Langmuir Wave Electric Fields Induced by Electron Beams in the Heliosphere

Solar electron beams responsible for type III radio emission generate Langmuir waves as they propagate out from the Sun. The Langmuir waves are observed via in-situ electric field measurements. These Langmuir waves are not smoothly distributed but occur in discrete clumps, commonly attributed to the turbulent nature of the solar wind electron density. Exactly how the density turbulence modulates the Langmuir wave electric fields is understood only qualitatively. Using weak turbulence simulations, we investigate how solar wind density turbulence changes the probability distribution functions, mean value and variance of the beam-driven electric field distributions. Simulations show rather complicated forms of the distribution that are dependent upon how the electric fields are sampled. Generally the higher magnitude of density fluctuations reduce the mean and increase the variance of the distribution in a consistent manor to the predictions from resonance broadening by density fluctuations. We also demonstrate how the properties of the electric field distribution should vary radially from the Sun to the Earth and provide a numerical prediction for the in-situ measurements of the upcoming Solar Orbiter and Solar Probe Plus spacecraft.