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

Conference · Wed Jan 01 04:00:00 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
• Country of Publication: United States
• Language: English

Related Subjects

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