If the electron-positron plasma flow from the pulsar environment is stationary, the two-stream instability does not have enough time to develop in the pulsar magnetosphere. In that case the outflowing electron-positron plasma gathers into separate clouds. The clouds move along magnetic field lines and disperse as they go farther from the pulsar. At a distance of about 10 to the 8th cm from the pulsar surface, the high-energy particles of a given cloud catch up with the low-energy particles that belong to the cloud going ahead of it. In this region of a pulsar magnetosphere, the energy distribution of plasma particles is two-humped, and a two-stream instability may develop. The growth rate of the instability is quite sufficient for its development.
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В. В. Усов (1987) studied this question.