Magnetic topology and the problem of its invariant definition

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Abstract
The evolution of an ideal plasma conserves magnetic lines of force and hence magnetic topology. However, magnetic topology, i.e. the structure and linkage of magnetic flux, is a property of the magnetic field alone. Therefore, the conservation of topology can also be a property of non‐ideal plasmas for which the plasma flow is not line conserving. A general definition of magnetic topology is given and it is shown that it yields a large set of non‐ideal topology‐conserving systems. In the application of the notion of magnetic topology to real plasmas problems arise concerning the stability of topology. Instability may inhibit one from defining the topology of a given real, i.e. not exactly prescribed, magnetic field configuration and makes it difficult to detect changes of magnetic topology, such as reconnection processes. This problem of structural instability of magnetic topology also appears in connection with changes of the frame of reference. A change of the frame of reference may lead to a transition in topology especially for topological unstable, non‐ideal systems.