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

The study addresses the long-standing problem of how turbulent energy in weakly collisional space plasmas is dissipated and partitioned among particle species. Turbulence transports energy from large-scale magnetic fields and plasma flows down to kinetic scales, where mechanisms such as resonant wave–particle interactions (Landau, transit-time, cyclotron damping), non-resonant processes (stochastic ion heating, magnetic pumping, viscous-like heating via temperature-anisotropy instabilities), and dissipation in coherent structures (e.g., reconnection) are believed to act. Developing predictive capability for species-specific heating is crucial for heliophysics and astrophysical contexts (e.g., interpreting emissions from black hole accretion flows). Prior observational inferences of ion cyclotron damping in the solar wind relied on temperature anisotropy constraints and correlations in velocity distributions, but alternative mechanisms like stochastic heating can produce similar signatures. The present work aims to directly identify ion cyclotron damping in turbulent magnetosheath plasma and quantify the associated ion energization rate by applying the field–particle correlation (FPC) technique to MMS in situ measurements, and to compare ion and electron energization to the turbulent cascade rate to assess energy partitioning.

Previous studies inferred ion cyclotron damping in the solar wind via proton and helium temperature anisotropy measurements versus plasma parameters and differential flows (e.g., Kasper et al. 2008, 2013), though stochastic ion heating can yield similar observational patterns. Parker Solar Probe (PSP) measurements using the Solar Probe Cup’s Flux Angle mode correlated perpendicular electric field fluctuations with variations in a narrow range of the proton distribution, indicating energy transfer between ICWs and protons. PSP observations at ~30 solar radii found perpendicular elongation of ion velocity distributions consistent with quasilinear diffusion by parallel ICWs and estimated heating rates using the measured left-handed fluctuation spectra. The FPC technique has previously been used to identify electron Landau damping in spacecraft observations and simulations, and to diagnose collisionless energy transfer across multiple plasma processes. Building on these works, the present study uses FPC with MMS to directly detect ion cyclotron damping and quantify ion energization in magnetosheath turbulence while comparing to analytical dispersion modeling.

Data and event: A 77 s MMS1 burst-mode interval (07:24:28–07:25:45 UT, 12 Jan 2016) in Earth’s magnetosheath near the dawnside sub-solar region was analyzed. Instruments: magnetic field from FGM at 128 Hz, electric field from EDP at 8192 Hz, and ion velocity distribution functions (iVDFs) from FPI-DIS at 150 ms cadence. Plasma parameters during the interval were approximately steady: |B0| = 48 ± 5 nT, ni = 8.6 ± 0.6 cm−3, Ti⊥ = 614 ± 30 eV, Ti∥ = 253 ± 14 eV (Ti ≈ 494 ± 22 eV), Te ≈ 37 ± 2 eV, v⊥i ≈ 343 ± 8 km/s, v∥i ≈ 220 ± 6 km/s, vA ≈ 355 ± 21 km/s, β∥i ≈ 0.383 ± 0.058, fci ≈ 0.73 ± 0.02 Hz, U0∥ ≈ 122 ± 38 km/s. Spectral and polarization analysis (Morlet wavelets) showed enhanced power at 0.2–0.5 Hz with left-handed polarization at f_icw ≈ 0.26 Hz (T_icw ≈ 3.85 s), consistent with ion cyclotron waves (ICWs). Measurements were high-pass filtered at f_cut = 0.1 Hz to remove low-frequency oscillatory transfer. Coordinate systems and transforms: Fields and distributions were Lorentz transformed to the mean ion bulk flow frame (E = E′ + U0 × B), down-sampled to match DIS cadence, and rotated into a field-aligned coordinate (FAC) system defined by the mean B0 and U0i. Field–particle correlation (FPC): Using the perpendicular electric field components in FAC (j = ⊥1, ⊥2), the alternative instantaneous correlation C_Ei(v,t;τ=0) = q E_i(t) f_i(v,t) was computed in Cartesian velocity bins, followed by finite-difference derivatives in velocity space to obtain the standard perpendicular FPC C_E⊥(v,t;τ) as per the established formulation. Time averaging over correlation intervals (up to the full 77 s) yielded gyrotropic signatures C_E⊥(v⊥,v∥;τ), reduced C_E⊥(v⊥;τ), time-stack C_E⊥(v⊥,t;τ), and perpendicular-plane signatures C_E11(v⊥1,v⊥2;τ) and C_E12(v⊥1,v⊥2;τ). Consistency check: The dependence of the ion energization rate on f_cut was evaluated, showing energy transfer concentrated between fci and fce, with a noise floor ≈ 10−13 W m−3 for f_cut ≥ fce. Analytical modeling: Linear Vlasov–Maxwell dispersion relations (PLUME solver) were used to compute ICW eigenfrequencies, damping/growth rates, and eigenfunction phase/amplitude relations for parameters representative of the interval. Cases with T∥i/T⊥i = 1.0 (damping) and 2.43 (instability) were examined. Based on measurements and estimates (k∥di ≈ 0.5–1.5), a representative model with k⊥di = 0.8, k∥di = 0.016 and E⊥/(B0 vA) = 0.15 was used to predict quadrupolar perpendicular velocity-space FPC signatures averaged over one ICW period. Turbulent cascade estimate: The inertial-range cascade rate ε was estimated from measured amplitudes at f = 0.2 Hz using a critically balanced anisotropic turbulence model, assuming equipartition between kinetic and magnetic energy, yielding ε ≈ 23 × 10−12 W m−3 for the interval. Additional diagnostics: Ion Landau damping was estimated by a procedure analogous to Chen et al., and stochastic heating was estimated using Bourouaine & Chandran’s expression with δv⊥ ≈ 30 km/s and ρi ≈ 75 km.

