Observations of the solar wind ion-charge states suggested that the origin of solar wind is associated with nanoflare-like impulsive events. It has been suggested by Che and Goldstein that the nearly isotropic electron halo observed in the solar wind electron velocity distribution function may originate from nanoflare-accelerated electron beams below 1.1 R_{sun} from the solar surface through the non-linear electron two-stream instability (ETSI). This model unifies the origins of kinetic waves, the electron halo, and the coronal weak Type III bursts, and establishes a link between the solar wind observables and the electron dynamics in nanoflares. One of the important predictions of this model is that the halo-core temperature ratio is anti-correlated with the density ratio, and the minimum halo-core temperature ratio is \sim 4 , a relic of the ETSI heating and has been found to be consistent with WIND, ACE and Helios observations. However, the density and the relative drift of the electron beams in the source region in the corona, which are essential for the evolution of ETSI, cannot be directly measured. In this paper, using a set of particle-in-cell simulations and kinetic theory, we show that a necessary condition for an isotropic halo to develop is that the ratio of beam density n_b and the background n_0 be lower than a critical value N_c ~ 0.3. Heating of the core electrons becomes weaker with decreasing beam density, while the heating of halo electrons becomes stronger. As a result, the temperature ratio of the halo and core electrons increases with the decrease of the beam density. We apply these results to the current observations and discuss the possible electron beam density produced in the nanoflares.