Optical magnetic helicity with binormal electromagnetic vortex filament flows in MHD

Abstract

In this paper, we construct new efficient insight into the understanding of the configurations of the binormal electromagneto-vortex formation and their consequences in the energy dissipation and magnetic helicity in magnetohydrodynamics (MHD). Firstly, we introduce new formulations of the magnetic helicity of the Lorentz force of the Serret–Frenet frame vectors and associated electromagnetic vector fields of the binormal electromagnetic field lines E − B. Then, we investigate the Godbillon–Vey helicity model. We also compute the time evolution of the binormal 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 binormal electromagnetic field lines and magnetic vector potential in MHD. Finally, for a better comprehension of the time evolution of the binormal electromagnetic field lines, we consider the traveling wave transformation and the Riccati differential equation system to evaluate the evolution of the magnetic helicity and energy dissipation based on the calculation of the theoretical models.