Simulation of the beam plasma interaction in randomly inhomogeneous solar wind

Solar type III radio bursts are amongst the most intense emissions found within Solar System. The bursts are generated by the relativistic electron beams ejected from the Sun as they propagate through the corona and solar wind. One the key parameters that can control beam plasma interactions is level of the density fluctuations. The density fluctuations can change the local phase velocity of the Langmuir waves generated by the beam instability, resulting in changes of the resonant conditions of wave-particle interaction. Changes in the wave phase velocity during the wave propagation can be described in terms of probability distribution function determined by distribution of the density fluctuations. This enables an approach that describes beam-plasma interaction with a system of equations, similar to well known quasi-linear approximation, but with the conventional velocity diffusion coefficient and the wave growth rate are replaced by the averaged in the velocity space. This approach, known as probabilistic model, allows to describe generation of the Langmuir waves in randomly inhomogeneous solar wind in self-consistent manner. Although previous version of the probabilistic model could explain some of the observational features of the emission, it had significant limitation, as it did not include time of flight effects. Here we present results of the numerical simulation based on an updated set of equations that can describe generation of the Langmuir waves by the electron beam as it propagates from the source region up to 10 Solar radii.