Resonant behaviour of MHD waves on magnetic flux tubes

Sakurai, Takashi; Goossens, Marcel; Hollweg, Joseph V.

doi:10.1007/bf00149888

Cited by 265 publications

(279 citation statements)

References 17 publications

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“…This is the same conservation law as that in ideal and dissipative MHD (e.g., Sakurai et al 1991;Goossens et al 1995;Tirry & Goossens 1996). The Lagrangian displacement perpendicular to the magnetic field lines, ξ i⊥ = ξ iϕ B z − ξ iz B ϕ /B, is related to C A as …”

Section: Behavior Of Perturbations Around the Resonance Positionmentioning

confidence: 86%

“…We follow the notation used in, e.g., Sakurai et al (1991); Goossens et al (1992Goossens et al ( , 1995. We combine Eqs.…”

Section: General Expressions For Resonant Alfvén Wavesmentioning

confidence: 99%

“…Figure 1 displays the real and imaginary parts of functions F (τ) and G(τ). Ion-neutral collisions generate a collisional layer around the location of the resonance, i.e., τ = 0, in a similar way as resistivity and/or viscosity generate a dissipative layer (see, e.g., Hollweg & Yang 1988;Poedts et al 1990a;Sakurai et al 1991). The thickness of the collisional layer, δ, is proportional to Λ I , namely…”

Section: Behavior Of Perturbations Around the Resonance Positionmentioning

confidence: 99%

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Resonant Alfvén waves in partially ionized plasmas of the solar atmosphere

Soler

Andries

Goossens

2012

A&A

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Context. Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. In magnetic waveguides resonant absorption due to plasma inhomogeneity naturally transfers wave energy from large-scale motions to small-scale motions. In the cooler parts of the solar atmosphere as, e.g., the chromosphere, effects due to partial ionization may be relevant for wave dynamics and heating. Aims. We study resonant Alfvén waves in partially ionized plasmas. Methods. We use the multifluid equations in the cold plasma approximation. We investigate propagating resonant MHD waves in partially ionized flux tubes. We use approximate analytical theory based on normal modes in the thin tube and thin boundary approximations along with numerical eigenvalue computations. Results. We find that the jumps of the wave perturbations across the resonant layer are the same as in fully ionized plasmas. The damping length due to resonant absorption is inversely proportional to the frequency, while that due to ion-neutral collisions is inversely proportional to the square of the frequency. For observed frequencies in the solar atmosphere, the amplitude of MHD kink waves is more efficiently damped by resonant absorption than by ion-neutral collisions. Conclusions. Most of the energy carried by chromospheric kink waves is converted into localized azimuthal Alfvén waves that can deposit energy in the coronal medium. The dissipation of wave energy in the chromosphere due to ion-neutral collisions is only effective for high-frequency waves. The chromosphere acts as a filter for kink waves with periods shorter than 10 s.

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Section: Behavior Of Perturbations Around the Resonance Positionmentioning

confidence: 86%

“…We follow the notation used in, e.g., Sakurai et al (1991); Goossens et al (1992Goossens et al ( , 1995. We combine Eqs.…”

Section: General Expressions For Resonant Alfvén Wavesmentioning

confidence: 99%

Section: Behavior Of Perturbations Around the Resonance Positionmentioning

confidence: 99%

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Resonant Alfvén waves in partially ionized plasmas of the solar atmosphere

Soler

Andries

Goossens

2012

A&A

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“…Combining long-wavelength and thin boundary (l/a ≪ 1) approximations, analytic expressions for the damping time over the period can be written as (e.g., Hollweg and Yang, 1988;Sakurai et al, 1991;Goossens et al, 1992Goossens et al, , 1995Ruderman and Roberts, 2002):…”

Section: Damping Of Prominence Thread Oscillations By Resonant Absorpmentioning

confidence: 99%

Physics of Solar Prominences: II—Magnetic Structure and Dynamics

et al. 2010

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Observations and models of solar prominences are reviewed. We focus on non-eruptive prominences, and describe recent progress in four areas of prominence research: (1) magnetic structure deduced from observations and models, (2) the dynamics of prominence plasmas (formation and flows), (3) Magneto-hydrodynamic (MHD) waves in prominences and (4) the formation and large-scale patterns of the filament channels in which prominences are located. Finally, several outstanding issues in prominence research are discussed, along with observations and models required to resolve them.

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“…Twisted magnetic tubes have also been studied in relation to the magnetohydrodynamic (MHD) wave resonant absorption (e.g. Sakurai et al 1991;Goossens et al , 2011Ballai & Erdélyi 2002). Wave propagation in twisted magnetic tubes has been investigated by Bogdan (1984), Bennett et al (1999), Erdélyi & Carter (2006), Carter & Erdélyi (2007, Erdélyi & Fedun (2007), and Terradas & Goossens (2012).…”

Section: Introductionmentioning

confidence: 99%

Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

Terradas

2015

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In this article we study standing kink waves in twisted magnetic tubes. We use the cold plasma and thin tube approximation. We assume that the plasma density is constant inside and outside the tube. We also assume that the magnetic twist is weak and take the ratio of the azimuthal and axial component of the magnetic field to be of the order of ratio of the tube radius and tube length. The azimuthal component of the magnetic field is proportional to the distance from the tube axis inside the tube, and inversely proportional to this distance outside the tube. Using the method of asymptotic expansions we derived the governing integral equation that determines the eigenfrequencies and eigenmodes of the tube kink oscillations. In the approximation of a very weak twist, we calculated analytically the corrections to the frequencies of the fundamental mode and first overtone of a straight magnetic tube related to the presence of twist. The analytical results are compared with the numerical results obtained using the full set of linear ideal magnetohydrodynamic equations. We also calculated the ratio of frequencies of the fist overtone and fundamental mode. We found that the magnetic twist enhances this ratio for moderate values of the density ratio, and reduces this ratio for large values of the density ratio. In general, the deviation of the frequency ratio from 2 caused by the magnetic twist is comparable to that found in simultaneous observations of the fundamental mode and first overtone of the coronal loop kink oscillations. Finally, we studied the eigenmode polarization. We found that, in a particular case of linear polarization, the polarization direction rotates along the tube.

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Resonant behaviour of MHD waves on magnetic flux tubes

Cited by 265 publications

References 17 publications

Resonant Alfvén waves in partially ionized plasmas of the solar atmosphere

Resonant Alfvén waves in partially ionized plasmas of the solar atmosphere

Physics of Solar Prominences: II—Magnetic Structure and Dynamics

Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

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