DIRECTIONAL MAGNETIC AND ELECTRIC VORTEX LINES AND THEIR GEOMETRIES

In this study, we firstly introduce a different type of directional
Fermi-Walker transportations along with vortex lines of a non-vanishing
vector field in three-dimensional space. Thus we conclude that geometric
quantities, which are used to characterize vortex lines, are also
associated with the geometric phase and angular velocity vector (Darboux
vector) of the system. Then we present directional magnetic vortex lines
by computing the Lorentz force. Hence, we reach a remarkable relation
between directional magnetic vortex lines and angular velocity vector of
vortex lines with a non-rotating frame. We later determine the
directional electric vortex lines by considering the electromagnetic
force equation. We finally investigate the conditions of being uniform
for magnetic fields of directional magnetic vortex lines and we improve
a remarkable approach to find the electromagnetic curvature, which
contains many geometrical features belonging to directional electric
vortex line.