Magnetorotational instability
Encyclopedia
The magnetorotational instability or MRI is a fluid
instability
that arises when the angular velocity
of a magnetized fluid decreases as the distance from the rotation center increases. It can also be known as the Velikhov-Chandrasekhar instability or Balbus-Hawley instability in the literature; not to be confused with the Velikhov instability which is the electrothermal instability
. The MRI is of particular relevance in astrophysics
where it is an important part of the dynamics in accretion disc
s. Balbus and Hawley were the first to realize the astrophysical importance of this instability and explain its physical mechanism. Their original discovery paper now has over 1,600 citations.
A rotating hydrodynamic fluid disc (e.g. a nonmagnetic accretion disc) will remain in a laminar flow
state as long as the angular momentum (per unit mass) increases outwards. This is also known as the Rayleigh stability criterion:
where
is the angular velocity of a fluid element and 
is its distance to the rotation center. Instabilities leading ultimately to turbulence occur if a magnetic field is present and the angular velocity decreases with radius:
Most accretion discs will meet this criterion.
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. His result was later generalized by S. Chandrasekhar
in 1960. This mechanism was proposed by Acheson & Hide (1973) to perhaps play a role in the context of the Earth's geodynamo problem. The applicability of this mechanism to the problem of accretion disks was appreciated when S. A. Balbus and J. F. Hawley established that weak magnetic fields can substantially alter the stability character of accretion disks.
A simple model illustrates the main effect of the instability. Consider a rotating fluid disc in the presence of a weak axial magnetic field. Two radially neighboring fluid elements behave as two mass points connected by a massless spring, the spring tension playing the role of the magnetic tension. In a Keplerian disc the inner fluid element orbits more rapidly than the outer, causing the spring to stretch. The inner fluid element is then forced by the spring to slow down, reduce correspondingly its angular momentum, and therefore move to a lower orbit. The outer fluid element, meanwhile, is forced by the spring to speed up, increase correspondingly its angular momentum, and therefore move to a higher orbit. The spring tension increases as the two fluid elements grow further apart, and eventually the process runs away.
The observed accretion rates in astrophysical objects cannot be explained by a molecular viscosity, as the outward angular momentum transport in that case would not be enough to account for the inward flow of mass. The MRI provides a mechanism to account for the additional outward angular momentum transport. It is intrinsically a magnetohydrodynamic (MHD)
phenomenon, with no hydrodynamic analog. Dynamo action
is usually invoked to justify the existence of the magnetic field required for the instability to set in.
Considerable effort has been put into realizing the MRI in a controlled laboratory experiment. Results from these experiments will also allow testing of the accuracy of computer simulations involving the MRI.
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
instability
Instability
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds...
that arises when the angular velocity
Angular velocity
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...
of a magnetized fluid decreases as the distance from the rotation center increases. It can also be known as the Velikhov-Chandrasekhar instability or Balbus-Hawley instability in the literature; not to be confused with the Velikhov instability which is the electrothermal instability
Electrothermal instability
The electrothermal instability is a magnetohydrodynamic instability appearing in magnetized non-thermal plasmas used in MHD converters...
. The MRI is of particular relevance in astrophysics
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
where it is an important part of the dynamics in accretion disc
Accretion disc
An accretion disc is a structure formed by diffuse material in orbital motion around a central body. The central body is typically a star. Gravity causes material in the disc to spiral inward towards the central body. Gravitational forces compress the material causing the emission of...
s. Balbus and Hawley were the first to realize the astrophysical importance of this instability and explain its physical mechanism. Their original discovery paper now has over 1,600 citations.
A rotating hydrodynamic fluid disc (e.g. a nonmagnetic accretion disc) will remain in a laminar flow
Laminar flow
Laminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross currents...
state as long as the angular momentum (per unit mass) increases outwards. This is also known as the Rayleigh stability criterion:
where
is the angular velocity of a fluid element and is its distance to the rotation center. Instabilities leading ultimately to turbulence occur if a magnetic field is present and the angular velocity decreases with radius:Most accretion discs will meet this criterion.
The MRI was first noticed in a non-astrophysical context by Evgeny Velikhov
Evgeny Velikhov
Evgeny Pavlovich Velikhov is a physicist and scientific leader in the Russian Federation. His scientific interests include plasma physics, lasers, controlled nuclear fusion, power engineering and magnetohydrodynamics...
in 1959 when considering the stability of Couette flow
Couette flow
In fluid dynamics, Couette flow refers to the laminar flow of a viscous fluid in the space between two parallel plates, one of which is moving relative to the other. The flow is driven by virtue of viscous drag force acting on the fluid and the applied pressure gradient parallel to the plates...
of an ideal hydromagnetic
Magnetohydrodynamics
Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
fluid. His result was later generalized by S. Chandrasekhar
Subrahmanyan Chandrasekhar
Subrahmanyan Chandrasekhar, FRS ) was an Indian origin American astrophysicist who, with William A. Fowler, won the 1983 Nobel Prize for Physics for key discoveries that led to the currently accepted theory on the later evolutionary stages of massive stars...
in 1960. This mechanism was proposed by Acheson & Hide (1973) to perhaps play a role in the context of the Earth's geodynamo problem. The applicability of this mechanism to the problem of accretion disks was appreciated when S. A. Balbus and J. F. Hawley established that weak magnetic fields can substantially alter the stability character of accretion disks.
A simple model illustrates the main effect of the instability. Consider a rotating fluid disc in the presence of a weak axial magnetic field. Two radially neighboring fluid elements behave as two mass points connected by a massless spring, the spring tension playing the role of the magnetic tension. In a Keplerian disc the inner fluid element orbits more rapidly than the outer, causing the spring to stretch. The inner fluid element is then forced by the spring to slow down, reduce correspondingly its angular momentum, and therefore move to a lower orbit. The outer fluid element, meanwhile, is forced by the spring to speed up, increase correspondingly its angular momentum, and therefore move to a higher orbit. The spring tension increases as the two fluid elements grow further apart, and eventually the process runs away.
The observed accretion rates in astrophysical objects cannot be explained by a molecular viscosity, as the outward angular momentum transport in that case would not be enough to account for the inward flow of mass. The MRI provides a mechanism to account for the additional outward angular momentum transport. It is intrinsically a magnetohydrodynamic (MHD)
Magnetohydrodynamics
Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
phenomenon, with no hydrodynamic analog. Dynamo action
Dynamo theory
In geophysics, dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field. The theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time...
is usually invoked to justify the existence of the magnetic field required for the instability to set in.
Considerable effort has been put into realizing the MRI in a controlled laboratory experiment. Results from these experiments will also allow testing of the accuracy of computer simulations involving the MRI.