AN INTEGRAL EQUATION TECHNIQUE FOR THE EXTERIOR AND INTERIOR NEUMANN PROBLEM IN TOROIDAL REGIONS
For a given magnetic field B-o(divB-o=O,curlB-o=j) (toroidal region, bounded by a surface) a magnetic vacuum field B-1="DEL"PHI can be calculated with superposition of the two fields B=B-o>f5<&f1<"DEL"PHI tangential on the surface. This leads for PHI to the Neumann problem of finding a function PHI which satisfies "DEL"PHI=O in a region, and whose normal derivative takes given values on the boundary. For only one boundary one gets one integral equation where x,x' are points on the surface and G(x,x')=1//x-x'/ is the Green's function. The integral equation is solved by representing toroidal surface and potential PHI by Fourier series of two angle like variables (u,v). A set of linear equations for the Fourier coefficients of the potential PHI is obtained. The singularity of the Green's function and its derivative are treated by a subtraction method. Two applications: 1. Toroidal vacuum fields can be generated with a magnetic surface on the boundary. For appropriate boundaries configurations with "good" magnetic surfaces in the whole region may exist. Results on l=2 stellarator configurations with substantial values of iota**2/A are presented. 2. The vacuum field contribution in the 3D equilibrium problem can be calculated, with the fields produced by the external currents included. In this case an exterior Neumann problem is solved by considering the infinite region exterior to the toroidal surface.
Bibliographic Reference: 5TH INTERNATIONAL WORKSHOP ON STELLARATORS, SCHLOSS RINGBERG, BAVARIA (GERMANY), SEPT. 24-28, 1984 VOL. I, PP. 387-400, EUR 9618 EN (1985) FS, VOL. I AND VOL. II, 787 P., BFR 3500 (BOTH VOLUMES), EUROFFICE, LUXEMBOURG, POB 1003
Record Number: 1989124118700 / Last updated on: 1987-01-01
Available languages: en