  The self-consistent description of Langmuir wave and ion-sound wave
turbulence in the presence of an electron beam is presented for inhomogeneous
non-isothermal plasmas. Full numerical solutions of the complete set of kinetic
equations for electrons, Langmuir waves, and ion-sound waves are obtained for a
inhomogeneous unmagnetized plasma. The result show that the presence of
inhomogeneity significantly changes the overall evolution of the system. The
inhomogeneity is effective in shifting the wavenumbers of the Langmuir waves,
and can thus switch between different process governing the weakly turbulent
state. The results can be applied to a variety of plasma conditions, where we
choose solar coronal parameters as an illustration, when performing the
numerical analysis.
