  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.
