The long-distance stable transport of relativistic electron beams (REBs) in plasmas is studied by full three-dimensional particle-in-cell simulations. Theoretical analysis shows that the beam transport is mainly influenced by three transverse instabilities, where the excitation of self-modulation instability, and the suppression of the filamentation instability and the hosing instability are important to realize the beam stable transport. By modulating the transport parameters such as the electron density ratio, the relativistic Lorentz factor, the beam envelopes and the density profiles, the relativistic bunches having a smooth density profile and a length of several plasma wave periods can suppress the beam-plasma instabilities and propagate in plasmas for long distances with small energy losses. The results provide a reference for the research of long-distance and stable transport of REBs, and would be helpful for new particle beam diagnosis technology and space active experiments.
