Flowing plasmas are of significant interest due to their role in astrophysical phenomena and potential applications in magnetic-confined fusion and spacecraft propulsion. The acceleration of a charge-neutral plasma beam using the radio-frequency self-bias concept could be particularly useful for the development of neutralizer-free propulsion sources. However, the mechanisms that lead to space-charge compensation of the exhaust beam are unclear. Here, we spatially and temporally resolve the propagation of electrons in an accelerated plasma beam that is generated using the self-bias concept with phase-resolved optical emission spectroscopy. When combined with measurements of the extraction-grid voltage, ion and electron currents, and plasma potential, the pulsed-periodic propagation of electrons during the interval of sheath collapse at the grids is found to enable the compensation of space charge.