Kadomtsev proposed a self-generation mechanism of microislands (whose half-width is smaller than the Larmor radius of the ions) based on momentum and energy exchange between the electrostatic field of the islands and the ions of the background tokamak plasma. In this paper we study the motion of the ions intersecting, within a Larmor rotation, the electric field in the interspace between adjacent microisland chains. After appropriate average over the ensemble of ions and island chains, the interaction with the electric field gives rise to a net slow cumulative drift of the assembly of ions in the outward direction of the major radius. This effect is the consequence of nonlinearity and toroidal geometry in the equation of motion. The outward motion is associated with a decrease of the perpendicular plasma kinetic energy and a concomitant increase of the island's electrostatic energy, which can be described consistently by a ‘pumping term’ in the energy integral of the magnetohydrodynamic reduced equations for the islands. The pumping term can be contrasted by anomalous dissipation due to resonant interaction between the background electrons and the island waves. A stationary system of self-sustained microisland chains can then be formed in the tokamak plasma preferentially in the region $q > 2$ of the safety factor. Thus, the plasma acquires a spongy structure, where the sponginess (that is to say, the density of packing of the island structures) is measured by the ratio, lower than one, between the island width and the distance between adjacent rational surfaces. This structure determines an electron heat conductivity, which is strictly related to the sponginess and to the macroscopic equilibrium. Examples of scalings of the electron confinement time, predicted in zero-dimensional approximation, are given for typical tokamak conditions.