Stochastic growth theory of spatially‐averaged distributions of Langmuir Fields in Earth's foreshock

Abstract

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 (log E) 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 (log E), when the observed power‐law variations of the mean and standard deviation of log E with position are combined with the log normal statistics predicted by SGT at each location.