Damping of Slow Surface Kink Modes in Solar Photospheric Waveguides Modeled by One-dimensional Inhomogeneities

Abstract

Given the recent interest in magnetohydrodynamic (MHD) waves in pores and sunspot umbrae, we examine the damping of slow surface kink modes (SSKMs) by modeling solar photospheric waveguides with a cylindrical inhomogeneity comprising a uniform interior, a uniform exterior, and a continuous transition layer (TL) in between. Performing an eigen-mode analysis in linear, resistive, gravity-free MHD, our approach is idealized in that, among other things, our equilibrium is structured only in the radial direction. We can nonetheless address two damping mechanisms simultaneously, one being the Ohmic resistivity, and the other being the resonant absorption of SSKMs in the cusp and Alfvén continua. We find that the relative importance of the two mechanisms depends sensitively on the magnetic Reynolds number (R m ). Resonant absorption is the sole damping mechanism for realistically large values of R m , and the cusp resonance in general dominates the Alfvén one unless the axial wavenumbers are at the lower end of the observationally relevant range. We also find that the thin-boundary approximation holds only when the TL-width-to-radius ratios are much smaller than nominally expected. The Ohmic resistivity is far more important for realistically small R m . Even in this case, SSKMs are only marginally damped, with damping-time-to-period-ratios reaching ∼ 10 in the parameter range we examine.

Oblique Quasi-kink Modes in Solar Coronal Slabs Embedded in an Asymmetric Magnetic Environment: Resonant Damping, Phase and Group Diagrams

“…Now move on to the right column, where one sees that the approximate expressions perform even better than the iterative solutions in reproducing the resistive results, despite that the iterative approach is more self-consistent in principle. Overall, Figure 3 offers yet another piece of evidence that the TB expectations for coronal equilibria may hold well beyond their nominal range of applicability (e.g., Van Doorsselaere et al 2004;Soler et al 2013;Chen et al 2021). We conclude further that faith can be placed in our resistive approach, which will be consistently adopted hereafter.…”

“…Resonantly damped modes stand out in that their eigenfrequencies become R m -independent for sufficiently large R m . This behavior was first shown by Poedts & Kerner (1991) in fusion contexts, and later demonstrated for an extensive set of solar configurations (e.g., Van Doorsselaere et al 2004;Terradas et al 2006;Guo et al 2016;Chen et al 2018Chen et al , 2021. The same behavior is seen in Figure 2, where the ratios of the oscillation frequency to the damping rate (ω/|γ|) are plotted against the magnetic Reynolds number R m for a number of ρ i / ρ R as labeled, with the combination [ρ i /ρ L , l/d, k y d, k z d] fixed at [10, 0.5, 0.5, π/50].…”

“…Furthermore, destructive interference has gained new attention as a unifying process (see Cally 1991, and references therein for motivating ideas) that underlies the key notions of lateral leakage (e.g., Andries & Goossens 2007;Oliver et al 2015;Li et al 2022), resonant damping, and phase mixing (Ruderman & Roberts 2002;Soler & Terradas 2015; also references therein). Note that these notions themselves are not specific to a particular mode, an example being the relevance of resonant damping to both kink and sausage modes (e.g., Giagkiozis et al 2016;Chen et al 2021;Goossens et al 2021). Note also that new physics has also been gathered by considering those equilibria where the inhomogeneity can be rendered 1D by appropriate coordinate transformations, but the configuration itself may differ considerably from ER83.…”

Quasimodes in the cusp continuum in nonuniform magnetic flux tubes

“…The present study focuses on quasimodes with the oscillatory part of their frequency within the cusp continuum, and so photospheric conditions are of particular interest, because in a cylinder with a discontinuous boundary, the slow surface mode has its frequency within the interval that becomes the cusp continuum when an inhomogeneous layer is included (Edwin & Roberts 1983). The efficiency of damping due to resonant absorption of the slow surface mode in the cusp continuum compared to purely resistive damping was studied by Chen et al (2018) for the sausage mode and Chen et al (2021) for the kink mode, both in photospheric conditions. Their results suggest electrical resistivity is more efficient overall by about an order of magnitude, although damping due to resonant absorption of the slow surface kink mode in the cusp continuum dominates both damping due to resonant absorption in the Alfvén continuum and resistive damping at the lower end of the relevant values of resistivity.…”

Quasimodes in the cusp continuum in nonuniform magnetic flux tubes

“…As the current paper focuses on quasimodes with the oscillatory part of their frequency within the cusp continuum, photospheric conditions are of particular interest since then, in a cylinder with a discontinuous boundary, the slow surface mode has its frequency within the interval that becomes the cusp continuum when an inhomogeneous layer is included (Edwin & Roberts 1983). The efficiency of damping due to resonant absorption of the slow surface mode in the cusp continuum compared to purely resistive damping has been studied by Chen et al (2018) for the sausage mode and Chen et al (2021) for the kink mode, in photospheric conditions. Their results suggest electrical resistivity is more efficient overall by about an order of magnitude, although damping due to resonant absorption of the slow surface kink mode in the cusp continuum dominates both damping due to resonant absorption in the Alfvén continuum and resistive damping at the lower end of the relevant values of resistivity.…”