Scattering and collpase of Langmuir waves driven by a weak electron beam

The evolution of Langmuir waves predicted by the beam-driven Zakharov equations is studied numerically with high resolution in one and two dimensions, for parameters appropriate to type III solar radio bursts at 0.5 a.u. It is found that collapse is preceded by momentum transfer to ion-acoustic quasimodes even in the absence of a weak solar magnetic field. The early evolution is similar in one and two dimensions. A zero momentum condensate forms in both cases, but its subsequent behavior differs in one dimension and two dimensions. The corresponding real-space wave packets collapse rapidly in two dimensions, but evolve as slowly growing solitons in one dimension. Detailed comparisons are made with other (one-dimensional) models of ’’strong’’ Langmuir turbulence associated with type III bursts.