Contribution of observed multi frequency spectrum of Alfvén waves to coronal heating

Context. Whilst there are observational indications that transverse magnetohydrodynamic (MHD) waves carry enough energy to maintain the thermal structure of the solar corona, it is not clear whether such energy can be efficiently and effectively converted into heating. Phase-mixing of Alfvén waves is considered a candidate mechanism, as it can develop transverse gradient where magnetic energy can be converted into thermal energy. However, phase-mixing is a process that crucially depends on the amplitude and period of the transverse oscillations, and only recently have we obtained a complete measurement of the power spectrum for transverse oscillations in the corona. Aims. We aim to investigate the heating generated by phase-mixing of transverse oscillations triggered by buffeting of a coronal loop that follows from the observed coronal power spectrum as well as the impact of these persistent oscillations on the structure of coronal loops. Methods. We considered a 3D MHD model of an active region coronal loop and we perturbed its footpoints with a 2D horizontal driver that represents a random buffeting motion of the loop footpoints. Our driver was composed of 1000 pulses superimposed to generate the observed power spectrum. Results. We find that the heating supply from the observed power spectrum in the solar corona through phase-mixing is not sufficient to maintain the million-degree active region solar corona. We also find that the development of Kelvin–Helmholtz instabilities could be a common phenomenon in coronal loops that could affect their apparent life time. Conclusions. This study concludes that is unlikely that phase-mixing of Alfvén waves resulting from an observed power spectrum of transverse coronal loop oscillations can heat the active region solar corona. However, transverse waves could play an important role in the development of small scale structures.

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Phase Mixing of Propagating Alfvén Waves

Symposium - International Astronomical Union ◽

10.1017/s0074180900075835 ◽

1985 ◽

Vol 107 ◽

pp. 365-369

Author(s):

L. Nocera ◽

B. Leroy ◽

E. R. Priest

Keyword(s):

Solar Corona ◽

Solar Atmosphere ◽

Outer Part ◽

Alfven Waves ◽

Mhd Waves ◽

Alfvén Waves ◽

Phase Mixing ◽

The Waves

Among MHD waves, Alfvén waves have been proved to be the best candidates to reach the solar corona and, eventually, to be responsible for the heating of this outer part of the solar atmosphere. The problem arises, however, about the mechanism able to transform the energy stored in the waves into heat.

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Investigating the damping rate of phase-mixed Alfvén waves

Astronomy and Astrophysics ◽

10.1051/0004-6361/201936658 ◽

2019 ◽

Vol 632 ◽

pp. A93 ◽

Cited By ~ 3

Author(s):

A. P. K. Prokopyszyn ◽

A. W. Hood

Keyword(s):

Wave Energy ◽

Alfven Waves ◽

Alfvén Waves ◽

Coronal Loops ◽

Phase Mixing ◽

Heating Mechanism ◽

At Resonance ◽

Damping Rate ◽

Field Lines ◽

The Waves

Context. This paper investigates the effectiveness of phase mixing as a coronal heating mechanism. A key quantity is the wave damping rate, γ, defined as the ratio of the heating rate to the wave energy. Aims. We investigate whether or not laminar phase-mixed Alfvén waves can have a large enough value of γ to heat the corona. We also investigate the degree to which the γ of standing Alfvén waves which have reached steady-state can be approximated with a relatively simple equation. Further foci of this study are the cause of the reduction of γ in response to leakage of waves out of a loop, the quantity of this reduction, and how increasing the number of excited harmonics affects γ. Methods. We calculated an upper bound for γ and compared this with the γ required to heat the corona. Analytic results were verified numerically. Results. We find that at observed frequencies γ is too small to heat the corona by approximately three orders of magnitude. Therefore, we believe that laminar phase mixing is not a viable stand-alone heating mechanism for coronal loops. To arrive at this conclusion, several assumptions were made. The assumptions are discussed in Sect. 2. A key assumption is that we model the waves as strictly laminar. We show that γ is largest at resonance. Equation (37) provides a good estimate for the damping rate (within approximately 10% accuracy) for resonant field lines. However, away from resonance, the equation provides a poor estimate, predicting γ to be orders of magnitude too large. We find that leakage acts to reduce γ but plays a negligible role if γ is of the order required to heat the corona. If the wave energy follows a power spectrum with slope −5/3 then γ grows logarithmically with the number of excited harmonics. If the number of excited harmonics is increased by much more than 100, then the heating is mainly caused by gradients that are parallel to the field rather than perpendicular to it. Therefore, in this case, the system is not heated mainly by phase mixing.

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Chromospheric evaporation and phase mixing of Alfvén waves in coronal loops

Astronomy and Astrophysics ◽

10.1051/0004-6361/201937266 ◽

2020 ◽

Vol 635 ◽

pp. A174

Author(s):

H. J. Van Damme ◽

I. De Moortel ◽

P. Pagano ◽

C. D. Johnston

Keyword(s):

