Stochastic growth theory of spatially-averaged distributions of Langmuir fields in Earth's foreshock

Langmuir-like waves in the foreshock of Earth are characteristically bursty and irregular, and are the subject of a number of recent studies. Averaged over the foreshock, it is observed that the probability distribution (P) o ver bar (logE) is power-law in the wave field E, with the bar denoting this averaging over position. In this paper it is shown that stochastic growth theory (SGT) can explain power-law spatially-averaged distributions (P) ove r bar (logE), when the observed power-law variations of the mean and standa rd deviation of log E with position are combined with the log normal statis tics predicted by SGT at each location.