Tokamaks often show improved core confinement when the magnetic shear
in the central region is reversed. Furthermore tokamaks operating in a
mode in which the current is mostly sustained by bootstrap current te
nd to naturally form reversed shear profiles. For a fixed heating prof
ile the improved core confinement will cause the pressure profile to p
eak which effects the equilibrium through the bootstrap current term.
We show that equilibria do not necessarily exist for tokamaks that hav
e a high bootstrap current fraction and enhanced confinement in the re
versed shear region.