Electrostatic turbulence develops in current carrying plasmas when the relative electron-ion drift exceeds the critical value for laminar current flow. Recent 2D computer experiments (Barnes, 1982) indicate that many weak ion acoustic double layers form in such turbulence when the plasma is strongly magnetized (ωce ≳ ωpe), the electron/ion temperature ratio is large (≳10), and the relative electron-ion drift is comparable to or less than the electron thermal speed. The double layers emerge from the incoherent spectrum of electrostatic ion cyclotron and ion acoustic waves as intense localized electric field structures propagating subsonically relative to the ion bulk flow. The occurrence of weak ion acoustic double layers, excited by field-aligned currents in the Earth's auroral regions, has also been reported from in situ spacecraft measurements (Temerin et al., 1982). An important question concerns the effect of these coherent electric fields on plasma transport properties such as bulk heating and acceleration. For example, one might expect nonlinear diffusion processes, manifested as distinct nonthermal features in the particle spectra, to accompany the quasilinear diffusion of ions as they traverse turbulent regions in space. This idea motivates the work presented here.