Ballooning instability

The ballooning instability (a.k.a. ballooning mode instability) is a type of internal pressure-driven plasma instability usually seen in tokamak fusion power reactors^[1] or in space plasmas.^[2] It is important in fusion research as it determines a set of criteria for the maximum achievable plasma beta.^[3] The name refers to the shape and action of the instability, which acts like the elongations formed in a long balloon when it is squeezed. In literature, the structure of these elongations are commonly referred to as 'fingers'.^[4][5][6]

The narrow fingers of plasma produced by the instability are capable of accelerating and pushing aside the surrounding magnetic field in order to cause a sudden, explosive release of energy. Thus, the instability is also known as the explosive instability.^[7][8][9]

Dispersion Relation

The dispersion relation is

${\displaystyle \omega (\omega -\omega _{*}pi)=[Sk_{\parallel }^{2}-2\mu _{0}\kappa \nabla P/\beta ^{2}](1+b_{i})V_{A}^{2}}$where

${\displaystyle S=1+n_{e}\delta /n_{e}c}$ ,

${\displaystyle \delta =\beta _{e}/(\omega _{*}pi-\omega _{*}ep)/2(\omega -q_{i}T_{-}\omega _{*}pi)b_{i})/(\omega -\omega _{*}e)-3/2(\omega -\omega _{*}pe)b_{i}/(\omega -\omega -\omega _{*}e)(\omega _{B}e+\omega _{k}e)/2\omega }$

Relation to interchange instability

See also: Interchange instability

The interchange instability can be derived from the equations of the ballooning instability as a special case in which the ballooning mode does not perturb the equilibrium magnetic field.^[2] This special limit is known as the Mercier criterion.^[3]