On the Grad--Shafranov equation as an eigenvalue problem, with implications for [ital q] solvers

Journal Article · Sat Jan 01 04:00:00 EST 1994 · Physics of Plasmas; (United States)

DOI:https://doi.org/10.1063/1.870464· OSTI ID:5184789

LoDestro, L L; Pearlstein, L D ^[1]

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1. Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)

It is shown that the Grad--Shafranov equation for toroidally symmetric ideal-magnetohydrodynamic (MHD) equilibria is a conventional albeit nonlinear eigenvalue problem. That this has been generally overlooked with limited consequences has been made possible by the existence of a scale-invariant transformation of the equation. If the safety factor [ital q] is chosen in place of the toroidal field as one of the free flux functions specifying the source (numerical Grad--Shafranov solvers with this capability are called [ital q] solvers''), the eigenvalue is 1 and the scale-transformation factor drops out of the problem. It is shown how this is responsible for the numerical problems that have plagued a class of [ital q] solvers, and a simple remedy is suggested. This has been implemented in Livermore's toroidal equilibrium code (TEQ), and as an example, a quasistatically evolved vertical event is presented.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5184789
• Journal Information: Physics of Plasmas; (United States), Journal Name: Physics of Plasmas; (United States) Vol. 1:1; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700370* -- Plasma Fluid & MHD Properties-- (1992-)
ANNULAR SPACE
CLOSED CONFIGURATIONS
CLOSED PLASMA DEVICES
COMPUTER CODES
CONFIGURATION
CONFINEMENT
DIFFERENTIAL EQUATIONS
EIGENVALUES
EQUATIONS
EQUILIBRIUM
GRAD-SHAFRANOV EQUATION
INVARIANCE PRINCIPLES
MAGNETIC FIELD CONFIGURATIONS
MHD EQUILIBRIUM
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA CONFINEMENT
SCALE INVARIANCE
SPACE
THERMONUCLEAR DEVICES
TOKAMAK DEVICES
TOROIDAL CONFIGURATION