Magnetohydrodynamic equilibria and cusp formation at an X-type neutral line by footpoint shearing

G. E. Vekstein*, E. R. Priest

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


Some results concerning two-dimensional (∂/∂y = 0) magnetohydrodynamic equilibria in the presence of an X-type neutral line are presented. It is shown that in the framework of ideal MHD the latter is structurally unstable: shearing of an initial potential poloidal magnetic field results in the splitting of an X-point into a current sheet with cusp-points (or Y-points for some particular cases) at its ends. At the same time, one finds the formation of current sheets all along the separatrices even for a footpoint shearing displacement that is finite as the separatrix is approached. Scale-invariant or similarity solutions for the poloidal magnetic field inside the cusp are found. They are valid in the vicinity of a cusp-point on lengths much smaller than the global scale. These solutions predict fractional power-law singularities in the current density at the separatrix as well as a universal behavior for the poloidal magnetic field strength Bp near a cusp point, namely Bp ~∼ r1-3. Discussion is presented regarding the global geometry of the poloidal magnetic field produced by different types of footpoint shearing motions.

Original languageEnglish
Pages (from-to)333-340
Number of pages8
JournalAstrophysical Journal
Issue number1
Publication statusPublished - 1992


  • MHD
  • Sun: Corona


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