Hamiltonian approach to the magnetostatic equilibrium problem
- Universita di Trieste (Italy)
- Princeton Univ., NJ (United States). Plasma Physics Lab.
The purpose of this paper is to investigate the classical scalar-pressure magnetostatic equilibrium problem for non-symmetric configurations in the framework of a Hamiltonian approach. Requiring that the equilibrium admits locally, in a suitable subdomain, a family of nested toroidal magnetic surfaces, the Hamiltonian equations describing the magnetic flux lines in such a subdomain are obtained for general curvilinear coordinate systems. The properties of such Hamiltonian system are investigated. A representation of the magnetic field in terms of arbitrary general curvilinear coordinates is thus obtained. Its basic feature is that the magnetic field must fulfill suitable periodicity constraints to be imposed on arbitrary rational magnetic surfaces for general non-symmetric toroidal equilibria, i.e., it is quasi-symmetric. Implications for the existence of magnetostatic equilibria are pointed out. In particular, it is proven that a generalized equilibrium equation exists for such quasi-symmetric equilibria, which extends the Grad-Shafranov equation to fully three-dimensional configurations. As an application, the case is considered of quasi-helical equilibria, i.e., displaying a magnetic field magnitude depending on the poloidal ({chi}) and toroidal ({var_theta}) angles only in terms of {alpha}={chi}-N{theta} with N an arbitrary integer.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC02-76CH03073
- OSTI ID:
- 10115867
- Report Number(s):
- PPPL-3035; ON: DE95007356; TRN: 95:001627
- Resource Relation:
- Other Information: PBD: Feb 1995
- Country of Publication:
- United States
- Language:
- English
Similar Records
Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria
Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles