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Author: Matt Landreman
Requested Type: Poster
Submitted: 2016-02-01 12:08:08

Co-authors: A.H.Boozer

Contact Info:
University of Maryland
8223 Paint Branch Dr.
College Park, Maryland   20742

Abstract Text:
The magnetic field that supports tokamak and stellarator plasmas must be produced by coils well separated from the plasma. However the larger the separation, the more difficult it is to produce a given magnetic field in the plasma region, so plasma configurations should be chosen that can be supported as efficiently as possible by distant coils. A magnetic field pattern from currents outside the plasma can be called efficient if its decay in space between the coils and plasma is small, and a plasma shape can be called efficient if the external field required to support the shape is efficient. Plasma shapes with low curvature and spectral width may be inefficient, whereas plasma shapes with sharp edges may be efficient. Two definitions of magnetic field efficiency, which correctly identify such differences in difficulty, will be examined and compared. In terms of a toroidal control surface far from the plasma, the two definitions correspond to (B_n on plasma surface) / (current potential on control surface) and (B_n on plasma surface) / (B_n on control surface), with B_n the magnetic field normal to the surface. Both efficiency measures can be expressed as matrices, and a singular value decomposition (SVD) of either matrix yields an efficiency-ordered orthonormal basis for the magnetic field distributions. Numerical calculations of magnetic field efficiency and plasma shape efficiency are carried out for both tokamak and stellarator cases. For axisymmetric surfaces with circular cross-section, the SVDs are also calculated analytically, and the range of poloidal and toroidal mode numbers that can be controlled to a given desired level is determined. If formulated properly, these efficiency measures are independent of the coordinates used to parameterize the surfaces.