The structure of three-dimensional magnetic neutral points

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Abstract
The local configurations of three‐dimensional magnetic neutral points are investigated by a linear analysis about the null. It is found that the number of free parameters determining the arrangement of field lines is four. The configurations are first classified as either potential or non‐potential. Then the non‐potential cases are subdivided into three cases depending on whether the component of current parallel to the spine is less than, equal to or greater than a threshold current; therefore there are three types of linear non‐potential null configurations (a radial null, a critical spiral and a spiral). The effect of the four free parameters on the system is examined and it is found that only one parameter categorizes the potential configurations, whilst two parameters are required if current is parallel to the spine. However, all four parameters are needed if there is current both parallel and perpendicular to the spine axis. The magnitude of the current parallel to the spine determines whether the null has spiral, critical spiral or radial field lines whilst the current perpendicular to the spine affects the inclination of the fan plane to the spine. A simple method is given to determine the basic structure of a null given M the matrix which describes the local linear structure about a null point.