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Title: Hamiltonian approach to the magnetostatic equilibrium problem

Abstract

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.

Authors:
;  [1];  [2]
  1. Universita di Trieste (Italy)
  2. Princeton Univ., NJ (United States). Plasma Physics Lab.
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
10115867
Report Number(s):
PPPL-3035
ON: DE95007356; TRN: 95:001627
DOE Contract Number:  
AC02-76CH03073
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: Feb 1995
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; MAGNETIC FIELD CONFIGURATIONS; EQUILIBRIUM; MAGNETIC CONFINEMENT; HAMILTONIAN FUNCTION; 700390; OTHER PLASMA PHYSICS STUDIES

Citation Formats

Tessarotto, M, Zheng, Lin Jin, and Johnson, J L. Hamiltonian approach to the magnetostatic equilibrium problem. United States: N. p., 1995. Web. doi:10.2172/10115867.
Tessarotto, M, Zheng, Lin Jin, & Johnson, J L. Hamiltonian approach to the magnetostatic equilibrium problem. United States. https://doi.org/10.2172/10115867
Tessarotto, M, Zheng, Lin Jin, and Johnson, J L. 1995. "Hamiltonian approach to the magnetostatic equilibrium problem". United States. https://doi.org/10.2172/10115867. https://www.osti.gov/servlets/purl/10115867.
@article{osti_10115867,
title = {Hamiltonian approach to the magnetostatic equilibrium problem},
author = {Tessarotto, M and Zheng, Lin Jin and Johnson, J L},
abstractNote = {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.},
doi = {10.2172/10115867},
url = {https://www.osti.gov/biblio/10115867}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 1995},
month = {Wed Feb 01 00:00:00 EST 1995}
}