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This Chapter outlines the basic properties of waves in solar partially ionized plasmas. It provides a summary of the main sets of equations, from the single-fluid formalism, to the multi-fluid one, giving examples for purely hydrogen, and for hydrogen-helium plasmas. It then discusses the solutions for waves under the single-fluid frame: the influence of the ambipolar diffusion, diamagnetic effect, and the Hall effect on the propagation, dissipation, and mode conversion of the magnetohydrodynamic waves. The Chapter continues by outlining the wave solutions in the multi-fluid formalism: the influence of the elastic inter-particle collisions into the propagation, damping and dissipation of different magnetohydrodynamic modes. Both parts discuss linear and non-linear wave solutions, and the effects of the gravitational stratification of the solar atmosphere., Comment: Chapter 6 in "Magnetohydrodynamic Processes in Solar Plasmas", ed. A.K. Srivastava, M. Goossens and I. Arregui, Elsevier (2024), pp. 203-271. https://www.sciencedirect.com/book/9780323956642/magnetohydrodynamic-processes-in-solar-plasmas

In this paper we present a numerical study of the dynamics of partially ionized coronal rain blobs. We use a two-fluid model to perform a high-resolution 2D simulation that takes into account the collisional interaction between the charged and neutral particles contained in the plasma. We follow the evolution of a cold plasma condensation as it falls through an isothermal vertically stratified atmosphere that represents the much hotter and lighter solar corona. We study the consequences of the different degrees of collisional coupling that are present in the system. On the one hand, we find that at the dense core of the blob there is a very strong coupling and the charged and neutral components of the plasma behave as a single fluid, with negligible drift velocities (of a few cm s^-1). On the other hand, at the edges of the blob the coupling is much weaker and larger drift velocities (of the order of 1 km s^-1) appear. In addition, frictional heating causes large increases of temperature at the transition layers between the blob and the corona. For the first time we show that such large drift velocities and temperature enhancements can develop as a consequence of ion-neutral decoupling associated to coronal rain dynamics. This can lead to enhanced emission coming from the plasma at the coronal rain-corona boundary, which possesses transition region temperature., Comment: 11 pages, 7 figures, and 1 animation. Accepted for publication in The Astrophysical Journal Letters

Prominence threads are very long and thin flux tubes which are partially filled with cold plasma. Observations have shown that transverse oscillations are frequent in these solar structures. The observations are usually interpreted as the fundamental kink mode, while the detection of the first harmonic remains elusive. Here, we aim to study how the density inhomogeneity in the longitudinal and radial directions modify the periods and damping times of kink oscillations, and how this effect would be reflected in observations. We solve the ideal magnetohydrodynamics equations through two different methods: a) performing 3D numerical simulations, and b) solving a 2D generalised eigenvalue problem. We study the dependence of the periods, damping times and amplitudes of transverse kink oscillations on the ratio between the densities at the centre and at the ends of the tube, and on the average density. We apply forward modelling on our 3D simulations to compute synthetic H$\alpha$ profiles. We confirm that the ratio of the period of the fundamental oscillation mode to the period of the first harmonic increases as the ratio of the central density to the footpoint density is increased or as the averaged density of the tube is decreased. We find that the damping times due to resonant absorption decrease as the central to footpoint density ratio increases. Contrary to the case of longitudinally homogeneous tubes, we find that the damping time to period ratio also increases as the density ratio is increased or the average density is reduced. We present snapshots and time-distance diagrams of the emission in the H$\alpha$ line. The results presented here have implications for the field of prominence seismology. While the H$\alpha$ emission can be used to detect the fundamental mode, the first harmonic is barely detectable in H$\alpha$. This may explain the lack of detections of the first harmonic., Comment: 17 pages, 16 figures, 4 movies. Accepted for publication in Astronomy & Astrophysics

