 Flux expulsion

Flux expulsion is redistribution of magnetic flux out of the interiors of persistent circulating flows into their edges and surrounding regions. In two-dimensional incompressible flow, a magnetic flux function obeys ${\partial }_{t}A+\mathbf{u}\cdot \nabla A=\eta {\nabla }^{2}A$. At large but finite magnetic Reynolds number, circulation stretches gradients of $A$, enabling resistive smoothing and weak interior magnetic field with strong field near the circulation boundary. Finite magnetic diffusivity is essential to the eventual rearrangement; exact ideal magnetic flux freezing alone does not justify a flux-free steady cell. Magnetic back reaction can limit the process.