Knotty Invariants: Structure and Evolution of Magnetized Fluids.

Roth Ilan, ilan@ssl.berkeley.edu, University of California, Berkeley, United States

Abstract
The analogy between Magnetohydrodynamics and knot theory is implemented for classification of magnetic flux tubes. The crossings of a 3D structure are assigned mathematical operations, resulting in invariants which are preserved under stretching and bending. This construction forms robust topological invariants which are preserved in ideal MHD. It is conjectured that the field which emerges from the solar photosphere appears in the form prime knot, the simplestcomplex structure. Conservation of invariants for small diffusivity and the large size of the emerging flux tubes makes them impervious to large scale reconnection, hence they will be observed as extended prime knots at 1AU. Similarly, explanation of different decay rates for large diffusivity stems from the fact that more complex knot polynomials are harder to violate. Implications for dynamo processes, decay and stability of complex magnetic configurations with topological invariants are suggested.