Related Experiment Video
Updated: May 8, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Extending the range of the inductionless magnetorotational instability
Oleg N Kirillov1, Frank Stefani
1Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 510119, D-01314 Dresden, Germany. o.kirillov@hzdr.de
Physical Review Letters
|August 27, 2013
Summary
Inductionless magnetorotational instability (MRI) variants can destabilize accretion disks even in low magnetic Reynolds number regions. This research extends MRI applicability by analyzing helical and azimuthal MRI on Keplerian profiles.
Area of Science:
- Plasma Physics
- Astrophysical Fluid Dynamics
- Magnetohydrodynamics
Background:
- The magnetorotational instability (MRI) is crucial for angular momentum transport in accretion disks.
- A significant limitation of the MRI is its questionable effectiveness in regions with low magnetic Reynolds numbers.
- Previous studies established critical Rossby number limits (Liu limits) for MRI stability.
Purpose of the Study:
- To extend the applicability of the MRI to regions with low magnetic Reynolds numbers.
- To investigate the destabilizing effects of inductionless MRI variants on accretion disk profiles.
- To connect the lower and upper Liu limits of the critical Rossby number.
Main Methods:
- Utilized the WKB method for analyzing wave propagation and stability.
- Examined inductionless MRI variants, specifically helical and azimuthal MRI.
- Investigated the destabilization of Keplerian profiles (∝r(-3/2)) with modified azimuthal magnetic fields (∝r(-1)).
Main Results:
- Demonstrated that inductionless MRI variants can destabilize hydrodynamically stable Keplerian flows.
- Showed that slight modifications to the current-free azimuthal magnetic field profile enhance instability.
- Established a natural connection between the lower Liu limit (Ro≈-0.828) and the upper Liu limit (Ro≈+4.828).
Conclusions:
- Inductionless MRI variants significantly broaden the conditions under which MRI can operate in accretion disks.
- The study overcomes the limitations of low magnetic Reynolds number applicability for MRI.
- This work provides a unified understanding of MRI stability across a wider range of Rossby numbers.
Related Concept Videos
01:23Atomic Nuclei: Nuclear Relaxation Processes
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis. This...
01:28Magnetostatic Boundary Conditions
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
01:24Potential Due to a Magnetized Object
Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...
The vector...
01:26Divergence and Curl of Magnetic Field
The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
01:15Magnetic Vector Potential
In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...
01:26Diamagnetism
Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the moments opposite to the field are induced. Such materials are called diamagnets. Diamagnetism is the response of the diamagnets when placed in an external magnetic field.
Diamagnetism was discovered by Anton Brugmans in 1778 when he observed that bismuth gets repelled by magnetic fields, thus theorizing that diamagnets get repelled by magnets.
Diamagnetism was discovered by Anton Brugmans in 1778 when he observed that bismuth gets repelled by magnetic fields, thus theorizing that diamagnets get repelled by magnets.