= Parallel-propagating ideal magnetohydrodynamic wave
{title2=$\omega^2=k^2v_A^2\ \text{or}\ k^2c_s^2$}
In a uniform ideal-MHD <plasma> at rest, take the <wavevector> parallel to a nonzero background field. Projecting the linear <velocity> equation along and perpendicular to the field gives two transverse Alfvén <polarizations> at speed $v_A$ and one longitudinal acoustic <polarization> at speed $c_s$. Compression does not bend field lines for the longitudinal branch. The general oblique fast/slow magnetosonic modes reduce to the corresponding faster/slower parallel branches, with degeneracies when their speeds agree.
Back to article page
