Quenching of the beam-plasma instability by large-scale density fluctuations in 3 dimensions

The highly variable, yet low, level of Langmuir waves measured in situ by spacecraft when electron beams associated with type III solar bursts are passing by are addressed by a model based on the existence of large scale density fluctuations capable of sufficiently diffusing small-k beam-unstable Langmuir waves in phase space. The model is also informed by the presence of a significant isotropic nonthermal tail in the distribution function of the background electron population, which is capable of stabilizing larger k modes. The model is able to predict various levels of Langmuir waves, depending on the parameters; calculations indicate that, for realistic parameters, the most unstable small k modes are fully stabilized, while some oblique mode with higher k and lower growth rate may remain unstable.