Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem
- Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States)
A generalized energy principle for finite-pressure, toroidal magnetohydrodynamic (MHD) equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces (invariant tori), which act as barriers against leakage of magnetic flux, helicity, and pressure through chaotic field-line transport. It is argued that a necessary condition for such invariant tori to exist is that they have fixed, irrational rotational transforms. In the toroidal domains bounded by these surfaces, full Taylor relaxation is assumed, thus leading to Beltrami fields {nabla}xB={lambda}B, where {lambda} is constant within each domain. Two distinct eigenvalue problems for {lambda} arise in this formulation, depending on whether fluxes and helicity are fixed, or boundary rotational transforms. These are studied in cylindrical geometry and in a three-dimensional toroidal region of annular cross section. In the latter case, an application of a residue criterion is used to determine the threshold for connected chaos.
- OSTI ID:
- 20974986
- Journal Information:
- Physics of Plasmas, Vol. 14, Issue 5; Other Information: DOI: 10.1063/1.2722721; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
Similar Records
On three-dimensional toroidal surface current equilibria with rational rotational transform
Three dimensional magnetohydrodynamic simulation of linearly polarised Alfven wave dynamics in Arnold-Beltrami-Childress magnetic field