Non-existence of Normal Tokamak Equilibria with Negative Central Current
Authors: G.W. Hammett, S.C. Jardin, and B.C. Stratton
Date of PPPL Report: February 2003
Published in: Phys. Plasmas 10 (October 2003) 4048-4052.
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.