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Alfvén Waves in the Solar Atmosphere

Norbert Magyar

Centre for Mathematical Plasma-Astrophysics, Department of Mathematics, Katholieke Universiteit Leuven, Leuven, Belgium

ABSTRACT

Alfvén waves are propagating disturbances of magnetic tension and are one of the fundamental waves in plasma at large scales. The study of Alfvén waves in the solar corona has a long and continuing tradition, started way before Alfvén waves were found to be ever-present in the solar atmosphere. Their study is important for mainly two reasons. First, Alfvén waves might play a key role in the long-standing chromospheric and coronal heating problems, as well as the solar-wind acceleration problem, both for transmitting the energy in photospheric convection higher up in the atmosphere and more directly as a means of cascading and dissipating this energy through various mechanisms. Second, observed properties of Alfvén waves can be used to infer properties of the plasma through seismology. In this review, an overview of the basic theoretical understanding of magnetohydrodynamic (MHD) waves is presented, in an attempt to clarify the role that Alfvén waves play in the greater class of MHD waves encountered in the solar atmosphere. Furthermore, observational and theoretical findings on Alfvén waves in the solar atmosphere of the previous decade are reviewed, followed by a short summary of these results and still open questions.

2.1. INTRODUCTION

First derived by Alfvén (1942) as electromagnetic-hydrodynamic waves, confirmed experimentally in liquid mercury by Lundquist (1949), and needing the approval of such authorities in physics as Fermi to be taken seriously after years of disapproval by other world-renowned scientists (Dessler, 1970; Russell, 2018), the waves now bearing Hannes Alfvén's name were from their conception central to a better understanding of solar atmospheric processes. Alfvén himself first realized that such waves should in principle exist, through deep physical intuition, while thinking about the nature of sunspots (Alfvén & Lindblad, 1945), known to be strongly magnetized since Hale (1908). Other phenomena in which Alfvén waves might play a substantial role have been proposed shortly after, among the firsts being the then recently discovered coronal heating (Alfvén & Lindblad, 1947) and the existence of cosmic rays (Fermi, 1949). This interdisciplinary monograph, dedicated to reviewing recent advances in understanding Alfvén waves in the wide field of space physics, of which this chapter is part of, stands as proof of the everlasting impact that H. Alfvén made to the field, even 80 years on.

Although in his pioneering work Alfvén only derived a wave driven purely by the magnetic tension force, it had become increasingly crystallized in the 1950s that electroconducting fluids or plasmas whose dynamics can be described through the magnetohydrodynamic (MHD) equations admit various wave modes. This is caused by the interplay between various restoring forces, mostly magnetic and gas pressure forces. The different wave modes are clearly distinguishable under ideal and homogeneous conditions, leading to their usual identification as Alfvén, fast, and slow waves. Without entering too much into detail here, and instead allowing for an extended discussion on this subject in a dedicated section of this chapter, it is already important to point out the usually blurred lines between these adjectives, the properties assigned to these adjectives based on linear analysis under homogeneous conditions, and the actual wave properties, especially when accounting for inhomogeneities or other nonideal conditions present. It is important to stress that waves identified as "Alfvén" waves, either in laboratory experiments, observations, or numerical studies, would seldom share only the properties of a pure linear Alfvén wave encountered in an ideal and homogeneous plasma. Therefore, while going along with the usual broad interpretation of what an Alfvén wave is when selecting the studies to be included in this review, let us always keep in mind that pure Alfvén waves are a very special case of a plasma wave, probably seldom encountered in their pure form in nature, as will be argued later on.

