= Magnetohydrodynamic phase mixing
{title2=$\partial_R f(R,z+v(R)t)=f_R+t v'(R)f_z$}
Neighboring magnetic surfaces with different <Alfvén speeds> carry the same axial waveform at different rates. For a traveling profile $f(R,z+v(R)t)$, differentiation produces the displayed term, so transverse gradients grow even without axial wave steepening. Small <magnetic diffusivity> or <viscosity> can eventually act strongly on these gradients. The ideal process redistributes phase rather than directly dissipating wave energy.
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