Flexibility and rigidity of free boundary MHD equilibria. (5th May 2022)

• Record Type: Journal Article
• Authors: Constantin, Peter; Drivas, Theodore D; Ginsberg, Daniel
• Is Part Of: Nonlinearity. Volume 35:Number 5(2022)
• Page Start: 2363
• Page End: 2384
• Publication Date: 2022-05-05
• Subjects: free boundary magnetohydrodynamics -- plasma equilibria -- magnetic confinement fusion; 76W05 -- 35Q31 -- 35Q35; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac5d6a
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: 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.