Nonlinear stability of the ideal magnetohydrodynamic interchange mode at marginal conditions in a transverse magnetic field
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742-3511 (United States)
The stability of the ideal magnetohydrodynamic (MHD) interchange mode at marginal conditions is studied. A sufficiently strong constant magnetic field component transverse to the direction of mode symmetry provides the marginality conditions. A systematic perturbation analysis in the smallness parameter, |b{sub 2}/B{sub c}|{sup 1/2}, is carried out, where B{sub c} is the critical transverse magnetic field for the zero-frequency ideal mode and b{sub 2} is the deviation from B{sub c}. The calculation is carried out to third order including nonlinear terms. It is shown that the system is nonlinearly unstable in the short wavelength limit, i.e., a large enough perturbation results in instability even if b{sub 2}/B{sub c} > 0 (linearly stable). The normalized amplitude for instability is shown to scale as |b{sub 2}/B{sub c}|{sup 1/2}. A nonlinear, compressible, MHD simulation is done to check the analytic result. Good agreement is found, including the critical amplitude scaling.
- OSTI ID:
- 22047112
- Journal Information:
- Physics of Plasmas, Vol. 18, Issue 12; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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