- Direct detection of ion cyclotron damping (ICD) in turbulent magnetosheath plasma via FPC velocity-space signatures. Evidence includes: (i) gyrotropic signature C_E⊥(v⊥,v∥;τ) showing loss of phase-space energy density at v⊥/v_ti ≤ 1 and gain for 1 ≤ v⊥/v_ti ≤ 3; (ii) quadrupolar patterns in perpendicular-plane correlations C_E11 and C_E12 with opposite energization quadrants, consistent with analytical ICW eigenfunction predictions. - ICWs identified at f_icw ≈ 0.26 Hz (T_icw ≈ 3.85 s) with left-handed polarization; f_ci ≈ 0.73 Hz. Persistent perpendicular ion energization lasted ~30–70 s, over 10× the ICW period, coincident with the disappearance of the observed ICW power. - Quantified energization: Interval-averaged perpendicular ion energization rate ⟨E⊥⟩ = 9.1 × 10−12 W m−3. Previously measured electron Landau damping energization rate for the same interval ⟨E∥,e⟩ = 1.7 × 10−12 W m−3. Combined ⟨E⊥,i⟩ + ⟨E∥,e⟩ = 10.8 × 10−12 W m−3, in order-of-magnitude agreement with the estimated turbulent cascade rate ε ≈ 23 × 10−12 W m−3. - Linear dispersion analysis indicates that for parameters representative of the interval, ion cyclotron damping dominates over ion Landau and transit-time damping, and electron damping channels are weak for the observed fluctuations. Estimated k∥di ≈ 0.5–1.5 is consistent with significant ICD rates. - Alternative mechanisms constrained: Ion Landau energization rate is ≈ 10−14 W m−3 (below noise floor). Stochastic ion heating estimate Q_stoch ≈ 8.0 × 10−14 W m−3, negligible versus measured ion energization. Electron cyclotron damping is negligible due to low fluctuation energy at f ≥ fce and cadence limitations.

The findings directly address the research question by identifying ion cyclotron damping as a dominant channel of turbulent dissipation in the magnetosheath and by quantifying the associated ion energization. Velocity-space signatures uniquely distinguish ICD from other mechanisms such as stochastic ion heating or ion Landau damping. The persistence of perpendicular energization over multiple ICW periods and the agreement with analytical ICW eigenfunction-based predictions strengthen the causal link between observed ICWs and measured energization. The combined ion (ICD) and electron (Landau damping) energization rates constitute a substantial fraction of the turbulent cascade rate, supporting a picture in which these mechanisms account for the majority of small-scale turbulent dissipation in this interval. This advances the capability to observationally partition turbulent energy between species, a key need for predictive models of plasma heating in space and astrophysical environments.

This work provides the first direct measurement of ion cyclotron damping of turbulence in space plasma, using MMS in situ electric fields and ion distributions with the field–particle correlation technique to reveal diagnostic velocity-space signatures. The study also quantitatively demonstrates that ion cyclotron damping together with electron Landau damping accounts for an order-of-magnitude share of the turbulent cascade rate, establishing the dominant channels of turbulent dissipation and their partitioning between ions and electrons in the analyzed interval. Future work should extend FPC analyses to larger statistical datasets across varying plasma β, temperature anisotropies, and turbulence conditions to map out the dependence of dissipation channels and species partitioning on plasma parameters, refine cascade-rate estimates, and integrate these constraints into predictive global models.

- The origin of the observed ICWs is not definitively established; potential upstream generation (e.g., anisotropy-driven instabilities near the bow shock) is speculative. - Linear dispersion predictions assume static background conditions; in turbulence the background varies, and growth/damping rates may deviate. Anisotropy measurements may be biased by perpendicular wave motions (apparent temperature effects). - Electron cyclotron damping could not be evaluated due to DIS cadence limits (Nyquist ≪ fce) and low fluctuation power at f ≥ fce. - The turbulent cascade rate ε is an order-of-magnitude estimate based on model assumptions (critical balance, equipartition) and measurement at f ≈ 0.2 Hz; comparison has inherent uncertainty. - The energization rate calculations have a noise floor ≈ 10−13 W m−3; very weak channels (e.g., ion Landau damping) are near/below detectability. - Single-spacecraft, single-point measurements limit direct determination of wavevector; k∥ estimates rely on geometry and models and carry uncertainty.