1.3.3 Hydrodynamics equations including magnetic fields

The equations of ideal magneto-hydrodynamics (MHD) are

$\begin{displaymath} { \!\!\!\! \renewedcommand{arraystretch}{2.0} \begi... ...dmath$\scriptscriptstyle v$}}} \right) & = & 0 \end{array}} \end{displaymath}$

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with the magnetic field $\bgroup\color{HIGH1color}$\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle ... ...ox{\boldmath$\scriptstyle B$}} {\mbox{\boldmath$\scriptscriptstyle B$}}}$\egroup$ (with $\bgroup\color{DEFcolor}$\ensuremath{\mathchoice{\mbox{\boldmath$\nabla$}} {\mbox... ...boldmath$\scriptstyle B$}} {\mbox{\boldmath$\scriptscriptstyle B$}}} = 0$\egroup$ ) and the Maxwell stress tensor $\bgroup\color{HIGH1color}${\color{HIGH1color} \bar{\bar{\ensuremath{\mathsf{T}}}}_\mathrm{mag}}$\egroup$

$\begin{displaymath} \textstyle \bar{\bar{\ensuremath{\mathsf{T}}}}_\mathrm{mag... ...yle B$}} {\mbox{\boldmath$\scriptscriptstyle B$}}} \enspace . \end{displaymath}$

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The total energy $\bgroup\color{HIGH1color}$e_{\rm ikb}$\egroup$ now contains a contribution from the magnetic field,

$\begin{displaymath} \textstyle e_{\rm ikb}= e_{\rm i}+ \frac{1}{2} \ensuremat... ...} {\mbox{\boldmath$\scriptscriptstyle B$}}} / \rho \enspace . \end{displaymath}$

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