= Hall magnetohydrodynamics
{c}
{title2=Hall MHD}
= Hall MHD
{c}
{synonym}
<Hall magnetohydrodynamics> retains bulk <ion> inertia but freezes <magnetic flux> into the <Electron> velocity $\mathbf u_e=\mathbf u-\mathbf j/(en)$. With constant density, negligible <electrical resistivity> and <Electron> inertia, <Gaussian units> give $\mathbf j=c\nabla\times\mathbf B/(4\pi)$ and $\partial_t\mathbf B=\nabla\times[(\mathbf u-c\nabla\times\mathbf B/(4\pi en))\times\mathbf B]$. The <ion> velocity still satisfies the <magnetohydrodynamic momentum equation>. Neglecting that velocity gives <electron magnetohydrodynamics>, a further approximation rather than a synonym for the complete Hall system.
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