Damped Kinetic Alfvén Waves in Earth's Magnetosheath: Numerical Simulations and MMS Observations

TL;DR

This work addresses how collisionless Landau damping influences nonlinear kinetic Alfvén wave turbulence in Earth's magnetosheath. It introduces a Landau-damping–augmented two-fluid model that yields a modified nonlinear Schrödinger equation for KAW envelopes, solved with a high-accuracy pseudospectral method and validated against MMS observations. The main finding is that Landau damping suppresses small-scale magnetic structures and steepens the kinetic-range spectrum from $k_ot ρ_i^{-8/3}$ to $k_ot ρ_i^{-11/3}$, while preserving the inertial-range $k_ot ρ_i^{-5/3}$ scaling; MMS data show an intermediate damping regime, with the observed kinetic-range slope between the undamped and damped limits. This demonstrates Landau damping as a primary mechanism for dissipation at kinetic scales in collisionless magnetized plasmas and provides a framework for linking fluid and kinetic descriptions in space plasmas.

Abstract

The Earth's magnetosheath provides a high $β$ (ratio of electron thermal pressure to magnetic pressure) plasma environment where kinetic Alfvén waves (KAWs) strongly influence turbulence and energy dissipation. This study investigates how Landau damping modifies the nonlinear evolution of KAWs by solving a modified nonlinear Schrödinger equation that captures both dispersive and nonlinear effects. Without Landau damping, modulational instability drives rapid self-focusing into intense magnetic filaments, producing a turbulent cascade with $k_\perp^{-5/3}$ scaling in the inertial range ($k_\perpρ_i<1$) that transitions to $k_\perp^{-8/3}$ at sub-ion scales ($k_\perpρ_i>1$), here $k_\perp$ is the wavevector component perpendicular to the background magnetic field and $ρ_i$ the ion thermal gyroradius. When Landau damping is included, magnetic structures are significantly suppressed, and the spectrum steepens to $k_\perp^{-11/3}$ in the sub-ion range while the inertial range maintains $k_\perp^{-5/3}$ scaling. The damping acts across all scales through resonant wave-particle interactions, efficiently transferring energy from waves to particles. Direct comparison with Magnetospheric Multiscale (MMS) spacecraft observations shows that the observed kinetic range spectral slope falls between our undamped and damped simulation limits, consistent with an intermediate damping regime in magnetosheath turbulence. This agreement confirms that Landau damping is one of the primary mechanisms controlling turbulent energy dissipation at kinetic scales in collisionless plasmas.

Figures (7)

• Figure 1: Time evolution of normalized total magnetic energy $E_B(t)/E_B(0)$. The undamped case (blue solid line) conserves energy, while the Landau-damped case (red dashed line) shows monotonic decay with $27.3\%$ energy loss over $100\,\omega_{ci}^{-1}$.
• Figure 2: Spatial distribution of normalized magnetic field intensity $|\delta B_y|^2$ at $\omega_{ci}t = 100$. (a) Undamped case showing intense filamentary structures. (b) Damped case showing suppressed small-scale features.
• Figure 3: Time-averaged magnetic power spectra for $\omega_{ci}t = 40$--$100$. (a) Undamped case showing a $k^{-8/3}$ kinetic range. (b) Damped case showing a steeper $k^{-11/3}$ dissipation range due to Landau damping.
• Figure 4: Time evolution of discrete Fourier mode amplitudes normalized by initial pump energy ($|\delta B_k|^2/|\delta B_0|^2$). Top row (a1--a3): Undamped case showing persistent pump mode. Bottom row (b1--b3): Damped case showing pump mode decay due to Landau damping.
• Figure 5: MMS1 electromagnetic field analysis. Top three panels show the amplitudes of (a) perpendicular electric field $|\delta E_\perp|$, (b) perpendicular magnetic field $|\delta B_\perp|$, and (c) parallel electric field $|\delta E_\parallel|$. (d) The normalized ratio $|\delta E_\perp|/(|\delta B_\perp|v_A)$. The black dashed line marks the ideal MHD limit (ratio $\approx 1$), while the green shaded region indicates the expected range for KAWs.