The importance of boundary effects in the emission region of the pulsar magnetosphere

To model the pulsar radio emission zone we consider a relativistic beam (or plasma) that flows along curved open magnetic field lines, has a finite extent perpendicular to its flow and is bounded by interior and exterior plasmas. Such a framework is natural in view of most pulsar radio observations that show a hollow cone or a full cone of radio emission. The analysis of the instabilities that may develop in this system is made under the assumption that field lines have sufficient curvature. It shows that, in addition to the radiative instability and to the two-stream instability, well studied in the context of pulsar physics, an instability may arise for a one-component beam of relativistic particles that closely depends on the presence of the external plasmas. We call it the 'finite-beam' instability. A study of the growth rate and polarization of the unstable waves excited through this instability shows that they can play a dominant role near the surface of the neutron star. This suggests that, as originally proposed by Rankin, several instability mechanisms should be simultaneously considered to account for core and conal emissions.