A review of magneto-vorticity induction in Hall-MHD plasmas

The ideal induction of vector fields in fluids and plasmas is presented as invariance under local convection, `freezing' into flowlines and transfer of potential. Related consequences are discussed, namely the conservation of local flux and total helicity and the force-free relaxation state. In the framework of single-fluid Hall-MHD plasma flow model, the magnetic field and vorticity (which are formally analogous and generally anti-correlated, but each not ideally inducted, i.e. perfectly `frozen-into' the flow) are shown to combine in a unified magneto-vorticity field, which is ideally inducted in perfectly-conducting, however even forced, non-isentropic and viscous plasmas. Relaxation plasma states of conserved or extreme helicity magneto-vorticity fields are derived and shown to be generalized force-free states, similar to those previously derived in the framework of Hall-MHD and the multi-component plasma model. The magneto-vorticity induction in visco-resistive plasmas is also discussed. Application of the magneto-vorticity field concept in the study of type I superconductors and the spontaneous generation of magnetic fields are reviewed. The Cowling `anti-dynamo' theorem for axisymmetric flows is extended in Hall-MHD and for arbitrary flows and is shown that, in principle, the resistive (ohmic) dissipation of the magnetic field can be balanced by non-isentropic heating and/or helical forcing effects.