Evolution of ion distribution functions in ionospheric plasmas perturbed by Alfvén waves

TL;DR

This paper investigates ion-kinetic effects during the parametric decay instability (PDI) of parallel-propagating Alfvén waves in ultra-low-$\beta$ ionospheric-like plasmas using a 1D hybrid PIC framework. By systematically varying plasma beta, pump-wave amplitude/polarization, and ion composition, it shows that PDI can induce strong nonthermal modifications of the ion velocity distribution function (VDF), including parallel heating and ion-beam formation, with regimes controlled by a beta-star parameter $\beta^* = \frac{\beta_{tot}}{(\delta B/B_0)^2}$. A key finding is that when $1/\beta^* > 1$, rapid generation of harmonics, density/field fluctuations, and complete VDF broadening occur, offering a plausible mechanism for particle acceleration and precipitation in space weather contexts; time scales between wave impact and VDF modification are quantified (e.g., $t \sim 300\Omega_i^{-1}$, about 10 s). Using realistic 500 km ionospheric parameters and O$^+$–H$^+$ composition, the work provides quantitative benchmarks for wave–particle interactions in ultra-low-$\beta$ plasmas and highlights the potential relevance to ionospheric heating and precipitation processes, while noting the limitations of a 1D approach and outlining future extensions to higher dimensions and neutral collisions.

Abstract

This study investigates ion kinetic effects during the parametric decay instability (PDI) of parallel-propagating Alfvén waves under plasma conditions characteristic of the Earth's ionosphere. By using a series of hybrid particle-in-cell simulations, we examine the evolution of ion velocity distribution functions (VDFs) in ultra-low-beta plasmas. Our numerical campaign systematically explores the dependence on key parameters (plasma beta, pump-wave amplitude and polarization, and ion composition). To emphasize the role of kinetic effects, we choose to trigger the PDI with a dispersive mother wave with wavelength comparable to the ion characteristic inertial length. Our results reveal pronounced nonthermal VDF modifications, including parallel heating and the formation of secondary ion beams, linked to the nonlinear evolution of parametric decay instability. By varying the plasma beta and the pump-wave amplitude, we identify a critical regime where rapid and complete broadening of the velocity distribution function is observed, triggering bidirectional ion acceleration. Notably, simulations modeling realistic ionospheric conditions demonstrate that even low-amplitude Alfvénic perturbations can induce significant VDF spreading and ion beam generation, with hydrogen ions exhibiting stronger effects than oxygen. These nonthermal microscopic processes offer a plausible mechanism for particle precipitation in space weather events. This work represents the first comprehensive study with hybrid simulations of PDI-driven ion kinetics in ultra-low-beta plasmas, providing quantitative estimates for the time delay between electromagnetic wave impact and ion VDF modification and new insights into wave-particle interactions that may contribute to ion acceleration, precipitation processes and space plasma dynamics.

Figures (15)

• Figure 1: Run A: Time evolution of the energy components normalized to their respective initial values: kinetic energy $E_{\textrm{kin}}/E_{\textrm{kin},0}$ (blue), magnetic energy $E_{\textrm{mag}}/E_{\textrm{mag},0}$ (red), and total energy $E_{\textrm{tot}}/E_{\textrm{tot},0}$ (yellow). An horizontal dashed black line is overplotted for comparison to show a remarkably good energy conservation.
• Figure 2: Run A: Time evolution of the spatially-averaged Elsässer energies normalized to their initial values, $E_+/E_{+,0}$ (solid red), $E_-/E_{-,0}$ (solid blue) and of normalized cross-helicity $\sigma$ (dashed green). A dashed black line is included to indicate the zero reference.
• Figure 3: Run A: Power spectrum of the $y$ component of the magnetic field (blue) and ion density (black). Values at $t = 0$ are overlaid as thinner dashed lines of the same color. Vertical dashed lines highlight significant peaks corresponding to mother wave (blue), daughter wave (cyan) and acoustic wave (black). The respective wavenumbers ($w_\mathrm{m}$, $w_\mathrm{r}$ and $w_\mathrm{s}$) are indicated in the upper right corner with the same colors.
• Figure 4: Run A: Ion VDF displayed as a 3D color scale. Red lines represent VDF projections on the parallel and perpendicular directions. Black dashed lines denote the corresponding projections of the initial distribution (t=0).
• Figure 5: Run C: Time evolution of $E_{\textrm{kin}}/E_{\textrm{kin},0}$ (blue), $E_{\textrm{mag}}/E_{\textrm{mag},0}$ (red), and $E_{\textrm{tot}}/E_{\textrm{tot},0}$ (yellow). An horizontal dashed black line is overplotted to show energy conservation.