Conditions for the existence of an X‐point in a magnetic field

A sufficient condition for the existence of a node (i.e. an X‐point) in lines of a quasi‐static magnetic induction field is proved. The theoretical approach is developed for two‐dimensional fields. The problem of obtaining an X‐point in a magnetic induction field is encountered in toroidal devices (tokamaks) for controlled thermonuclear fusion experiments. The proposed method is capable of identifying possible X‐point locations through the knowledge of field variables which are easy to calculate and/or measure.