Linear damping of magneto-acoustic waves in two-fluid partially ionized plasmas

TL;DR

This work analyzes magneto-acoustic wave damping in partially ionized plasmas using a linear two-fluid model, focusing on waves driven periodically in a uniform background. It derives analytical approximations for wavenumbers and spatial damping rates in both weak and strong collisional coupling regimes, and validates them against full numerical solutions of the dispersion relation for various ionization degrees and propagation angles. The study covers perpendicular, oblique, and acoustic regimes, highlighting how the global fast/slow modes emerge in strong coupling and how damping scales with collision frequencies and phase speeds. It also compares periodic-driver results with impulsive-driver findings, discusses angle-dependent effects and ideal-MHD limits, and suggests extensions to include additional non-ideal processes and non-linear dynamics. The results provide actionable formulas applicable to hydrogen and other partially ionized plasmas in astrophysical and laboratory settings.

Abstract

Magneto-acoustic waves in partially ionized plasmas are damped due to elastic collisions between charged and neutral particles. Here, we use a linearized two-fluid model to describe the influence of this collisional interaction on the properties of small-amplitude waves propagating in a uniform and static background. Mainly focusing on the case of waves generated by a periodic driver, we perform a detailed study of the dependence of the wavenumbers and damping rates on the ionization degree of the plasma, the strength of the collisional coupling, and the angle of propagation. We describe how the different wave modes (fast, slow, acoustic) are related to the individual properties of each fluid in a wide range of physical conditions. In addition, we derive analytical approximations for the damping rates due to charge-neutral collisions in the limits of weak and strong coupling and check their range of validity in comparison with the exact numerical results. These approximations can be generally applied to a large variety of astrophysical and laboratory partially ionized plasmas, but here we also discuss the particular application to plasmas only composed of hydrogen.

Figures (6)

• Figure 1: Normalized wavenumbers (panels a, c, and e) and damping rates (panels b, d, and f) as functions of the coupling degree, $\nu / \omega$, for magneto-acoustic waves propagating in the perpendicular direction to the background magnetic field ($\theta = \pi / 2$), in a hydrogen plasma with $c_{\rm{A}}^{2} = 10 c_{\rm{c}}^{2}$. Top, middle and bottom panels correspond to the density ratios $\chi = 0.01$, $\chi =1$ and $\chi = 100$, respectively. Symbols represent the exact solutions from the dispersion relation, while dotted and solid lines represent the analytical approximations for the weak and strong coupling regimes.
• Figure 2: Normalized wavenumbers (panels a, c, and e) and damping rates (panels b, d, and f) as functions of the coupling degree, $\nu / \omega$, for magneto-acoustic waves propagating at an angle $\theta = \pi /4$ with respect to the background magnetic field, in a hydrogen plasma with $c_{\rm{A}}^{2} = 10 c_{\rm{c}}^{2}$. Top, middle and bottom panels correspond to the density ratios $\chi = 0.01$, $\chi =1$ and $\chi = 100$, respectively. Symbols represent the exact solutions from the dispersion relation, while dotted and solid lines represent the analytical approximations for the weak and strong coupling regimes.
• Figure 3: Normalized wavenumbers (a, c, and e) and damping rates (b, d, and f) as functions of the coupling degree, $\nu / \omega$, for magneto-acoustic waves propagating along the parallel direction to the background magnetic field ($\theta = 0$), in a hydrogen plasma with $c_{\rm{A}}^{2} = 10 c_{\rm{c}}^{2}$. Top, middle and bottom panels correspond to the density ratios $\chi = 0.01$, $\chi =1$ and $\chi = 100$, respectively. Symbols represent the exact solutions from the dispersion relation, while dotted and solid lines represent the analytical approximations for the weak and strong coupling regimes.
• Figure 4: Normalized wavenumber of the ideal MHD magneto-acoustic waves as functions of the angle of propagation. A hydrogen plasma with $c_{\rm{A}}^{2} = 10 c_{\rm{c}}^{2}$ and $\chi = 100$ is considered.
• Figure 5: Normalized wavenumbers (panel a) and damping rates (panel b) of 2F magneto-acoustic waves as functions of $\theta$ for a case with a strong collisional coupling given by $\nu / \omega = 10^{3}$. Global fast and slow modes are represented by blue long-dashed and red solid lines, respectively, while the green dashed lines correspond to the mode given by Eq. (\ref{['eq:k3_general']}). Same plasma parameters as in Fig. \ref{['fig:kr_theta_ideal']} have been used. The black crosses represent the values of the strongly attenuated mode for perpendicular propagation given by Eq. (\ref{['eq:sols_perp_strong2']}).