A theory for the Langmuir waves in the electron foreshock

Abstract

A theory for the Langmuir (L) waves observed in the electron foreshock is suggested. Free energy for the Langmuir wave growth is contained in cutoff distributions of energetic electrons streaming from the bow shock. These cutoff distributions drive Langmuir wave growth primarily by the kinetic version of the beam instability, and wave growth is limited by quasi‐linear relaxation. The observed bump‐on‐tail electron distributions are interpreted as the remnants of cutoff distributions after quasi‐linear relaxation has limited the wave growth. Only plausibility arguments for this theory are given since suitable treatments of quasi‐linear relaxation are not presently available. However, it is shown that the wave processes L ± S → L′ and L ± S → T (where S and T denote ion sound and transverse waves, respectively), refraction in steady‐state density structures, diffusion due to interactions with ion sound turbulence, and effects due to wave convection and spatial gradients in the beam velocity, are unable to suppress the beam instability. The theory leads to natural interpretations of the Langmuir electric field waveforms observed and of the decrease in the Langmuir wave electric fields with increasing distance from the foreshock boundary. The theory for the beam instability is reviewed, and previous analytic and numerical treatments of the beam instability are related. A difficulty in recent theoretical interpretations of broadband wave growth below the plasma frequency, relating to the version of the beam instability considered giving rise only to narrow‐band growth, is pointed out and suggestions for resolving this difficulty are made.