Magnetic axial angular momentum flux (${\mathbf{F}}_{J,p}=-R{B}_{\varphi }{\mathbf{B}}_p/{\mu }_0$)

The magnetic tension stress transports axial angular momentum along a poloidal magnetic field. In purely azimuthal ideal flow the poloidal energy flux is ${\mathbf{F}}_{E,p}=\Omega {\mathbf{F}}_{J,p}$. This proportionality is valid even at vanishing flux, where an ordinary ratio is undefined. The coupled fluxes explain how a torsional Alfvén wave redistributes rotation.