= Magnetic pressure discontinuity in an isothermal atmosphere
{title2=$\rho_+-\rho_-=(B_-^2-B_+^2)/(2\mu_0c_T^2)$}
Two uniform horizontal <magnetic fields> on either side of a horizontal interface exert no bulk force, but their <magnetic pressures> differ. For a common-temperature <isothermal atmosphere> with sound-speed squared $c_T^2=\mathcal RT_0$ and gravity $g$, <hydrostatic equilibrium> gives $p_i=c_T^2\rho_i$ and $p_i(z)=p_i(0)e^{-z/H}$, $H=c_T^2/g$. Continuity of <magnetohydrodynamic total pressure> gives the displayed density jump. A stronger field below means denser gas above, supplying a <Rayleigh-Taylor instability> even though each half-space is hydrostatic.
// Target: continuum-mechanics.bigb
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