Damping and excitation of Langmuir waves in an inhomogeneous relativistic plasma; general theory and pulsar applications

The damping of Langmuir waves during the propagation in the relativistic plasma along the density decrease direction is studied. It is shown that these waves damp over the distance being not greater than the characteristic gradient length scale. The influence of plasma inhomogeneity on the excitation of Langmuir waves by the high energy particle beam is cleared up. Such influence can be essential if the beam density is sufficiently small. It is supposed the results can be of interest in connection with the further development of the theories of pulsar radio radiation based on the assumption that Langmuir waves are essential.