Terrestrial foreshock Langmuir waves: STEREO observations, theoretical modeling, and quasi‐linear simulations

Langmuir waves in the terrestrial electron foreshock are investigated using observations from the STEREO spacecraft, theoretical modeling, and quasi‐linear simulations. Emphases are placed on spatial variations of Langmuir field strength with distance between the spacecraft and the tangent point and on the effects of ambient density fluctuations on these variations. The STEREO mission provides new observations of foreshock Langmuir waves at distances more than twice as far from Earth as previously observed. Based on established geometric properties of the foreshock region, two methods are developed for separating Langmuir waves of foreshock origin from those of solar and/or heliospheric origins. The observed maximum foreshock Langmuir field strength falls with distance via a power law with an exponent −1.01 ± 0.12. The theory and simulations predict field strengths and power law spatial variations in field strengths that are consistent with the observations when scattering of Langmuir waves by density fluctuations is included. The power law exponents predicted by both theory and simulations fall within the uncertainty of the observations for the typical solar wind conditions observed but differ by a factor of ≈1.5 from simulations that assume density homogeneity. This indicates that density fluctuations play an important role in the beam‐Langmuir wave dynamics in the foreshock.