Structure of a long-wave Langmuir oscillation spectrum in an inhomogeneous plasma

The problem has been solved on the structure of a stationary spectrum of Langmuir oscillations established under the action of two counteracting factors: 1) spectral over pumping of oscillations into the range of low values of the wave vector k because of induced scattering on plasma ions and 2) an increase of the wave vector due to plasma density inhomogeneity. The stationary spectrum presents a narrow peak in the k-space. The position of the peak k0 and its width are related to the complete energy of oscillations. The result obtained shows that the plasma inhomogeneity prevents from the production of a condensate at the point k=0 and permits the presence of the stationary spectrum not subjected to modulation instability