Conditions for the development of a two-stream instability in a pulsar magnetosphere are deduced from specific dispersion relations for plane wave perturbations, that depend on the distribution functions of the involved particles. Three different approaches are investigated.

Firstly, using relativistic one-dimensional Juttner Synge distribution functions appropriate to describe pulsar pair plasmas flows, we analytically derive the dispersion relation anew, precisely determining the dependence of its coefficients on the temperature, fluid velocity and associated Lorentz factor. We obtain modified frequencies for quasi-longitudinal waves and specific conditions for a two-stream instability to develop.

Secondly, the importance of two-stream instabilities is tested numerically on two different timescales, that concern stationary and non-stationary properties of pair plasma flows. The linear analysis involves Gaussian distribution functions of the momentum, factorized with functions that depend on the localisation of the different groups of particles, and shows results that agree with observed luminosities.

Finally as derived from fluid equations, the nonlinear evolution of such an instability process allows to associate the high level of radio radiation observed from pulsars with the existence of a lattice of radiating ‘Langmuir‘ soliton-like structures in a pulsar emission region. Actually, pair plasma particles follow the bundle of diverging magnetic field lines in the open magnetosphere and ‘Langmuir‘ soliton-like solutions, modified by magnetic field and density gradients, imply additional radiation.