Magnetorotational instability

The magnetorotational instability or MRI is a fluid instability that causes an accretion disk orbiting a massive central object to become turbulent. It arises when the angular velocity of a conducting fluid in a magnetic field decreases as the distance from the rotation center increases. It is also known as the Velikhov-Chandrasekhar instability or Balbus-Hawley instability in the literature, not to be confused with the electrothermal Velikhov instability. The MRI is of particular relevance in astrophysics where it is an important part of the dynamics in accretion disks.

Gases or liquids containing mobile electrical charges are subject to the influence of a magnetic field. In addition to hydrodynamical forces such as pressure and gravity, an element of magnetized fluid also feels the Lorentz force ${\displaystyle {\boldsymbol {J}}\times {\boldsymbol {B}}\ ,}$ where ${\displaystyle {\boldsymbol {J}}}$ is the current density and ${\displaystyle {\boldsymbol {B}}}$ is the magnetic field vector. If the fluid is in a state of differential rotation about a fixed origin, this Lorentz force can be surprisingly disruptive, even if the magnetic field is very weak. In particular, if the angular velocity of rotation ${\displaystyle \Omega }$ decreases with radial distance ${\displaystyle R\ ,}$ the motion is unstable: a fluid element undergoing a small displacement from circular motion experiences a destabilizing force that increases at a rate which is itself proportional to the displacement. This process is known as the Magnetorotational Instability, or "MRI".

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