The kink instability in infinite cylindrical flux tubes: Eigenvalues for power-law twist profiles |
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Authors: | I J D Craig T D Robb A D Sneyd A N McClymont |
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Institution: | (1) University of Waikato, Hamilton, New Zealand;(2) Institute for Astronomy, University of Hawaii, Hawaii, U.S.A. |
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Abstract: | We develop simple accurate methods of calculating ideal MHD instability eigenvalues for infinitely-long cylindrical tubes, with twist functionT(r)=B
/rB
z
. A complete theoretical treatment is presented for force-free magnetic equilibria with arbitraryT(r), and detailed semi-analytic results for the kink instability are given for the particular case of a power-law twistT(r)=r
, where the index is non-negative. Our results show that the most rapidly growing and energetic instabilities occur in the Gold-Hoyle =0 field, with the instability progressively weakening with increasing . However, the maximum force eigenvalue is always small, so that even in the Gold-Hoyle case (where =O(10–2) in dimensionless units) only a small proportion of the available magnetic energy can be released in the linear phase. Our results also confirm that the linear pinch ( = ) is remarkably weak ( =O(10–3)) yet relatively resistant to line-tying! It is shown that the weakness of the force eigenvalue implies that the influence of uniform gas pressure on stability is negligible. Implications for the energy-release mechanism in solar flares are discussed. |
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Keywords: | |
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