Flexibility and rigidity of free boundary MHD equilibria

Peter Constantin, Theodore D. Drivas, Daniel Ginsberg

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study stationary free boundary configurations of an ideal incompressible magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply connected domains, we prove that if the magnetic field and velocity field are never commensurate, the only possible domain for any such equilibria is a disk, and the velocity and magnetic field are circular. We give examples of non-symmetric equilibria occupying a domain of any shape by imposing an external magnetic field generated by a singular current sheet charge distribution (external coils). Some results carry over to 3D axisymmetric solutions. These results highlight the importance of external magnetic fields for the existence of asymmetric equilibria.

Original languageEnglish (US)
Pages (from-to)2363-2384
Number of pages22
Issue number5
StatePublished - May 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


  • 35Q31
  • 35Q35
  • 76W05
  • free boundary magnetohydrodynamics
  • magnetic confinement fusion
  • plasma equilibria


Dive into the research topics of 'Flexibility and rigidity of free boundary MHD equilibria'. Together they form a unique fingerprint.

Cite this