The HAWC collaboration has recently uncovered a new class of gamma-ray source around evolved pulsars: the gamma-ray halos. The origin of these halos is still uncertain and debated. In this study, we conduct 1D particle-in-cell (PIC) and particle-in-cell-magnetohydrodynamic simulations of a hot super-Alfvénic electron-positron (e-e+) beam pervading a cold electron-proton (e-p+) background. We investigate the growth and the saturation of the resonant streaming instability triggered by the e-e+ beam. We confirm quasi-linear growth rates and a saturated amplitude of waves to be consistent with a momentum exchange criterion between the decelerating beam and growing magnetic waves. We discuss how these results transpose to the case of e-e+ confinement around evolved pulsars. We explicitly discuss the case of Geminga.