The report presents the recent results of experiments with deuterium neutral beam injection in the Gas Dynamic Trap (GDT) device. The experiments were to demonstrate the peaking up of the DD reaction near the fast ion turning points that represents the essential feature of the GDT-based neutron source (GDT-NS). The critical assumption for feasibility of GDT-NS is that the fast ion relaxation in the warm target plasma is to be determined by two-body Coulomb collisions without considerable increase of the scattering rate caused by instabilities, otherwise the neutron flux peaks may strongly flatten out. The comparison of the measured axial profile of the DD reaction intensity with simulation results allows to validate this assumption for the plasma parameters of GDT device