  Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field
can be reduced, up to a selection of ions and electrons distributions
functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice
of the distributions functions. In contrast to two-dimensional translationally
symmetric equilibria whose electron distribution function consists of a
displaced Maxwellian, the toroidal equilibria need deformed Maxwellians. In
order to be able to carry through the calculations, this deformation is
produced by means of either a Heaviside step function or an exponential
function. The resulting Grad-Shafranov-like equations are established
explicitly.