In the absence of an initial seed, the Biermann battery term of a non-ideal induction equation acts as a source that generates weak magnetic fields. These fields are then amplified via a dynamo mechanism. The Kelvin-Helmholtz instability is a fluid phenomenon that takes place in many astrophysical scenarios and can trigger the action of the Biermann battery and dynamo processes. We aim to investigate the effect that the ionisation degree of the plasma and the interaction between the charged and neutral species have on the generation and amplification of magnetic fields during the different stages of the instability. We use the two-fluid model implemented in the numerical code Mancha-2F. We perform 2D simulations starting from a configuration with no initial magnetic field and which is unstable due to a velocity shear. We vary the ionisation degree of the plasma and we analyse the role that the different collisional terms included in the equations of the model play on the evolution of the instability and the generation of magnetic field. We find that when no collisional coupling is considered between the two fluids, the effect of the Biermann battery mechanism does not depend on the ionisation degree. However, when elastic collisions are taken into account, the generation of magnetic field is increased as the ionisation degree is reduced. This behaviour is slightly enhanced if the process of charge-exchange is also considered. We also find a dependence on the total density of the plasma related to the dependence on the coupling degree between the two fluids. As the total density is increased, the results from the two-fluid model converge to the predictions of single-fluid models., Comment: 20 pages, 13 figures, 2 movies. Accepted for publication in Astronomy & Astrophysics

Aims. We aim to improve the understanding of the physical mechanisms behind the slower than free-fall motion and the two-stage evolution (an initial phase of acceleration followed by an almost constant velocity phase) detected in coronal rain events. Methods. Using the Mancha3D code, we solve the 2D ideal MHD equations. We represent the solar corona as an isothermal vertically stratified atmosphere with a uniform vertical magnetic field and the plasma condensation as a density enhancement described by a 2D Gaussian profile. We analyse the temporal evolution of the descending plasma and study its dependence on parameters such as density and magnetic field strength. Results. We confirm previous findings that the pressure gradient is the main force that opposes the action of gravity and slows down the blob descent and that larger densities require larger pressure gradients to reach the constant speed phase. We find that the shape of a condensation with a horizontal variation of density is distorted as it falls, due to the denser parts of the blob falling faster than the lighter ones. This is explained by the fact that the duration of the initial acceleration phase, and therefore the maximum falling speed attained by the plasma, increases with the ratio of blob to coronal density. We also find that the magnetic field plays a fundamental role in the evolution of the descending condensations. A strong enough magnetic field (greater than 10 G in our simulations) forces each plasma element to follow the path given by a particular field line, which allows to describe the evolution of each vertical slice of the blob in terms of 1D dynamics, without influence of the adjacent slices. In addition, under the typical conditions of the coronal rain events, the magnetic field prevents the development of the Kelvin-Helmholtz instability., Comment: 14 pages, 11 figures; submitted to Astronomy & Astrophysics

In the interior of neutron stars, the induction equation regulates the long-term evolution of the magnetic fields by means of resistivity, Hall dynamics and ambipolar diffusion. Despite the apparent simplicity and compactness of the equation, the dynamics it describes is not trivial and its understanding relies on accurate numerical simulations. While a few works in 2D have reached a mature stage and a consensus on the general dynamics at least for some simple initial data, only few attempts have been performed in 3D, due to the computational costs and the need for a proper numerical treatment of the intrinsic non-linearity of the equation. Here, we carefully analyze the general induction equation, studying its characteristic structure, and we present a new Cartesian 3D code, generated by the user-friendly, publicly available {\em Simflowny} platform. The code uses high-order numerical schemes for the time and spatial discretization, and relies on the highly-scalable {\em SAMRAI} architecture for the adaptive mesh refinement. We present the application of the code to several benchmark tests, showing the high order of convergence and accuracy achieved and the capabilities in terms of magnetic shock resolution and three-dimensionality. This paper paves the way for the applications to a realistic, 3D long-term evolution of neutron stars interior and, possibly, of other astrophysical sources., Comment: 23 pages, 13 figures. In press

