Some properties of the two-stream instability at large amplitudes

The behavior of the electric two-stream instability for electrons streaming through ions is investigated by treating the relevant Vlasov equations as partial differential equations and integrating them on a computer. As was shown by Buneman, the growth of the instability provides a friction between the electrons and ions. It is shown that the friction is proportional to the mean square electric field, approximately, and the coefficient is derived analytically and checked by the computer calculations. The friction converts the relative motion into heat, and the ratio between the heating of the electrons and the ions is shown to be of the order of the square root of the mass ratio.