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ace and Fundamental Modes of Oscillations in Thin Coronal Loops Yu. D. Zhugzhda* Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radiowave Propagation, Russian Academy of Sciences, Kaluzhskoe sh. 4, Troitsk, Moscow, 108840 Russia Received January 26, 2020; revised March 21, 2020; accepted March 24, 2020

Abstract—The oscillations in thin magnetic flux tubes in the solar corona are considered. The surface and fundamental modes of oscillations are shown to be the main modes of fast and slow oscillations. The slow surface and fundamental modes are waveguide ones. The fast surface mode is a leaky one, while the fast fundamental mode is a waveguide one. The fundamental modes considered by us exist only in magnetic flux tubes affected by the environment. Our definition of the fundamental modes does not coincide with the universally accepted one. Present-day observations of oscillations in coronal loops can hardly record the slow sausage modes, the first of which is considered as the fundamental one. The fast sausage modes should not be observed at a poor spatial resolution either. The first fast sausage mode, which is commonly considered as the fundamental one, is an exception. However, this mode is absent in thin magnetic flux tubes. DOI: 10.1134/S1063773720040076 Keywords: magnetic flux tubes, coronal loops, modes of oscillations, coronal seismology.

INTRODUCTION The theory of waves in thin magnetic flux tubes is particularly topical in connection with the seismology of the solar corona. There are a number of extensive reviews and books devoted to both the theory of waves in magnetic flux tubes and its applications to coronal seismology (see, e.g., Stepanov and Zaitsev 2019; Nakariakov et al. 2016; Stepanov et al. 2012). The pioneering works that initiated the development of this branch of solar physics should be mentioned (Meerson et al. 1978; Edwin and Roberts 1983; Spruit 1982). This paper is aimed at drawing attention to some details of the theory of waves in thin magnetic flux tubes to which, from our point of view, no due attention has been given so far. We have in mind the surface modes of oscillations and the fundamental modes of oscillations that, in our opinion, have been misdefined. An important fact to which no attention has been drawn is that not all of the sausage modes can be detected due to the insufficient spatial resolution of present-day observations. We will restrict our consideration to thin flux tubes, because this allows our analysis to be simplified. The thin-flux-tube approximation suggests that the longitudinal wavelength is great compared to the magnetic flux tube diameter. This is usually written as kz R0  1, where kz is the longitudinal wave vector *

and R0 is the flux tube radius. In some sense we will work within the approximation of thin flux tubes of finite size and not in the approximation of an infinitely thin flux tube proposed by Roberts and Webb (1978), which does not allow all of the possible modes of oscillations to be considered. This does not mean that the effects considered take place o