Hybrid helicity and magneto-vorticity flux conservation in superdense npe-plasma

Abstract

In this paper, it is shown that the magnetic helicity dissipation per unit volume, coupled with the longitudinal conductivity, causes enhancement of the kinematic rotation of the electric (and magnetic) lines if the npe-plasma vorticity vector aligns with the electric (or the magnetic) field. In the case of a rigidly rotating npe-plasma under the influence of a strong magnetic field, the electric lines are rotating faster than the magnetic lines. It is deduced that the orthogonality of the electric and magnetic fields is an essential condition for the conduction current to remain finite in the limit of infinite electric conductivity of the npe-plasma. In this case, the magnetic field is not frozen into the npe-plasma, but the magnetic flux in the magnetic tube is conserved. The hybrid helicity is conserved if the “magneto-vorticity” vector is tangent to the level surfaces of constant entropy per baryon. The “magneto-vorticity” lines are rotating on the level surfaces of constant entropy per baryon due to the electromagnetic energy flow in the direction of the npe-plasma vorticity and the chemical potential variation locked with the kinematic rotation of the npe-plasma flow lines. In the case of an isentropic npe-plasma flow, there exists a family of timelike 2-surfaces spanned by the “magneto-vorticity” lines and the npe-plasma flow lines. In this case, the electric field is normal to such a family of timelike 2-surfaces. Maxwell like equations satisfied by “magneto-vorticity” bivector field are solved in axially symmetric stationary case. It is shown that the npe-plasma is in differential rotation in such a way that its each plasma shell (i.e., plasma surface spanned by “magneto-vorticity” lines) is rotating differentially without continually winding up “magneto-vorticity” lines frozen into the npe-plasma. It is also found that gravitational isorotation and Ferraro’s law of isorotation are intimately connected to each other because of coexistence of both the plasma vorticity and the magnetic field due to interaction between the electromagnetic field and npe-plasma flows.