The AWAKE project at CERN will use a high-energy proton beam at 400 GeV/c to drive wake'elds in a plasma. The amplitude of these wake'elds will be probed by injecting into the plasma a low-energy electron beam (10-20 MeV/c), which will be accelerated to several GeV. Upstream of the plasma cell the two beams will either be transported coaxially or with an o'set of few millimetres for about 6 m. The interaction between the two beams in this beam line has been investigated in the past, with a dedicated simulation code tracking particles under the in'uence of direct space-charge e'ects. These simulations have recently been crosschecked with a new simulation code called RF-Track, developed at CERN to simulate low energy accelerators. RF-Track can track multiple-specie beams at arbitrary energies, taking into account the full electromagnetic particle-to-particle inter-action. For its characteristics RF-Track seems an ideal tool to study the AWAKE two-beam interaction. The results of these studies are presented in this paper and compared to the previous results. The implications for the facility performance are discussed.