Magnetic buoyancy

In plasma physics, magnetic buoyancy is an upward force exerted on magnetic flux tubes that are immersed in electrically conducting fluids and are under the influence of a gravitational force. It acts on magnetic flux tubes in stellar convection zones where it plays an important role in the formation of sunspots and starspots.^[1] It was first proposed by Eugene Parker in 1955.

Magnetic flux tubes

For a magnetic flux tube in hydrostatic equilibrium with the surrounding medium, the tube's interior magnetic pressure ${\displaystyle p_{m}}$ and fluid pressure ${\displaystyle p_{i}}$ must be balanced by the fluid pressure ${\displaystyle p_{e}}$ of the exterior medium, that is,

${\displaystyle p_{e}=p_{i}+p_{m}.}$

The magnetic pressure is always positive, so ${\displaystyle p_{e}>p_{i}.}$ As such, assuming that the temperature of the plasma within the flux tube is the same as the temperature of the surrounding plasma, the density of the flux tube must be lower than the density of the surrounding medium. Under the influence of a gravitational force, the tube will rise.^[2][3]

Instability

The magnetic buoyancy instability is a plasma instability that can arise from small perturbations in systems where magnetic buoyancy is present. The magnetic buoyancy instability in a system with magnetic field ${\displaystyle \mathbf {B} }$ and perturbation wavevector ${\displaystyle \mathbf {k} }$, has three modes: the interchange instability where the perturbation wavevector is perpendicular to the magnetic field direction ${\displaystyle \left(\mathbf {k} \perp \mathbf {B} \right)}$; the undular instability, sometimes referred to as the Parker instability or magnetic Rayleigh–Taylor instability, where the perturbation wavevector is parallel to the magnetic field direction ${\displaystyle \left(\mathbf {k} \parallel \mathbf {B} \right)}$; and the mixed instability, sometimes referred to as the quasi-interchange instability, a combination of the interchange and undular instabilities.^[3][4][5][6]

References

1. Guerrero, G.; Käpylä, P. J. (September 2011). "Dynamo action and magnetic buoyancy in convection simulations with vertical shear". Astronomy & Astrophysics. 533: A40. arXiv:1102.3598. Bibcode:2011A&A...533A..40G. doi:10.1051/0004-6361/201116749. S2CID 118582079.
2. Parker, Eugene N. (March 1955). "The Formation of Sunspots from the Solar Toroidal Field". The Astrophysical Journal. 121: 491. Bibcode:1955ApJ...121..491P. doi:10.1086/146010.
3. Acheson, D. J. (May 1979). "Instability by magnetic buoyancy". Solar Physics. 62 (1): 23–50. Bibcode:1979SoPh...62...23A. doi:10.1007/BF00150129. S2CID 121629539.
4. Matsumoto, R.; Tajima, T.; Shibata, K.; Kaisig, M. (September 1993). "Three-dimensional magnetohydrodynamics of the emerging magnetic flux in the solar atmosphere". The Astrophysical Journal. 414: 357. Bibcode:1993ApJ...414..357M. doi:10.1086/173082.
5. Gilman, Peter A. (24 January 2018). "Magnetic Buoyancy and Rotational Instabilities in the Tachocline". The Astrophysical Journal. 853 (1): 65. Bibcode:2018ApJ...853...65G. doi:10.3847/1538-4357/aaa4f4. S2CID 126268222.
6. Kim, J.; Ryu, D.; Hong, S. S.; Lee, S. M.; Franco, J. (2005). "The Parker Instability". How Does the Galaxy Work?. Astrophysics and Space Science Library. 315: 315–322. doi:10.1007/1-4020-2620-X_65. ISBN 1-4020-2619-6.