Direct observation of ion cyclotron damping of turbulence in Earth's magnetosheath plasma

Plasma turbulence is a crucial process in space and astrophysical environments, facilitating energy transport from large-scale magnetic fields and plasma flows to kinetic scales. At these smaller scales, the turbulence dissipates, heating the plasma. Understanding the underlying dissipation mechanisms is vital for improving predictive models of turbulent heating, which are crucial for global models of heliospheric energy flow and the interpretation of astronomical observations (e.g., black hole accretion disks). Several mechanisms are proposed for turbulent dissipation in weakly collisional space plasmas, including resonant wave-particle interactions (Landau damping, transit-time damping, cyclotron damping), non-resonant interactions (stochastic ion heating, magnetic pumping, viscous heating), and dissipation in coherent structures (magnetic reconnection). Previous studies have indirectly inferred ion cyclotron damping based on temperature anisotropy measurements or have provided limited direct evidence using correlation techniques. This study aims to provide direct observational evidence of ion cyclotron damping in Earth's turbulent magnetosheath and quantify the resulting ion energization rate. This will help refine our understanding of turbulent energy dissipation and its impact on plasma heating.

Prior research has explored ion cyclotron damping indirectly, using proton and helium temperature anisotropy measurements in the solar wind to suggest its role in enhanced perpendicular ion temperatures. However, alternative mechanisms, like stochastic ion heating, could produce similar observations. Studies using the Parker Solar Probe (PSP) have shown evidence of energy transfer between ion cyclotron waves (ICWs) and protons, supporting the presence of cyclotron damping. These studies provide some support for the hypothesis but lack the direct measurement of the energy transfer that this study aims to achieve. The field-particle correlation (FPC) technique has been successfully applied to investigate collisionless damping of plasma waves and kinetic turbulence in both numerical simulations and spacecraft observations, offering a promising tool for the current study.

The study analyzes a 77-second interval of burst-mode data from the MMS1 spacecraft, focusing on a magnetosheath region where the turbulent cascade is well-developed. Data from the Fluxgate Magnetometers (FGM) for magnetic fields, Electric Field Double Probes (EDP) for electric fields, and Fast Plasma Investigation Dual Ion Spectrometers (DIS) for ion velocity distribution functions (IVDFs) were used. The field-particle correlation (FPC) technique was applied. This technique uses single-point measurements of electric fields and particle velocity distributions to determine the energy transfer to particles as a function of their velocity, which reveals the underlying wave-particle interactions. The FPC analysis involved Lorentz transforming measurements to the mean ion bulk flow frame, rotating them into a magnetic field-aligned coordinate (FAC) system, high-pass filtering the electric field to remove low-frequency fluctuations, and computing the instantaneous and time-averaged field-particle correlations. The analysis also involved calculating and interpreting gyrotropic and perpendicular velocity-space signatures to identify ion cyclotron damping. An analytical model, using solutions of the linear Vlasov-Maxwell dispersion relation for Alfvén/ion cyclotron waves, was developed for comparison with the observations and interpretation of the quadrupolar structures observed in velocity-space. The turbulent energy cascade rate was estimated using a cascade model for anisotropic plasma turbulence. The potential contribution of other proposed dissipation mechanisms (ion Landau damping, stochastic ion heating, electron cyclotron damping, and viscous heating) was assessed. The instantaneous alternative field-particle correlation was calculated as `C<sub>E⊥</sub>(v, t; t=0) = qE<sub>j</sub>(t)f<sub>i</sub>(v, t)`, where j indicates the vector component in the magnetic FAC system. These values were then summed in Cartesian velocity bins, velocity-space derivatives were computed, and the results combined to yield the perpendicular field-particle correlation `C<sub>E⊥</sub>(v, t; τ)` in 3D velocity space. Time-averages were calculated by averaging over the correlation interval τ.

The analysis revealed a significant presence of left-hand polarized ion cyclotron waves (ICWs) within the turbulent spectrum, with a frequency of approximately 0.26 Hz. The time-averaged IVDF exhibited features consistent with ICW pitch-angle scattering through cyclotron resonance, lacking the core flattening expected from stochastic ion heating. The FPC analysis yielded velocity-space signatures that directly confirmed ion cyclotron damping. These signatures included: (i) a gyrotropic velocity-space signature showing a loss of phase-space energy density at low perpendicular velocities and a gain at higher velocities; and (ii) perpendicular velocity-space signatures exhibiting characteristic quadrupolar patterns. These quadrupolar signatures showed excellent qualitative agreement with analytical predictions from the Vlasov-Maxwell linear dispersion relation solver. The time-averaged perpendicular correlation showed persistent ion energization over a period exceeding ten times the ICW period. The ion energization rate due to ion cyclotron damping was found to be 9.1 × 10⁻¹² W m⁻³, which, when added to the previously determined electron Landau damping rate (1.7 × 10⁻¹² W m⁻³), resulted in a combined dissipation rate of 10.8 × 10⁻¹² W m⁻³, roughly matching the estimated turbulent cascade rate (23 × 10⁻¹² W m⁻³). Analysis indicated negligible contributions from other mechanisms such as ion Landau damping and stochastic ion heating.

The results definitively establish ion cyclotron damping and electron Landau damping as the primary mechanisms for dissipating turbulent energy in the observed magnetosheath interval. The observed velocity-space signatures provide unique identifiers for distinguishing between ion cyclotron damping and stochastic ion heating. The close agreement between the combined ion and electron energization rates and the estimated turbulent cascade rate strongly supports the identified mechanisms as the dominant contributors to dissipation. The study demonstrates the effectiveness of the FPC technique in identifying energy transfer mechanisms, offering a powerful tool for analyzing spacecraft observations.

This study presents the first direct measurement of ion cyclotron damping of turbulence in a space plasma using the FPC technique. The observed velocity-space signatures provide clear identification of this damping mechanism. The quantitative assessment of ion and electron energization rates, combined with estimates of the turbulent cascade rate, reveals the dominant channels of energy dissipation and their relative contributions. Future work should extend this analysis to a larger statistical sample of MMS observations to further characterize the dependence of energy partitioning on plasma and turbulence parameters and develop predictive models of turbulent dissipation and plasma heating.

The analysis focused on a single 77-second interval, limiting the statistical significance of the findings. The estimation of the turbulent cascade rate is an order-of-magnitude estimate, introducing uncertainty in the comparison of dissipation rates. The analytical model relies on linear theory and might not fully capture the complexities of nonlinear wave-particle interactions in a turbulent environment. The assumption of a hydrogenic plasma might not be completely accurate in the real magnetosheath environment.