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

Abstract

In this paper, we attempt to introduce a new approach to determine the magnetic helicity and energy dissipation of the normal electromagnetic vortex filaments in magnetohydrodynamics (MHD). We successfully compute the vector potential and magnetic helicity of Frenet–Serret vectors and associated electromagnetic fields in the existence of the Lorentz force. We further describe a set of differential equations relating the magnetic vector potential of the electromagnetic vector fields and the Godbillon–Vey helicity model. Then, we focus on the time evolution of the normal electromagnetic field lines in MHD to evaluate the evolution of the magnetic helicity and energy dissipation theoretically. As a result, we obtain analytical solutions and numerical simulations of the time evolution equations of both geometric quantities as well as the magnetic and electric field vectors.