Multi-Spacecraft Observations of Linear Modes and Sideband Waves in Ion-Scale Solar Wind Turbulence

Abstract

In the scenario of weak turbulence, energy is believed to be cascaded from smaller to larger wave numbers and frequencies due to weak wave–wave interactions. Based on its perturbative treatment one may regard plasma turbulence as a superposition of linear modes (or normal modes) and sideband waves (or nonlinear modes). In this study, we use magnetic field and plasma measurements of nine solar wind events obtained by the Cluster spacecraft and make extensive use of a high-resolution wave vector analysis method, the Multi-point Signal Resonator technique, to find frequencies and wave vectors of discrete modes on ion kinetic scales in the plasma rest frame. The primarily unstructured wave observations in the frequency–wave number diagram are classified into three distinct linear modes (proton Bernstein modes, helium-alpha Bernstein modes, and kinetic Alfvén waves) and the sideband waves by comparing with the dispersion relations derived theoretically from linear Vlasov theory using observational values of the plasma parameter beta and the propagation angle from the mean magnetic field. About 60% of the observed discrete modes can be explained by the linear modes, primarily as the proton Bernstein and the kinetic Alfvén waves, within the frequency uncertainties, while the rest of the population (about 40%) cannot be classified as linear modes due to the large deviation from dispersion relations. We conclude that both the linear modes and sideband wave components are needed to construct the wave picture of solar wind turbulence on ion-kinetic scales.