Magnetorotational instability
It arises when the angular velocity of a conducting fluid in a magnetic field decreases as the distance from the rotation center increases.
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.
The MRI was first noticed in a non-astrophysical context by Evgeny Velikhov in 1959 when considering the stability of Couette flow of an ideal hydromagnetic fluid.
[2][3] This mechanism was proposed by David Acheson and Raymond Hide (1973) to perhaps play a role in the context of the Earth's geodynamo problem.
[4] Although there was some follow-up work in later decades (Fricke, 1969; Acheson and Hide 1972; Acheson and Gibbons 1978), the generality and power of the instability were not fully appreciated until 1991, when Steven A. Balbus and John F. Hawley gave a relatively simple elucidation and physical explanation of this important process.
Normally, such a force is restoring, a strongly stabilizing influence that would allow a type of magnetic wave to propagate.
If mi is allowed to orbit a little bit closer to the center than mo, it will have a slightly higher angular velocity.
mo, on the other hand, experiences a positive torque, acquires more angular momentum, and moves outward to a higher orbit.
Let us now consider small departures from the circular motion of the orbiting mass element caused by some perturbing force.
We transform variables into a rotating frame moving with the orbiting mass element at angular velocity
In our solar system, for example, deviations from a sun-centered circular orbit that are familiar ellipses when viewed by an external viewer at rest, appear instead as small radial and azimuthal oscillations of the orbiting element when viewed by an observer moving with the undisturbed circular motion.
The specific angular momentum must increase outward if stable epicyclic oscillations are to exist, otherwise displacements would grow exponentially, corresponding to instability.
The conditions inside a perfectly conducting fluid in motion is often a good approximation to astrophysical gases.
) A magnetic field exerts a force per unit volume on an electrically neutral, conducting fluid equal to
In astrophysics, one is generally interested in the case for which the disk is supported by rotation against the gravitational attraction of a central mass.
Interest in the MRI is based on the fact that it appears to give an explanation for the origin of turbulent flow in astrophysical accretion disks (Balbus and Hawley, 1991).
A promising model for the compact, intense X-ray sources discovered in the 1960s was that of a neutron star or black hole drawing in ("accreting") gas from its surroundings (Prendergast and Burbidge, 1968).
But how an element of gaseous fluid managed to lose its angular momentum and spiral onto the central object was not at all obvious.
The presence of shear-generated turbulence, in turn, produces the powerful torques needed to transport angular momentum from one (inner) fluid element to another (farther out).
The breakdown of shear layers into turbulence is routinely observed in flows with velocity gradients, but without systematic rotation.
This is an important point, because rotation produces strongly stabilizing Coriolis forces, and this is precisely what occurs in accretion disks .
These oscillations are present under much more general conditions as well: a recent laboratory experiment (Ji et al., 2006) has shown stability of the flow profile expected in accretion disks under conditions in which otherwise troublesome dissipation effects are (by a standard measure known as the Reynolds number) well below one part in a million.
Large scale numerical simulations of the MRI indicate that the rotational disk flow breaks down into turbulence (Hawley et al., 1995), with strongly enhanced angular momentum transport properties.
The formation of stars (Stone et al., 2000), the production of X-rays in neutron star and black hole systems (Blaes, 2004), and the creation of active galactic nuclei (Krolik, 1999) and gamma ray bursts (Wheeler, 2004) are all thought to involve the development of the MRI at some level.
The process by which fluid motions are converted to magnetic field energy is known as a dynamo (Moffatt, 1978); the two best studied examples are the Earth's liquid outer core and the layers close to the surface of the Sun.
Whether the MRI is an efficient dynamo process in accretion disks is currently an area of active research (Fromang and Papaloizou, 2007).
Internal rotation in stars (Ogilvie, 2007), and even planetary dynamos (Petitdemange et al., 2008) may, under some circumstances, be vulnerable to the MRI in combination with convective instabilities.
A claimed detection of the MRI in a spherical shell experiment (Sisan et al., 2004), in which the underlying state was itself turbulent, awaits confirmation at the time of this writing (2009).
Because it is less sensitive to stabilizing ohmic resistance than is the classical MRI, this helical magnetic instability is easier to excite in the laboratory, and there are indications that it may have been found (Stefani et al., 2006).
The spring-mass analogue of the standard MRI has been demonstrated in rotating Taylor–Couette / Keplerian-like flow (Hung et al. 2019).
