Ballooning instability explained

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

\omega (\omega - \omega _{*pi)} = [Sk ^{2} _{\parallel} -2 \mu _{0} \kappa \nabla P /\beta ^{2} ]( 1+ b _{i} )V ^{2} _{A} whereS =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

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. This special limit is known as the Mercier criterion.

Notes and References

1. Dobrott . D. . Nelson . D. B. . Greene . J. M. . Glasser . A. H.. Alan Herbert Glasser . Chance . M. S. . Frieman . E. A. . 1977-10-10 . Theory of Ballooning Modes in Tokamaks with Finite Shear . Physical Review Letters . 39 . 15 . 943–946 . 10.2172/5115796 . 5115796.
2. Hameiri. E.. Laurence. P.. Mond. M.. 1991-02-01. The ballooning instability in space plasmas. Journal of Geophysical Research: Space Physics. en. 96. A2. 1513–1526. 10.1029/90ja02100. 0148-0227. 1991JGR....96.1513H.
3. Book: P., Freidberg, Jeffrey. Ideal magnetohydrodynamics. 1987. Plenum Press. 0306425122. New York. 15428479.
4. Kleva. Robert G.. Guzdar. Parvez N.. 2001. Fast disruptions by ballooning mode ridges and fingers in high temperature, low resistivity toroidal plasmas. Physics of Plasmas. en. 8. 1. 103–109. 10.1063/1.1331098. 1070-664X. 2001PhPl....8..103K.
5. Cowley. Steven C.. Wilson. Howard. Hurricane. Omar. Fong. Bryan. 2003. Explosive instabilities: from solar flares to edge localized modes in tokamaks. Plasma Physics and Controlled Fusion. en. 45. 12A. A31. 10.1088/0741-3335/45/12A/003. 0741-3335. 2003PPCF...45A..31C. 250824453 .
6. Panov. E. V.. Sergeev. V. A.. Pritchett. P. L.. Coroniti. F. V.. Nakamura. R.. Baumjohann. W.. Angelopoulos. V.. Auster. H. U.. McFadden. J. P.. 2012. Observations of kinetic ballooning/interchange instability signatures in the magnetotail. Geophysical Research Letters. en. 39. 8. n/a. 10.1029/2012gl051668. 0094-8276. 2012GeoRL..39.8110P. free.
7. Hamasaki. Seishi. 1971. Self-Consistent Calculation of an Explosive Instability. Physics of Fluids. en. 14. 7. 1441–1451. 10.1063/1.1693626. 0031-9171. 1971PhFl...14.1441H.
8. Jones. Michael E.. Fukai. J.. 1979. Evolution of the explosive instability in a simulated beam plasma. Physics of Fluids. en. 22. 1. 132. 10.1063/1.862440. 0031-9171. 1979PhFl...22..132J.
9. Cowley. S. C.. Cowley. B.. Henneberg. S. A.. Wilson. H. R.. 2015-08-08. Explosive instability and erupting flux tubes in a magnetized plasma. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 471. 2180. 20140913. 10.1098/rspa.2014.0913. 1364-5021. 4550006. 26339193. 2015RSPSA.47140913C. 1411.7797.