The field line topology of a uniform magnetic field superposed on the field of a distributed ring current

Abstract

Abstract A magnetic field line topology with nulls, generated by superimposing a uniform magnetic field onto the field from a distributed ring current, is analyzed. This simple model, which is reminiscent of the structures found in laboratory field reversed configurations and detached plasmoids, is amenable to substantial analytical progress and also facilitates the visualization of the three dimensional field geometry. Four nulls are seen to exist and representative field lines and tubes of flux found by numerical integration are presented. An infinite number of topologically distinct flux bundles is found. These are distinguished by the number of times they encircle a circular magnetic field line. A convenient mapping is described which proves very useful in distinguishing between and following the paths of the different tubes of flux as they traverse through the null system. The separatrices that divide these flux bundles are described. The complexities already present in this simple but nontrivial configuration serve to emphasize the difficulties in analyzing more complicated geometries, but the intuition gained from this study proves beneficial in those cases. One such example is the comparison of the generic features of our model with those found in a topologically different model of plasmoid formations in the earth's magnetotail.