= Reduced magnetohydrodynamics
{title2=$k_\parallel/k_\perp\ll1$}
= Reduced MHD
{synonym}
= RMHD
{c}
{synonym}
<Reduced magnetohydrodynamics> is the leading ideal-fluid description of small, anisotropic fluctuations about a strong uniform guide field, with $k_\parallel/k_\perp\sim\delta B_\perp/B_0\sim\delta u_\perp/v_A\ll1$. Its <solenoidal> perpendicular <Elsässer variables> obey
$$
\partial_t\mathbf z^\pm_\perp\mp v_A\partial_z\mathbf z^\pm_\perp+(\mathbf z^\mp_\perp\cdot\nabla_\perp)\mathbf z^\pm_\perp=-\nabla_\perp\Pi.
$$
The parallel magnetic derivative includes bending of field lines: $\nabla_\parallel=\partial_z+(\delta\mathbf B_\perp/B_0)\cdot\nabla_\perp$. Slow compressive and <entropy mode> fluctuations are passively transported at this order. The system excludes the rapidly propagating <fast magnetosonic wave> sector rather than describing all possible <MHD> perturbations.
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