The multi-fluid modelling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamics waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfv\'en waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves. By means of numerical simulations and analytical approximations, we examine how the collisional interaction between ions and neutrals affects the nonlinear evolution. The friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat and consequently rises the temperature of the plasma. As an application, we investigate frictional heating in a plasma with physical conditions akin to those in a solar quiescent prominence., Comment: 26 pages, 15 figures, 3 movies. Accepted for publication in The Astrophysical Journal

The presence of neutral species in a plasma has been shown to greatly affect the properties of magnetohydrodynamic waves. For instance, the interaction between ions and neutrals through momentum transfer collisions causes the damping of Alfv\'en waves and alters their oscillation frequency and phase speed. When the collision frequencies are larger than the frequency of the waves, single-fluid magnetohydrodynamic approximations can accurately describe the effects of partial ionization, since there is a strong coupling between the various species. However, at higher frequencies, the single-fluid models are not applicable and more complex approaches are required. Here, we use a five-fluid model with three ionized and two neutral components, which takes into consideration Hall's current and Ohm's diffusion in addition to the friction due to collisions between different species. We apply our model to plasmas composed of hydrogen and helium, and allow the ionization degree to be arbitrary. By means of the analysis of the corresponding dispersion relation and numerical simulations, we study the properties of small-amplitude perturbations. We discuss the effect of momentum transfer collisions on the ion-cyclotron resonances and compare the importance of magnetic resistivity, ion-neutral and ion-ion collisions on the wave damping at various frequency ranges. Application to partially ionized plasmas of the solar atmosphere are performed., Comment: 24 pages, 15 figures. Revised version published in The Astrophysical Journal

Ideal MHD provides an accurate description of low-frequency Alfv\'en waves in fully ionized plasmas. However, higher frequency waves in many plasmas of the solar atmosphere cannot be correctly described by ideal MHD and a more accurate model is required. Here, we study the properties of small-amplitude incompressible perturbations in both the low and the high frequency ranges in plasmas composed of several ionized species. We use a multi-fluid approach and take into account the effects of collisions between ions and the inclusion of Hall's term in the induction equation. Through the analysis of the corresponding dispersion relations and numerical simulations we check that at high frequencies ions of different species are not as strongly coupled as in the low frequency limit. Hence, they cannot be treated as a single fluid. In addition, elastic collisions between the distinct ionized species are not negligible for high frequency waves since an appreciable damping is obtained. Furthermore, Coulomb collisions between ions remove the cyclotron resonances and the strict cut-off regions that are present when collisions are not taken into account. The implications of these results for the modelling of high-frequency waves in solar plasmas are discussed., Comment: 29 pages, 15 figures. Accepted for publication in The Astrophysical Journal

Context. Recent observations of solar prominences show the presence of turbulent flows that may be caused by Kelvin-Helmholtz instabilites (KHI). However, the observed flow velocities are below the classical threshold for the onset of KHI in fully ionized plasmas. Aims. We investigate the effect of partial ionization on the onset of KHI in dense and cool cylindrical magnetic flux tubes surrounded by a hotter and lighter environment. Methods. The linearized governing equations of a partially ionized two-fluid plasma are used to describe the behavior of small-amplitude perturbations superimposed on a magnetic tube with longitudinal mass flow. A normal mode analysis is performed to obtain the dispersion relation for linear incompressible waves. We focus on the appearance of unstable solutions and study the dependence of their growth rates on various physical parameters. An analytical approximation of the KHI linear growth rate for slow flows and strong ion-neutral coupling is obtained. An application to solar prominence threads is given. Results. The presence of a neutral component in a plasma may contribute to the onset of the KHI even for sub-Alfv\'enic longitudinal shear flows. Collisions between ions and neutrals reduce the growth rates of the unstable perturbations but cannot completely suppress the instability. Conclusions. Turbulent flows in solar prominences with sub-Alfv\'enic flow velocities may be interpreted as consequences of KHI in partially ionized plasmas., Comment: 8 pages, 4 figures. Accepted for publication in A&A