Statistically determined dispersion relations of magnetic field fluctuations in the terrestrial foreshock

TL;DR

This study derives dispersion relations of magnetic field fluctuations in the terrestrial foreshock using Cluster spacecraft data, revealing different wave modes depending on plasma beta conditions.

Contribution

It introduces a method to reconstruct dispersion relations from two-point measurements in the foreshock, covering a broad wave vector range and identifying dominant wave modes.

Findings

Fast magnetosonic and beam resonant modes dominate high plasma beta intervals.

Alfvén and fast magnetosonic modes are observed in magnetically dominated intervals.

Multiple dispersion branches are identified, associated with different fluctuation powers.

Abstract

We obtain dispersion relations of magnetic field fluctuations for two crossings of the terrestrial foreshock by Cluster spacecraft. These crossings cover plasma conditions which differ significantly in their plasma $\beta$ but not in the properties of the encountered ion population, both showing shell-like distribution function. Dispersion relations are reconstructed using two-point instantaneous wave number estimations from pairs of Cluster spacecraft. The accessible range of wave vectors, limited by the available spacecraft separations, extends to $\approx \!2 \times 10^4$ km. Results show multiple branches of dispersion relation, associated with different power of magnetic field fluctuations. We find that Sunward propagating fast magnetosonic waves and beam resonant modes are dominant for the high plasma $\beta$ interval, while the dispersions of magnetically dominated interval include Alfv\'{e}n and fast magnetosonic modes propagating Sunward and unit-Sunward.