Mixed properties of magnetohydrodynamic waves undergoing resonant absorption in the cusp continuum

Goossens, Marcel; Chen, S. X.; Geeraerts, Michaël; Li, B.; Doorsselaere, Tom Van

doi:10.1051/0004-6361/202039780

Cited by 11 publications

(14 citation statements)

References 45 publications

(65 reference statements)

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“…Our continuum eigenfunctions match the resistive eigenfunctions of Fig 1 . in Goossens et al (2021) quite well, except for ξ r . In Fig.…”

Section: Kink Modesmentioning

confidence: 82%

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Quasimodes in the cusp continuum in nonuniform magnetic flux tubes

Geeraerts,

Vanmechelen,

Van Doorsselaere

et al. 2022

Preprint

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Context. The study of magnetohydrodynamic (MHD) waves is important both for understanding heating in the solar atmosphere (and in particular the corona) and for solar atmospheric seismology. The analytical investigation of wave mode properties in a cylinder is of particular interest in this domain, as many atmospheric structures can be modelled as such in a first approximation. Aims. The aim of this paper is to use linearized ideal MHD to study quasimodes (global modes that are damped through resonant absorption) with a frequency in the cusp continuum, in a straight cylinder with a circular base and an inhomogeneous layer at its boundary which separates two homogeneous plasma regions inside and outside. We are in particular interested in the damping of these modes, and shall hence try to determine their frequency as a function of background parameters. Methods. After linearizing the ideal MHD equations, we find solutions to the second-order differential equation for the perturbed total pressure in the inhomogeneous layer in the form of Frobenius series around the regular singular points that are the Alfvén and cusp resonant positions, as well as power series around regular points. By connecting these solutions appropriately through the inhomogeneous layer and with the solutions of the homogeneous regions inside and outside the cylinder, we derive a dispersion relation for the frequency of the eigenmodes of the system. Results. From the dispersion relation, it is also possible to find the frequency of quasimodes even though they are not eigenmodes.As an example, we find the frequency of the slow surface sausage quasimode as a function of the inhomogeneous layer's width, for values of the longitudinal wavenumber relevant for photospheric conditions. The results were found to match well the results found in another paper which studied the resistive slow surface sausage eigenmode. We also discuss the perturbation profiles of the quasimode and the eigenfunctions of continuum modes.

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“…Our continuum eigenfunctions match the resistive eigenfunctions of Fig 1 . in Goossens et al (2021) quite well, except for ξ r . In Fig.…”

Section: Kink Modesmentioning

confidence: 82%

“…The eigenfunctions P 1 , ξ r , ξ ϕ and ξ z of the continuum mode obtained from our series method in ideal MHD and corresponding to the resistive kink eigenmode shown by Goossens et al (2021) in their Fig. 1 and Fig.…”

Section: Kink Modesmentioning

confidence: 99%

Quasimodes in the cusp continuum in nonuniform magnetic flux tubes

Geeraerts,

Vanmechelen,

Van Doorsselaere

et al. 2022

Preprint

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“…it is compressible as a magnetoacoustic wave but has also non-zero parallel vorticity as an Alfvén waves. This is explained in, e.g., Goossens et al (2021). When the discontinous variation of density is replaced by a continuous variation in a transitional layer Goossens et al (2012) found that the fundamental radial mode of kink waves is resonantly damped but has both non-zero Eulerian perturbation of total pressure everywhere and nonzero parallel vorticity in the non-uniform transitional layer.…”

Section: Various Mhd Modes and Kink Waves In Structured Non-uniform F...mentioning

confidence: 97%

Chromospheric Heating by MHD Waves and Instabilities

Srivastava,

Ballester,

Cally

et al. 2021

Preprint

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The importance of the chromosphere in the mass and energy transport within the solar atmosphere is now widely recognised. This review discusses the physics of magnetohydrodynamic (MHD) waves and instabilities in large-scale chromospheric structures as well as in magnetic flux tubes. We highlight a number of key observational aspects that have helped our understanding of the role of the solar chromosphere in various dynamic processes and wave phenomena, and the heating scenario of the solar chromosphere is also discussed. The review focuses on the physics of waves and invokes the basics of plasma instabilities in the context of this important layer of the solar atmosphere. Potential implications, future trends and outstanding questions are also delineated.

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“…This would result in the possibility of resonance occuring between the main oscillation of the structure and local slow mode oscillations in the boundary layer, as studied theoretically by Yu et al (2017). The analytical derivations of Goossens et al (2021) show that, when slow waves are resonantly absorbed in the cusp continuum, both the azimuthal component of vorticity and the parallel component of the plasma displacement are large. The huge amount of vorticity could indicate the possibility of the KHI developing in those conditions.…”

Section: Modelmentioning

confidence: 98%

“…(30) therein). Assuming a sinusoidal transition profile with width l = 0.1R (where R is the radius of the pore) in the squared cusp and sound speeds, a ratio of external to internal magnetic field of B 0ze /B 0zi = 0.33, a cusp resonant position at r C = 0.955R (based on the numerical computations of Goossens et al (2021)), a value for the perturbed total pressure at the resonant position equal to its value on the interface for the corresponding surface mode in the absence of the transition layer, a real part of the frequency equal to the frequency of the corresponding surface mode in the absence of the transition layer, and a magnetic Reynolds number of 10 7 to have a lowerbound on resistivity and thus an upperbound on realistic values for the longitudinal velocity at the resonance, we found a value of M A = 0.36 around the cusp resonance point for a sausage mode with k z R = 2. This value of k z R is within the range of validity for the longitudinal wavenumber of the observed slow surface sausage mode in a photospheric pore by Grant et al (2015).…”

Section: Photospheric Poresmentioning

confidence: 99%

Stability of solar atmospheric structures harboring standing slow waves

Geeraerts

Doorsselaere

2021

A&A

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Context. In the context of the solar coronal heating problem, one possible explanation for the high coronal temperature is the release of energy by magnetohydrodynamic (MHD) waves. The energy transfer is believed to be possible, among others, by the development of the Kelvin-Helmholtz instability (KHI) in coronal loops. Aims. Our aim is to determine if standing slow waves in solar atmospheric structures such as coronal loops, and also prominence threads, sunspots, and pores, can trigger the KHI due to the oscillating shear flow at the structure’s boundary. Methods. We used linearized nonstationary MHD to work out an analytical model in a cartesian reference frame. The model describes a compressible plasma near a discontinuous interface separating two regions of homogeneous plasma, each harboring an oscillating velocity field with a constant amplitude which is parallel to the background magnetic field and aligned with the interface. The obtained analytical results were then used to determine the stability of said interface, both in coronal and photospheric conditions. Results. We find that the stability of the interface is determined by a Mathieu equation. In function of the parameters of this equation, the interface can either be stable or unstable. For coronal as well as photospheric conditions, we find that the interface is stable with respect to the KHI. Theoretically, it can, however, be unstable with respect to a parametric resonance instability, although it seems physically unlikely. We conclude that, in this simplified setup, a standing slow wave does not trigger the KHI without the involvement of additional physical processes.

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Mixed properties of magnetohydrodynamic waves undergoing resonant absorption in the cusp continuum

Cited by 11 publications

References 45 publications

Quasimodes in the cusp continuum in nonuniform magnetic flux tubes

Quasimodes in the cusp continuum in nonuniform magnetic flux tubes

Chromospheric Heating by MHD Waves and Instabilities

Stability of solar atmospheric structures harboring standing slow waves

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