Alfvén waves play multiple important roles in our quest for a better understanding of the physics of the solar atmosphere. First, they potentially act as means of transmitting the energy available in the convective buffeting of the photosphere, thought as the ultimate energy source for heating the corona and accelerating the solar wind, along magnetic field lines reaching into the solar atmosphere. Once inside the chromosphere or corona, Alfvén wave energy could be dissipated by various proposed mechanisms. Dissipation in the almost ideal conditions of the solar plasma presupposes that small enough scales are generated (large spatial gradients in Alfvén wave perturbation field), at which thermalization is supposedly taken over by kinetic processes. These small-scale generation mechanisms range from linear processes such as phase mixing and resonant absorption to nonlinear shock dissipation and generation of Alfvén wave turbulence. Second, Alfvén waves could be the causing factor of various phenomena observed in the solar atmosphere, such as in increasing height from the photosphere, photospheric vortices, umbral and penumbral shocks, spicules, coronal jets, switchbacks, and so on, some of which phenomena will be discussed in detail later on. Last but not least, through the seismology of the observed waves, where the correct identification of the waves as outlined earlier is particularly important, physical properties of the local plasma through which the Alfvén waves are propagating could be inferred by comparing measured oscillation properties with the ones derived from MHD wave theory. These oscillation properties often depend on various properties of the plasma, such as magnetic field intensity, mass density, gravitational scale height, polytropic index, to name a few.

This chapter is dedicated to reviewing advances in the research and application of Alfvén waves in the solar atmosphere published in the last decade. According to the Smithsonian Astrophysical Observatory/National Aeronautics and Space Administration (SAO/NASA) Astrophysics Data System, there have been roughly 500 peer-reviewed publications since 2012, uniformly distributed through the years, on the subject. The search criteria were based on words found in the abstract, specifically the combination of "Alfvén," "wave," "solar," and "photosphere" or "chromosphere" or "corona." The study of Alfvén waves in the extended solar atmosphere and inner heliosphere, such as the outer corona and solar wind, has a separate chapter dedicated to it within this monograph. It is also important to note that this chapter only considers plasma for which the fluid approximation is valid; that is, for which MHD is a good approximation, and does not touch upon kinetic dynamics, such as kinetic Alfvén waves (e.g., Chen et al., 2021). At the spatial and temporal scales that waves are observed in the solar atmosphere, the fluid approximation holds to a very good degree. Besides giving my perspective on the current state of research on Alfvén waves in the solar atmosphere and guiding the reader through a summary of these advances, the task is to present the most important findings in a hopefully comprehensive manner in the following text.

Many helpful reviews of Alfvén waves in the solar atmosphere have been published in the preceding years. These discuss in detail some of the milestone observational, numerical, and theoretical findings of the previous decades, such as the theoretical breakthroughs of phase mixing, mode conversion, and resonant absorption (Goossens et al., 2011; Roberts, 2000), Alfvén wave turbulence (Schekochihin, 2022), the observational firsts of directly imaged large-amplitude transverse waves in coronal loops (Aschwanden et al., 1999; Nakariakov et al., 1999), the ubiquitous propagating waves first observed using the Coronal Multi-Channel Polarimeter (CoMP, Mathioudakis et al., 2012; Tomczyk et al., 2007), torsional Alfvén waves in the chromosphere (Jess et al., 2009, 2012), and advances in the field of coronal seismology (De Moortel & Nakariakov, 2012), among other related areas, such as decayless kink waves and the effects of thermal misbalance (Nakariakov et al., 2016; Nakariakov & Kolotkov, 2020). Additionally, the dynamics of Alfvén waves have been a part of several textbooks on MHD and plasma dynamics (Aschwanden, 2005; Goedbloed & Poedts, 2004; Priest, 2014; Somov, 2006), with even a dedicated book on the subject published decades ago but still remaining relevant (Hasegawa & Uberoi, 1982).

The first section of this review deals with the often overlooked but particularly important aspects of nomenclature and semantics of MHD waves, a problem already mentioned above, with some theoretical background to support the narrative. The second section is dedicated to recent observational identifications of Alfvén waves in the solar atmosphere, categorized according to the different atmospheric layers. In the third section, recent theoretical and...