Physics
Scientific paper
Mar 2012
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012aps..aprq16004b&link_type=abstract
American Physical Society, APS April Meeting 2012, March 31-Apr 3, 2012, abstract #Q16.004
Physics
Scientific paper
The nonlinear stability of the ideal magnetohydrodynamic interchange mode for plasma immersed in a constant transverse magnetic field near marginal conditions is studied. We use reduced equations for a strong axial field to find an analytic solution for the nonlinear behaviour as a function of the deviation from marginality. The study is motivated in order to assess B-field tolerances in stellarator coil design. A systematic perturbation analysis in the smallness parameter, |b2/Bc|^1/2, is carried out, where Bc is the critical transverse magnetic field for the marginally stable ideal mode, and b2 is the deviation from Bc. The lowest order expansion yields an eigenvalue equation for the magnitude of the critical field required for marginal stability, Bc. The calculation is carried out to third order, including nonlinear terms, and a time-evolution equation for the amplitude is found. In the short wavelength limit we find that the system is nonlinearly unstable for large enough perturbations even if b2/Bc>0 (linearly stable). This result is similar to that of Cowley and Artun ootnotetextS. C. Cowley and M. Artun, Physics Reports 283, 185 (1997). for the marginally stable line-tied g-mode. If the system is driven nonlinearly unstable, the resulting growt
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