The magnetorotational instability destabilizes a magnetized differentially rotating flow when angular velocity decreases outward. Magnetic tension couples neighboring fluid elements, allowing the inner one to lose angular momentum and fall inward while the outer one gains angular momentum and moves outward.
For a vertical magnetic field in a Keplerian disk, axisymmetric vertical MRI modes are unstable when . The shortest unstable wavelength is .
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Magnetorotational instability (MRI) is a fundamental instability that occurs in differentially rotating astrophysical fluids in the presence of a magnetic field. It plays a critical role in the dynamics of accretion disks, such as those found around black holes, neutron stars, and young stellar objects, as well as in the formation of stars and planets.