Magnetic helicity and electromagnetic vortex filament flows under the influence of Lorentz force in MHD

Abstract

This paper is intended to present a useful insight into the comprehension of the configurations of electromagneto-vortex formation and their implications in the magnetic helicity and energy dissipation in magnetohydrodynamics (MHD). We introduce the formulations of magnetic helicity of the Lorentz force of the Serret–Frenet frame vectors and associated electromagnetic vector fields E − B firstly. Then, we investigate the Godbillon–Vey helicity model and figure out the intrinsic geometric characterizations of the electromagnetic vector fields and magnetic vector potential under the influence of vanishing magnetic helicity. We also compute the time evolution of the electromagnetic field lines of the Frenet–Serret vectors and associated geometric quantities in MHD. Then, we determine a set of partial differential equation systems describing the Hall effect, which establishes the time evolution relation between the electromagnetic field lines and magnetic vector potential in MHD. Finally, for a better comprehension of the time evolution of the electromagnetic field lines, we improve an appropriate approach to evaluate the evolution of the magnetic helicity and energy dissipation based on calculations on theoretical models.