The micromaps description of a beam with space charge

In high-intensity accelerators the dominant nonlinear forces are due the sp ace charge but the effect of multipolar errors and synchro-betatron couplin g should be taken into account. The micromaps approach allows, for a linear lattice, to iteratively obtain the self-consistent solution and can be ext ended to include the lattice nonlinearities. We investigate here the conver gence of the method for a constant focusing and a FODO cell. In both cases we prove the convergence to the exact solution up to a limit current corres ponding to a significant limit tune shift.