Abstract
This chapter treats MHD instabilities of ideal plasmas. Section 6.1 explains interchange instability (Rayleigh–Taylor (RT) instability) intuitionally. MHD equation is linearized to (6.32) in Sect. 6.2 and the growth rate of RT instability (6.52) is derived in systematic way. Section 6.3 treats sausage and kink instabilities of a simple cylindrical plasmas with sharp boundary. Section 6.4 derives energy integral (6.76)–(6.78). The solution of eigenvalue problem for the growth rate is equivalent to the solution based on the calculus of variation of energy integral. Section 6.5 discusses instability of diffuse boundary configuration with use of energy integral. Section 6.6 explains the exact Hain Lüst MHD equation of cylindrical plasmas to find the growth rate. Section 6.7 treats the ballooning instability driven by plasma pressure gradient and Sect. 6.8 treats the eta-i mode due to density and ion temperature gradient.
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Miyamoto, K. (2016). Magnetohydrodynamic Instabilities. In: Plasma Physics for Controlled Fusion. Springer Series on Atomic, Optical, and Plasma Physics, vol 92. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49781-4_6
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