  Spin dynamics of two-dimensional electrons in moderate in-plane electric
fields is studied theoretically. The streaming regime is considered, where each
electron accelerates until reaching the optical phonon energy, then it emits an
optical phonon, and a new period of acceleration starts. Spin-orbit interaction
and elastic scattering result in anisotropic relaxation of electron spin
polarization. The overall spin dynamics is described by a superposition of spin
modes in the system. The relaxation time of the most long-living mode depends
quasi-periodically on the inverse electric field. The spin modes can be
conveniently revealed by means of spin noise spectroscopy. It is demonstrated
that the spectrum of spin fluctuations consists of peaks with the low-frequency
peak much narrower than satellite ones, and the widths of the peaks are
determined by the decay times of the modes.
