On the relationship between equilibrium bifurcations and ideal MHD instabilities for line-tied coronal loops

T. Neukirch, Z. Romeou

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
1 Downloads (Pure)

Abstract

For axisymmetric models for coronal loops the relationship between the bifurcation points of magnetohydrodynamic (MHD) equilibrium sequences and the points of linear ideal MHD instability is investigated, imposing line-tied boundary conditions. Using a well-studied example based on the Gold -aEuro parts per thousand Hoyle equilibrium, it is demonstrated that if the equilibrium sequence is calculated using the Grad -aEuro parts per thousand Shafranov equation, the instability corresponds to the second bifurcation point and not the first bifurcation point, because the equilibrium boundary conditions allow for modes which are excluded from the linear ideal stability analysis. This is shown by calculating the bifurcating equilibrium branches and comparing the spatial structure of the solutions close to the bifurcation point with the spatial structure of the unstable mode. If the equilibrium sequence is calculated using Euler potentials, the first bifurcation point of the Grad -aEuro parts per thousand Shafranov case is not found, and the first bifurcation point of the Euler potential description coincides with the ideal instability threshold. An explanation of this results in terms of linear bifurcation theory is given and the implications for the use of MHD equilibrium bifurcations to explain eruptive phenomena is briefly discussed.

Original languageEnglish
Pages (from-to)87-106
Number of pages20
JournalSolar Physics
Volume261
Issue number1
Early online date15 Dec 2009
DOIs
Publication statusPublished - Jan 2010

Keywords

  • Corona, structures
  • Flares, relation to magnetic field
  • Instabilities
  • Magnetohydrodynamics
  • Free cylindrical equilibria
  • Solar eruptive processes
  • Kink instability
  • Numerical simulations
  • Stability analysis
  • Onset conditions
  • Magnetic-fields
  • Current layers
  • Current sheets
  • Evolution

Fingerprint

Dive into the research topics of 'On the relationship between equilibrium bifurcations and ideal MHD instabilities for line-tied coronal loops'. Together they form a unique fingerprint.

Cite this