Methods for finding magnetic nulls and reconstructing field topology: A review

In this chapter, we review and compare the methods for finding magnetic nulls and reconstructing field topology. Regarding the null finding, we focus on the Poincare index (PI) method and the first-order Taylor expansion (FOTE) method; we find that these two methods are generally consistent, except that the FOTE method can overcome certain limitations of the PI method. Regarding the topology reconstruction, we focus on the spherical-harmonic-function (SHF) method and FOTE method; we find that the SHF method is suitable for reconstruction of a null pair, while the FOTE method is suitable for reconstruction of an isolated null.