Alfvén characteristic eigenvector
= Alfvén characteristic eigenvector
{c}
{title2=$r_{A,s}$}
For propagation along $x$, the Alfvén right <eigenvector> has $\delta\rho=\delta p=\delta u_x=\delta B_x=0$, $\mathbf B_\perp\cdot\delta\mathbf u_\perp=0$ and $\delta\mathbf B_\perp=-s\sqrt{\mu_0\rho}\,\delta\mathbf u_\perp$. Its speed is $u_x+sB_x/\sqrt{\mu_0\rho}$, $s=\pm1$. When the transverse background field vanishes, both transverse polarizations are allowed.