Damping of Alfven waves in solar partially ionized plasmas: effect of neutral helium in multi-fluid approach

Chromospheric and prominence plasmas contain neutral atoms, which may change the plasma dynamics through collision with ions. Most of the atoms are neutral hydrogen, but a significant amount of neutral helium may also be present in the plasma with a particular temperature. Damping of MHD waves due to ion collision with neutral hydrogen is well studied, but the effects of neutral helium are largely unknown. We aim to study the effect of neutral helium in the damping of Alfven waves in solar partially ionized plasmas. We consider three-fluid magnetohydrodynamic (MHD) approximation, where one component is electron-proton-singly ionized helium and other two components are the neutral hydrogen and neutral helium atoms. We derive the dispersion relation of linear Alfven waves in isothermal and homogeneous plasma. Then we solve the dispersion relation and derive the damping rates of Alfven waves for different plasma parameters. The presence of neutral helium significantly enhances the damping of Alfven waves compared to the damping due to neutral hydrogen at certain values of plasma temperature (10000-40000 K) and ionization. Damping rates have a peak near the ion-neutral collision frequency, but decrease for the higher part of wave spectrum. Collision of ions with neutral helium atoms can be of importance for the damping of Alfven waves in chromospheric spicules and in prominence-corona transition regions.

💡 Research Summary

The paper investigates how neutral helium influences the damping of Alfvén waves in partially ionized solar atmospheric plasmas, such as the chromosphere, spicules, and prominence–corona transition regions. While previous studies have largely focused on the role of neutral hydrogen, the authors argue that neutral helium can be abundant in certain temperature ranges (10 000–40 000 K) and therefore may significantly affect wave dynamics.

To capture the physics beyond the single‑fluid MHD approximation, the authors adopt a three‑fluid model: (1) a charged fluid consisting of electrons, protons, and singly ionized helium (He⁺); (2) a neutral hydrogen fluid; and (3) a neutral helium fluid. Starting from the five‑fluid Braginskii equations, they combine the electron, proton, and He⁺ momentum equations (neglecting electron inertia) into a single charged‑fluid momentum equation, while retaining separate momentum equations for the two neutral species. Collisional momentum exchange is expressed through friction coefficients αₐb derived from classical cross‑section formulas, and the ion‑neutral collision frequency ν_in is defined as ν_in = α_in (1/m_i n_i + 1/m_n n_n), which accounts for the relative motion of both species.

Assuming a static, homogeneous, isothermal plasma with a uniform magnetic field B₀ along the z‑axis, the authors linearize the equations for transverse (y‑direction) perturbations and perform a Fourier analysis (∝ e^{i(k_z z − ωt)}). This yields a fourth‑order dispersion relation (Eq. 29) involving the dimensionless frequency Ω = ω/(k_z v_A), the density ratios ξ_H = ρ_H/ρ₀ and ξ_He = ρ_He/ρ₀, and the dimensionless collisional parameters a_H = k_z v_A ρ₀/α_H and a_He = k_z v_A ρ₀/α_He. The polynomial has four roots: two complex conjugates representing damped Alfvén waves and two purely imaginary roots corresponding to damped vortex modes of the neutral fluids.

Numerical solutions of the dispersion relation are obtained for a range of temperatures, ionization fractions, and neutral‑to‑ion density ratios appropriate to the solar atmosphere. The key findings are:

1. Neutral helium enhances damping – When neutral helium is present at a fraction of ~0.1–0.2 relative to neutral hydrogen (as indicated by the Fontenla et al. 1993 FAL93‑3 model), the combined collisional coefficient α_He becomes comparable to or larger than α_H. Consequently, the Alfvén wave damping rate can increase by a factor of 2–3 compared with a hydrogen‑only model.

2. Peak damping occurs near the ion‑neutral collision frequency – The imaginary part of ω reaches a maximum when the wave frequency ω ≈ ν_in. Because ν_in depends on temperature and density, the peak shifts across the spectrum; for typical chromospheric conditions (T ≈ 1.6 × 10⁴ K, n_e ≈ 10¹⁰ cm⁻³) the relevant ν_in values lie in the range 5–20 s⁻¹, corresponding to wavelengths of a few hundred kilometres.

3. High‑frequency waves are less affected – For ω ≫ ν_in the damping rate declines, reproducing the well‑known “collision‑frequency resonance” behavior seen in two‑fluid studies. This implies a transparent window for very short‑period Alfvén waves, even in the presence of neutral helium.

4. Altitude dependence – Using the FAL93‑3 atmospheric stratification, the authors show that below ~1500 km the neutral helium fraction is modest and its impact is limited. Above this height, especially near 1800–2000 km where the temperature rises sharply, the neutral helium fraction rises to ~0.15–0.2, and the enhanced damping becomes significant. This suggests that Alfvén waves generated in the lower chromosphere may be efficiently damped before reaching the corona, particularly in spicules and prominence‑corona transition regions.

The study’s novelty lies in the explicit inclusion of neutral helium within a multi‑fluid framework and the demonstration that its collisional coupling can dominate the damping under realistic solar conditions. The authors acknowledge several simplifications: neglect of Hall, Ohmic, and ambipolar diffusion terms; assumption of isothermal, homogeneous plasma; omission of electron‑neutral collisions; and linear treatment only. Nevertheless, the results provide a robust theoretical basis for interpreting observations of rapid Alfvén wave attenuation in the upper chromosphere and for improving models of wave‑driven heating and momentum transport in partially ionized solar plasma.