The compression of relativistic electron beams resulting from partial space charge neutralization by thermal ions is simulated to obtain self-consistent solutions. The numerical modeling is based on a finite difference approach, using under-relaxation to assure convergence in solving this nonlinear problem. The results show a nonuniform fraction of neutralization, increasing as a function of radius. Neutralization on axis is higher for colder compensating ions and for lower electron energy. In general, the temperature of the ions turns out to be higher than that of the electrons. With respect to the non-neutralized, not-thermally-dispersed beam, higher compression factors result at higher beam energies. The analytic solutions, known as the Bennett pinch, are well matched at corresponding settings of the parameters.
