Three-dimensional free boundary calculations using a spectral Green's function method

Conference · Wed Jan 01 00:00:00 EST 1986

OSTI ID:5272232

Hirshman, S P; van Rij, W I; Merkel, P

The plasma energy W/sub p/ = integral ..cap omega../sub p/(1/2B/sup 2/ + p)dV is minimized over a toroidal domain ..cap omega../sub p/ using an inverse representation for the cylindrical coordinates R = ..sigma..R/sub mn/(s)cos(mtheta - n zeta) and Z = ..sigma..Z/sub mn/(s)sin(mtheta - n zeta), where (s,theta,zeta) are radial, poloidal, and toroidal flux coordinates, respectively. The radial resolution of the MHD equations is significantly improved by separating R and Z into contributions from even and odd poloidal harmonics which are individually analytic near the magnetic axis. A free boundary equilibrium results when ..cap omega../sub p/ is varied to make the total pressure 1/2B/sup 2/ + p continuous at the plasma surface ..sigma../sub p/ and when the vacuum magnetic field B/sub ..nu../ satisfies the Neumann condition B/sub ..nu../ x d..sigma../sub p/ = 0. The vacuum field is decomposed as B/sub ..nu../ = B/sub 0/ + del Phi, where B/sub 0/ is the field arising from plasma currents and external coils and Phi is a single-valued potential necessary to satisfy B/sub ..nu../ x d..sigma../sub p/ = 0 when p not equal to 0. A Green's function method is used to obtain an integral equation over ..sigma../sub p/ for the scalar magnetic potential Phi = ..sigma..Phi/sub mn/sin(mtheta - n zeta). A linear matrix equation is solved for Phi/sub mn/ to determine 1/2 B/sub ..nu..//sup 2/ on the boundary. Real experimental conditions are simulated by keeping the external and net plasma currents constant during the iteration. Applications to l = 2 stellarator equilibria are presented.

• Research Organization: Oak Ridge National Lab., TN (USA). Fusion Energy Div.; Max-Planck-Institut fuer Plasmaphysik, Garching (Germany, F.R.)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 5272232
• Report Number(s): CONF-8605187-1; ON: DE86013407
• Resource Relation: Conference: Eibsee conference, Eibsee, F.R. Germany, 1 May 1986; Other Information: Portions of this document are illegible in microfiche products
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
EQUILIBRIUM PLASMA
PLASMA MACROINSTABILITIES
BOUNDARY CONDITIONS
GREEN FUNCTION
MAGNETIC SURFACES
MAGNETOHYDRODYNAMICS
PLASMA PRESSURE
STELLARATORS
THREE-DIMENSIONAL CALCULATIONS
CLOSED PLASMA DEVICES
FLUID MECHANICS
FUNCTIONS
HYDRODYNAMICS
INSTABILITY
MAGNETIC FIELD CONFIGURATIONS
MECHANICS
PLASMA
PLASMA INSTABILITY
THERMONUCLEAR DEVICES
700105* - Fusion Energy- Plasma Research- Plasma Kinetics-Theoretical- (-1987)