Open AccessNon-existence of Normal Tokamak Equilibria with Negative Central Current
Author(s) -
G. W. Hammett,
S.C. Jardin,
B. C. Stratton
Publication year - 2003
Language(s) - English
Resource type - Reports
DOI - 10.2172/812029
Subject(s) - tokamak , current (fluid) , magnetohydrodynamics , physics , virial theorem , constraint (computer aided design) , flux (metallurgy) , bootstrap current , mechanics , rotational symmetry , mathematics , plasma , mathematical analysis , thermodynamics , geometry , chemistry , quantum mechanics , organic chemistry , galaxy
Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current-drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal MHD equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) can not exist with negative central current. We extend that proof here to arbitrary aspect ratio, using a variant of the virial theorem to derive a relatively simple integral constraint on the equilibrium. However, this constraint does not, by itself, exclude equilibria with non-nested flux surfaces, or equilibria with singular fields and/or hollow pressure profiles that may be spontaneously generated