Magnetohydrodynamic stability of plasmas with ideal and relaxed regions
Abstract
A unified energy principle approach is presented for analysing the magnetohydrodynamic (MHD) stability of plasmas consisting of multiple ideal and relaxed regions. The gauge a = ξ × B for the vector potential, a, of linearized perturbations is used, with the equilibrium magnetic field B obeying a Beltrami equation, × B = αB, in relaxed regions. In a region with such a forcefree equilibrium Beltrami field we show that ξ obeys the same EulerLagrange equation whether ideal or relaxed MHD is used for perturbations, except in the neighbourhood of the magnetic surfaces where B · is singular. The difference at singular surfaces is analysed in cylindrical geometry: in ideal MHD only Newcomb's small solutions are allowed, whereas in relaxed MHD only the oddparity large solution and evenparity small solution are allowed. A procedure for constructing global multiregion solutions in cylindrical geometry is presented. Focusing on the limit where the two interfaces approach each other arbitrarily closely, it is shown that the singularlimit problem encountered previously by Hole et al. in multiregion relaxed MHD is stabilized if the relaxedMHD region between the coalescing interfaces is replaced by an idealMHD region. We then present a stable (k, pressure) phasespace plot, which allows us to determine the form a stable pressure and field profile must take in the region between the interfaces. From this knowledge, we conclude that there exists a class of singleinterface plasmas that were found to be stable by Kaiser and Uecker, but are shown to be unstable when the interface is resolved.
 Publication:

Journal of Plasma Physics
 Pub Date:
 October 2009
 DOI:
 10.1017/S0022377809008095
 arXiv:
 arXiv:0902.2612
 Bibcode:
 2009JPlPh..75..637M
 Keywords:

 Physics  Plasma Physics
 EPrint:
 doi:10.1017/S0022377809008095