The Structure of Magnetic Neutral Points in two Dimensions

Magnetic neutral points are of central importance in many solar phenomena, such as flares, reconnection and coronal structures. Despite their importance, the mathematical nature of magnetic neutral points has not previously come under detailed mathematical scrutiny. We present here a series of models for different types of neutral points in two dimensions. X-points have four separatrix field lines meeting at the neutral point and are a particular class of star-point which have an even number of separatrices. Asymmetric star-points (with an odd number of separatrices, at least one of which is a current sheet or a neutral sheet) include: Y-points with three separatrices intersecting at angles of 2π/3; cusp-points with two of the three separatrices touching at the neutral point; and T-points with two of the separatrices meeting the third at right angles.