emerging magnetic flux tube composed of strongly twisted field lines while the other is formed by a weakly twisted flux tube. By generalizing the concept of an axis field line in a uniformly twisted cylindrical flux tube, we introduce a topological object called the principal field line to represent magnetic structure reconstructed using a force-free field model. The principal field line and associated scatter plot of (α, ∇2α) provide a method reminiscent of active-region radiography, which could be used for quantitative classification of active regions with those magnetic configurations responsible for heating coronal plasmas, generating solar winds, and producing potentially harmful coronal explosive phenomena.

中文翻译：

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与日冕加热和太阳风产生有关的磁配置。二。基于无力α几何特性的有源区磁结构定量表征

我们研究了标量位置函数的几何特性，即所谓的无力 α，以了解它如何定量表征太阳活动区的磁结构，这让人想起静电势，其几何特性提供了有关结构的信息带电的物体。(α, ∇2α) 的散点图显示了两个模型有源区中扭曲磁场配置的特征形状，其中一个是由强扭曲磁力线组成的新兴磁通管形成的，而另一个是由弱扭曲磁通形成的管子。通过推广均匀扭曲的圆柱形通量管中的轴场线的概念，我们引入了一种称为主场线的拓扑对象来表示使用无力场模型重建的磁结构。