Topological features of the heliospheric magnetic fields.

The remote observations of braided solar coronal magnetic fields, together with in situ interplanetary measurements of (a) intermittent fluxes of energetic solar particles due to a large scale flaring magnetic field as well as (b) sustained small-scale magnetic fields reversals in the solar wind opens a new venue for interpretation of a wide range of heliospheric phenomena. The standard description of magnetic fields as a set of simple, (distorted) field lines is generalized to strongly structured topological features. Combining mathematical considerations, remote images and in situ satellite observations, we construct new characteristics of those topological magnetic structures, applying Braid and Knot Theory to physical configurations, deducing their topological invariants and constraining their evolution and stability, delineating the relaxation path to magnetized equilibria. The 3-dimensional interconnection between the mathematical braids and knots are applied to the topologically non-trivial magnetized structures from solar corona to the interplanetary medium. The analysis results in conjectures regarding (i) braids’ stability under oscillations and successive appearance and decay of magnetic loops, (ii) reconfiguration of braided structures into magnetic knotted configurations, (iii) their large-scale expansion into the solar wind resulting in the intermittent observation of the solar flare ions and (iv) emission of small-scale compound magnetic knots by solar wind resulting in switchback structures.  Future high-quality missions are expected to delineate in higher resolution the structure and evolution of all these topological forms together with the required constrains for their appearance.