Among the various plasma instabilities which could be responsible for coherent pulsar radio emission, we investigate the two-stream instability, first introduced by Ruderman and Sutherland (1975) in order to account for the physical situation expected in the environment of neutron stars. They describe how, in a polar cap model, pair creation arises and leads to the formation of a very energetic beam of e+ (and/or e−) and of an e−e+ plasma, both with relativistic bulk motion along the bundle of dipolar magnetic field lines. The study of their interaction is limited to the cone of open B lines, a site which provides a natural geometry for the radio emission zone, observed as core and/or conal emission by Lyne and Manchester (1988) and Rankin (1983, 1986, 1990).