Numerical study of the current instability in a two-dimensional electron fluid

Nonlinear evolution of the current instability in two-dimensional electron fluid is studied with the use of computer simulation. Recently it was found that this current instability may take place in a ballistic field-effect transistor. We show that the development of the instability results in an establishment of stationary periodic oscillations everywhere over the investigated area of parameters. In the case of small increments, the oscillation amplitude is proportional to the square root of the increment and is well described by the analytical theory. For higher increments the growth of the amplitude slows down. In this case, the steplike distributions of electron concentration and velocity, analogous to shock waves, are formed in the electron fluid. The dependence of the frequency of oscillations on their amplitude is calculated.