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Ballooning instability

The ballooning instability is a type of internal pressure-driven plasma instability usually seen in tokamak fusion power reactors or in space plasmas. It is important in fusion research as it determines a set of criteria for the maximum achievable plasma beta. 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'.

Dispersion Relation
The dispersion relation is \omega (\omega - \omega _*pi) = [Sk_\parallel ^2 -2\mu _0 \kappa \nabla P /\beta^2 ](1+b_i )V_A ^2 where S=1+n_e \delta/n_ec , \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_Be +\omega _ke) /2\omega == Relation to interchange instability ==
Relation to 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. This special limit is known as the Mercier criterion. ==References==
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