Rigidly connected magnetic lines: twisting and winding of magnetic lines

Abstract

The dynamical process of magnetic flux variation in a fluid’s stream tube is described by constructing $$1+1+ (2)$$ decomposition of the gradient of fluid’s 4-velocity. The necessary and sufficient conditions are obtained for a spacelike congruence to be a congruence of rigidly connected spacelike curves. The evolution of magnetic flux in a magnetic tube is explored under the assumptions that magnetic lines are rigidly connected and the chemical potential of the fluid is constant along a magnetic tube. The interplay between magnetic and stream tubes is demonstrated. It is shown that the growth of magnetic energy in a magnetic tube cannot exceed to that of a stream tube. It is found that the proper time variation of twist of magnetic lines is caused by gravitation inside a neutron star if magnetic lines are rigidly connected and charge neutrality condition holds. Helmholtz-like magnetic vorticity flux conservation in a magnetic tube constituted by rigidly connected geodetic magnetic lines is derived under the assumption that the charge neutrality condition holds. It is shown that the winding of frozen-in poloidal magnetic field due to differential rotation requires meridional circulation in an axisymmetric stationary hydromagnetic configuration.