= Flux-surface preservation during magnetic-tube expansion
Suppose the <Cartesian magnetic flux function> is advected, the initial axial velocity is zero, $B_y=f(\psi)$ initially, and $\nabla\cdot\mathbf u=g(\psi,t)$. Then $B_y=f(\psi)\exp[-\int_0^t g(\psi,s)\,ds]$ remains a function of the flux label and time. The axial <Lorentz force> vanishes because its transverse derivative along a <magnetic field line> vanishes. Smooth ideal evolution therefore preserves zero axial motion.
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