Linear MHD stability of infinitely long coronal flux tubes

Abstract

Twisted magnetic flux tubes are often used to model the filed in coronal loops, and much attention has been given to analysing their stability. Previous astrophysical studies have concentrated on establishing the existence of an instability or determining stability bounds, and little information seems available on the associated eigenvalues, which give crucial information on the energy released. This paper develops methods of determining eigenvalues for infinitely long flux tubes. The most striking feature of the results is that the eigenvalues are always small-of order 10−2 (in dimensionless units) even for the fastest helical kink modes (m=1). The more localized higher-m modes have even smaller eigenvalues. A family of flux tubes with field line twist proportional torν is investigated, and it appears that the most energetic instabilities occur in the Gold-Hoyle tube with uniform twist (ν=0). Implications of these results are discussed.