= Magnetized isothermal atmosphere
A plane-parallel <magnetostatic equilibrium> with constant downward <gravitational acceleration> $g$, horizontal <magnetic field>, constant <isothermal sound speed> $c_s$, and constant <Alfvén speed> $v_a$ has
$$
H=\frac{c_s^2+v_a^2/2}{g},\qquad \rho=\rho_0e^{-z/H},\qquad p=c_s^2\rho,\qquad B=B_0e^{-z/(2H)}.
$$
Indeed the <magnetohydrodynamic total pressure> is $(c_s^2+v_a^2/2)\rho$, and its vertical derivative is $-g\rho$. The <magnetic pressure> therefore increases the <scale height> above that of an unmagnetized atmosphere.
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