The topological underpinning of magnetic fields connected to a planar boundary is naturally described by field line winding. This observation leads to the definition of winding helicity, which is closely related to the more commonly calculated relative helicity. Winding helicity, however, has several advantages, and we explore some of these in this work. In particular, we show, by splitting the domain into distinct subregions, that winding helicity can be decomposed naturally into “self” and “mutual” components and that these quantities can be calculated, in practice, for magnetic fields with complex geometries and topologies. Further, winding provides a unified topological description from which known expressions for self and mutual helicity can be readily derived and generalized. We illustrate the application of calculating self and mutual winding helicities in a simulation of an evolving magnetic field with non-trivial field line topology.

连接到平面边界的磁场的拓扑基础自然由场线绕组来描述。这一观察导致了缠绕螺旋度的定义，它与更常见的计算相对螺旋度密切相关。. 然而，绕组螺旋度有几个优点，我们在这项工作中探索了其中的一些优点。特别是，我们通过将域分成不同的子区域，表明绕组螺旋度可以自然地分解为“自”和“互”分量，并且在实践中可以为具有复杂几何形状和拓扑结构的磁场计算这些量。此外，缠绕提供了一个统一的拓扑描述，可以很容易地推导出和概括已知的自螺旋和互螺旋的表达式。我们说明了计算自绕组和互绕组螺旋在具有非平凡场线拓扑的演化磁场的模拟中的应用。