Density Gradient ◽

High Frequency ◽

Coronal Loop ◽

Alfven Waves ◽

Alfvén Waves ◽

Mixing Process ◽

Phase Mixing ◽

Field Density ◽

Chromospheric Evaporation ◽

The Cross

Context. Phase mixing of Alfvén waves has been studied extensively as a possible coronal heating mechanism but without the full thermodynamic consequences considered self-consistently. It has been argued that in some cases, the thermodynamic feedback of the heating could substantially affect the transverse density gradient and even inhibit the phase mixing process. Aims. In this paper, for the first time, we use magnetohydrodynamic (MHD) simulations with the appropriate thermodynamical terms included to quantify the evaporation following heating by phase mixing of Alfvén waves in a coronal loop and the effect of this evaporation on the transverse density profile. Methods. The numerical simulations were performed using the Lagrangian Remap code Lare2D. We set up a 2D loop model consisting of a field-aligned thermodynamic equilibrium and a cross-field (background) heating profile. A continuous, sinusoidal, high-frequency Alfvén wave driver was implemented. As the Alfvén waves propagate along the field, they undergo phase mixing due to the cross-field density gradient in the coronal part of the loop. We investigated the presence of field-aligned flows, heating from the dissipation of the phase-mixed Alfvén waves, and the subsequent evaporation from the lower atmosphere. Results. We find that phase mixing of Alfvén waves leads to modest heating in the shell regions of the loop and evaporation of chromospheric material into the corona with upflows of the order of only 5–20 m s−1. Although the evaporation leads to a mass increase in the shell regions of the loop, the effect on the density gradient and, hence, on the phase mixing process, is insignificant. Conclusions. This paper self-consistently investigates the effect of chromospheric evaporation on the cross-field density gradient and the phase mixing process in a coronal loop. We found that the effects in our particular setup (small amplitude, high frequency waves) are too small to significantly change the density gradient.

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Overdense Threads in the Solar Corona Induced by Torsional Alfvén Waves

The Astrophysical Journal ◽

10.3847/2041-8213/ac39a3 ◽

2021 ◽

Vol 922 (2) ◽

pp. L26

Author(s):

Sergio Díaz-Suárez ◽

Roberto Soler

Keyword(s):

Magnetic Field ◽

High Resolution ◽

Solar Corona ◽

Alfven Waves ◽

Alfvén Waves ◽

Proof Of Concept ◽

Phase Mixing ◽

Synthetic Modeling ◽

The Magnetic Field ◽

High Cadence

Abstract High-resolution and high-cadence observations have shown that Alfvén waves are ubiquitous in the solar atmosphere. Theoretical works suggest their ability to transfer large energy fluxes from the photosphere to the corona and solar wind. In this proof-of-concept Letter we show that torsional Alfvén waves can induce the formation of filamentary plasma structures in the solar corona. We perform high-resolution 3D ideal MHD simulations in an initially uniform coronal plasma permeated by a line-tied twisted magnetic field. We find that torsional Alfvén waves develop Kelvin–Helmholtz instabilities as a result of the phase mixing process. The Kelvin–Helmholtz instability drives plasma compression that breaks the uniformity of density, creating elongated overdense threads aligned with the direction of the magnetic field. With synthetic modeling of SDO/AIA imaging we show that the overdense filaments could be seen in observations as fine strands that illuminate the underlying magnetic structure.

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Concerning the Dynamics of Energetic Protons in Coronal Magnetic Loops: Dispersion Effects of Alfven Waves

Symposium - International Astronomical Union ◽

10.1017/s007418090007618x ◽

1985 ◽

Vol 107 ◽

pp. 559-559

Author(s):

V. A. Mazur ◽

A. V. Stepanov

Keyword(s):

Magnetic Field ◽

Wave Dispersion ◽

Alfven Waves ◽

Alfven Wave ◽

Wave Number ◽

Alfvén Waves ◽

Coronal Loops ◽

Coronal Magnetic Loops ◽

The Magnetic Field ◽

Solar Coronal

It is shown that the existence of plasma density inhomogeneities (ducts) elongated along the magnetic field in coronal loops, and of Alfven wave dispersion, associated with the taking into account of gyrotropy U ≡ ω/ωi ≪ 1 (Leonovich et al., 1983), leads to the possibility of a quasi-longitudinal k⊥ < √U k‖ propagation (wave guiding) of Alfven waves. Here ω is the frequency of Alfven waves, ωi is the proton gyrofrequency, and k is the wave number. It is found that with the parameter ξ = ω2 R/ωi A > 1, where R is the inhomogeneity scale of a loop across the magnetic field, and A is the Alfven wave velocity, refraction of Alfven waves does not lead, as contrasted to Wentzel's inference (1976), to the waves going out of the regime of quasi-longitudinal propagation. As the result, the amplification of Alfven waves in solar coronal loops can be important. A study is made of the cyclotron instability of Alfven waves under solar coronal conditions.

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Relativistic Alfvén Waves on the jet of BL Lacertae

Proceedings of the International Astronomical Union ◽

10.1017/s1743921315002094 ◽

2014 ◽

Vol 10 (S313) ◽

pp. 147-152

Author(s):

Marshall H. Cohen ◽

David L. Meier

Keyword(s):

Magnetic Field ◽

Pitch Angle ◽

Lorentz Factor ◽

Alfven Waves ◽

Longitudinal Component ◽

Mhd Waves ◽

Alfvén Waves ◽

Bl Lacertae ◽

Pattern Speeds ◽

Helical Magnetic Field

AbstractThe jet of BL Lac displays transverse patterns that propagate downstream superluminally. We suggest that they are transverse Alfvén waves propagating on the longitudinal component of a helical magnetic field. The speed of the wave adds relativistically to the speed of the beam, and the apparent speed of the pattern is greater than the beam speed. Models for the jet and the MHD waves give values for the Lorentz factor of the beam of 3–4.4 and pitch angle of the helical magnetic field of 43° - 65°. These are consistent with other estimates, if the beam and pattern speeds are allowed to differ.

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