Nonlinear Saturation of the Buneman Instability

An analytical model is developed for the nonlinear evolution of electron-ion two-stream instability. The instability saturates when the electric field energy reaches $\sim 2{\left(\frac{m}{M}\right)}^{\frac{1}{3}}{W}_0$ ($W_0=\mathrm{initial}\mathrm{electron}\mathrm{drift}\mathrm{energy}\mathrm{density}$), and is then followed by an algebraic growth. Complete stabilization is caused by electron trapping in deformed potential wells due to the rise of higher harmonics. The analytical model results are in close agreement with nonlinear kinetic computer simulations.