Critical wavelength of the magnetorotational instability (${\lambda }_{\mathrm{crit}}$)

For a vertical magnetic field in a Keplerian disk, axisymmetric vertical MRI modes are unstable when $k^2{v}_A^2<3{\Omega }^2$. The shortest unstable wavelength is ${\lambda }_{\mathrm{crit}}=2\pi v_A/(\sqrt{3}\Omega )$.