  We describe the evolution of a plasma equilibrium having a toroidal topology
in the presence of constant electric resistivity. After outlining the main
analytical properties of the solution, we illustrate its physical implications
by reproducing the essential features of a scenario for the upcoming Italian
experiment Divertor Tokamak Test Facility, with a good degree of accuracy.
Although we find the resistive diffusion timescale to be of the order of
$10^4\,$s, we observe a macroscopic change in the plasma volume on a timescale
of $10^2\,$s, comparable to the foreseen duration of the plasma discharge by
design. In the final part of the work, we compare our self-consistent solution
to the more common Solov'ev one, and to a family of nonlinear configurations.
