The Farley-Buneman Spectrum in 2-D and 3-D Particle-in-Cell Simulations

Since the 1960s, the Farley-Buneman instability has played an important role in probing the E-region ionosphere. The intervening years have seen significant progress in the linear theory of this instability, its relation to other instabilities, and some of its observational signatures. However, the saturation mechanism and nonlinear behavior remain open topics because of their role in controlling energy flow in the E-region plasma. This paper explores the saturated state of the Farley-Buneman instability in 2-D and 3-D kinetic simulations of the high-latitude ionosphere, at three different simulated altitudes: 107, 110, and 113 km. These simulations show irregularity amplitude growth and saturation in all runs, but irregularity growth takes much longer in 2-D than in 3-D. Once the simulations reach saturation, wave power in the meter-scale regime falls off as a power law below the wavelength of peak growth, but the power law index is larger in 3-D than in 2-D. At longer wavelengths, the 3-D spectrum is much flatter than the 2-D spectrum. This implies that purely 2-D simulations of the Farley-Buneman instability may overestimate irregularity amplitudes at decameter scales and may also underestimate the efficiency of ion Landau damping at the ion mean-free-path scale. From a physical perspective, the relatively flat spectra above the wavelength of peak growth in 3-D simulations imply a wavelength-independent saturation mechanism across a range of altitudes. Finally, both 2-D and 3-D simulations demonstrate the importance of accounting for zeroth-order ion drift when estimating the flow angle of density irregularities.