= Magnetic-tension response to an incompressible displacement
{title2=$\delta\mathbf B=ikB_0\boldsymbol\xi,\quad\delta\mathbf f=-k^2B_0^2\boldsymbol\xi/\mu_0$}
In <ideal magnetohydrodynamics>, a small displacement of a uniform <magnetic field> obeys $\delta\mathbf B=\nabla\times(\boldsymbol\xi\times\mathbf B_0)$. For $\mathbf B_0=B_0\mathbf e_z$, a horizontal <Fourier mode> proportional to $e^{ikz}$ with $\nabla\cdot\boldsymbol\xi=0$ gives the displayed field and force perturbations. The linear <magnetic pressure> perturbation vanishes because $\delta B_z=0$. The remaining <magnetic tension> acts as a restoring spring, with <Alfvén frequency> $kv_A$.
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