Magnetic buoyancy

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]

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]