Abstract
The continuous spectrum of a 2D magnetostatic equilibrium with y-invariance is derived. It is shown that the continuous spectrum is given by an eigenvalue problem on each magnetic surface and is related to the different behaviour of the equilibrium quantities in different magnetic surfaces. The special case of a uniform poloidal magnetic field in a 1D equilibrium that is stratified with height, has been considered in detail and it is found that there is no continuous spectrum. It is shown that this result relies completely on the artificial property that the behaviour of the equilibrium quantities along a magnetic field line is independent of the field line considered. As a consequence the non-existence of a continuous spectrum in a 1D equilibrium with a uniform magnetic field cannot be used to argue that the continuous spectrum has no physical relevance.
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Research Assistant of the Belgian National Fund for Scientific Research.
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Goossens, M., Poedts, S. & Hermans, D. On the existence of the continuous spectrum of ideal MHD in a 2D magnetostatic equilibrium. Sol Phys 102, 51–66 (1985). https://doi.org/10.1007/BF00154037
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DOI: https://doi.org/10.1007/BF00154037