Dissipative MHD solutions for resonant Alfvén waves in two‐dimensional poloidal magnetoplasmas

Tirry, W. J.; Goossens, Marcel

doi:10.1029/95ja02691

Cited by 13 publications

(10 citation statements)

References 23 publications

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“…Here the Alfvén continuum is not affected by gravity, but the slow continuum is affected and it might be better referred to as the slow-gravity continuum. The singular solutions of the continuum Alfvén waves for 2D magnetostatic equilibrium models with a purely poloidal magnetic field were discussed in detail by Thompson & Wright (1993), Wright & Thompson (1994) and Tirry & Goossens (1995).…”

Section: The Continuous Spectrummentioning

confidence: 99%

Apparent Cross-Field Superslow Propagation of Magnetohydrodynamic Waves in Solar Plasmas

Kaneko

Goossens

Soler

et al. 2015

ApJ

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In this paper we show that the phase mixing of continuum Alfvén waves and/or continuum slow waves in magnetic structures of the solar atmosphere as, e.g., coronal arcades, can create the illusion of wave propagation across the magnetic field. This phenomenon could be erroneously interpreted as fast magnetosonic waves. The cross-field propagation due to phase mixing of continuum waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfvén and slow spectra in 2D Cartesian equilibrium models with a purely poloidal magnetic field. We show that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfvén waves and continuum slow waves that naturally live on those structures and phase mix as time evolves. The apparent cross-field phase velocity is related to the spatial variation of the local Alfvén/slow frequency across the magnetic surfaces and is slower than the Alfvén/sound velocities for typical coronal conditions. Understanding the nature of the apparent cross-field propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations.

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Section: The Continuous Spectrummentioning

confidence: 99%

Apparent Cross-Field Superslow Propagation of Magnetohydrodynamic Waves in Solar Plasmas

Kaneko

Goossens

Soler

et al. 2015

ApJ

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“…In onedimensional equilibrium models, the energy flux into the resonance is proportional to the magnetic pressure perturbation squared (Andries et al, 2000;Andries & Goossens, 2001), a result that was used by Arregui et al (2007b) to analyse the influence of the internal structuring of coronal loops on the damping by comparing the efficiency of the process at internal and external layers. In two-dimensional equilibrium states, the energy flux absorbed at a particular field line is proportional to the overlap integral between P T (r A , z), the profile of P T along the tube at the resonant position, and the resonant Alfvén eigenfunctions (Thompson & Wright, 1993;Tirry & Goossens, 1995). This is why the longitudinal profiles of b z and v ϕ , and their modification due to changes in the longitudinal density distribution are so relevant in determining kink mode damping times.…”

Section: Energy Analysismentioning

confidence: 99%

Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads

Arregui

Soler

Ballester

et al. 2011

A&A

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Aims. We analyse the oscillatory properties of resonantly damped transverse kink oscillations in two-dimensional prominence threads. Methods. The fine structures are modelled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary non-uniformly in both the transverse and the longitudinal directions. We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving the linear resistive magnetohydrodynamic (MHD) equations. Results. The relevant parameters are the length of the thread and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extent the damping ratios. The analysis of the spatial distribution of perturbations and of the energy flux into the resonances allows us to explain the obtained damping times. Conclusions. Implications for prominence seismology, the physics of resonantly damped kink modes in two-dimensional magnetic flux tubes, and the heating of prominence plasmas are discussed.

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“…Even under these most favorable of circumstances, the resultant PDEs are generally not solvable in terms of ODEs through the method of separation of variables. The critical layer phenomenon may also persist in these more general circumstances, but it generally requires line-tying of the magnetic Ðeld at a rigid boundary (e.g., Poedts & Goossens 1987, 1988Tirry & Goossens 1995).…”

Section: Exemplary Model Calculationsmentioning

confidence: 99%

Waves in the Magnetized Solar Atmosphere. I. Basic Processes and Internetwork Oscillations

Rosenthal

Bogdan

Carlsson

et al. 2002

ApJ

159

181

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We have modeled numerically the propagation of waves through magnetic structures in a stratiÐed atmosphere. We Ðrst simulate the propagation of waves through a number of simple, exemplary Ðeld geometries in order to obtain a better insight into the e †ect of di †ering Ðeld structures on the wave speeds, amplitudes, polarizations, direction of propagation, etc., with a view to understanding the wide variety of wavelike and oscillatory processes observed in the solar atmosphere. As a particular example, we then apply the method to oscillations in the chromospheric network and internetwork. We Ðnd that in regions where the Ðeld is signiÐcantly inclined to the vertical, refraction by the rapidly increasing phase speed of the fast modes results in total internal reÑection of the waves at a surface whose altitude is highly variable. We conjecture a relationship between this phenomenon and the observed spatiotemporal intermittancy of the oscillations. By contrast, in regions where the Ðeld is close to vertical, the waves continue to propagate upward, channeled along the Ðeld lines but otherwise largely una †ected by the Ðeld.

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Dissipative MHD solutions for resonant Alfvén waves in two‐dimensional poloidal magnetoplasmas

Cited by 13 publications

References 23 publications

Apparent Cross-Field Superslow Propagation of Magnetohydrodynamic Waves in Solar Plasmas

Apparent Cross-Field Superslow Propagation of Magnetohydrodynamic Waves in Solar Plasmas

Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads

Waves in the Magnetized Solar Atmosphere. I. Basic Processes and Internetwork Oscillations

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