Abstract :
The viscous forces on electrons and ions in a differentially rotating plasma drive an azimuthal current density j¿, with axial magnetic field Bz which is shown to be proportional to plasma vorticity. Field strengths in agreement with those observed for both stars and galaxies are obtained, assuming that reactive forces prevent radial drifts of electrons or ions. Hierarchical vorticity is required in order to reconcile the small-scale length required for field changes with the large-scale length of observed fields. A vortex tube with magnetic field (magnetic vortex tube-MVT) becomes the basic entity for the origin of magnetic fields. Twisting of field lines by differential rotation causes (1¿,Bz,) ¿(jz, B¿,). When jzB¿, > j¿, Bz the MVT suffers magnetic pinch, and the axial current in the pinch flows through a cylindrical sheath with a radial electric field due to plasma polarization. An instability of drift velocity denudes a length R of the current channel of free charges, and the inductively maintained current then requires a displacement current in R and hence a growing axial electric field Ez, Ez is limited by transfer of the energy in B¿, to Ez, and thereafter the energy oscillates between the fields. On the stellar scale, evidence for polar MVT´s comes from young stars with bipolar outflows of gas and jets. It is argued that end-on viewing of polar MVT´s accounts for the kilogauss fields of Ap stars and the 1-100-MG fields of magnetic white dwarfs.
