On the basis of the theory of weak turbulence it is shown that the principal mechanism limiting the development of ion-acoustic instability in a current-carrying plasma in an electric field can be the non-linear scattering of oscillations by electrons. The energy density of turbulent ion-acoustic pulsations is of the order W∼(2me/mi)n0 Te, where n0 is the plasma density, Te the electron temperature and m6ij the electron and ion mass.Electron scattering by turbulent pulsations occurs with an effective frequency νs ∼ (2me/mi) ωpe and leads to an anomalous effective plasma conductivity , where ωpe is the electron Langmuir frequency.Ion-acoustic instability develops in a plasma in weak electric fields (E<Ecr = (me/e) vthνs) when the current velocity is less than the thermal velocity of the electrons, . The critical field Ecr in a high-temperature dilute plasma is much stronger than the Dreicer field EDr = (me/e) vthνc, where νc is the electron-ion collision frequency.The estimates of σ and νs are in good agreement with conductivity measurements made in a number of turbulent plasma heating experiments.