25.03.2015 - GAST: DR. ILAN ROTH

Vom 28.-30. April 2015 ist Dr. Ilan Roth vom Space Scienses UC Berkeley, University of California, USA zu Gast bei Prof. Dr. Reinhard Schlickeiser (Theoretische Physik IV). Im Rahmen des Seminars "Weltraum- und Astrophysik" hält er am 29.4. um 10:15 Uhr (NB 7/67) einen Vortrag über "Knotty Invariants: Structure & Evolution of Magnetized Fluids" sowie am 30.4. um 10:15 Uhr (NB 7/67) über "Solar/Planetary/Galactic Relativistic Electrons: Common Denominator?". Interessierte sind herzlich willkommen!

Ilan Roth


Magnetic fields in the laboratory and in space are generally depicted as closed loops or curves anchored at physical foot-points, both deformed through a set of stretching and bending procedures. This classification allows one to describe most of the magnetic configurations in fusion research, in magnetic confinement and in astrophysical environments as 2D curves modified by slide, poke or twist.
However, dynamically evolving 3D magnetic structures may form loops which cannot be transformed to an equivalent closed (anchored) two-dimensional curve. Hence, the resulting curves' characterization may be generalized through their unique topology. The analogy between MHD and knot theory offers a new classification of magnetic flux tubes. Ideal MHD fluid describes non self-intersecting loops with smooth stretching and bending in the viscous surrounding fluid, identically to mathematical knots. The crossings of a 3D structure projection are assigned mathematical operations resulting in new invariants which are preserved under stretching and bending, forming robust entities. We conjecture that the field which emerges from the solar photosphere appears in the form of a prime knots, knots which cannot be composed from two nontrivial knots. Observations of intermittent ion flux drops in impulsive solar flares can be attributed to the formation of the simplest knotty structures – torus knots. Similarly, accumulation of small-scale localized spatial structures seen in simulations and inferred experimentally in the cascading solar wind plasma can be related to the stability of the 3D knots. Implications for dynamo processes and decay and for stability of complex magnetic configurations due to preservation of topological invariants are suggested.


Observations of electron distribution functions with sub or super relativistic tail or power law(s) at high energies and with elongated tails are common in space plasmas. These distributions are measured in situ or deduced remotely in various magnetized environments. The in situ measurements relate to enhanced fluxes of relativistic electrons principally (i) in the terrestrial outer radiation belts and (ii) at the interplanetary medium at heliospheric distances of 1 AU with related solar observations, or (iii) remotely at galactic distances through various radiation emissions. Due to the similarity between the observations at the relativistic radiation belts and solar electrons it is suggested that a specific bootstrap mechanism to relativistic electrons operates at these environments. Several possible solutions to previously ignored aspects of the mechanism will be offered. New mathematical description for the formation of an energetic distribution function tail will be described.