The Nonlinear Alfvn Wave Model for Solar Coronal Heating and Nanoflares

Moriyasu, S.; Kudoh, Takahiro; Yokoyama, T.; Shibata, Kazunari

doi:10.1086/381779

Cited by 104 publications

(105 citation statements)

References 29 publications

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“…In particular, the effects of heating, radiation, and conduction were first studied by Mariska & Hollweg (1985), and the effects of a body force were originally discussed by Sterling & Hollweg (1988). The model has been applied to both linear and nonlinear problems in various solar and stellar contexts (Sterling & Hollweg 1984;Mariska & Hollweg 1985;Kudoh & Shibata 1997;Moriyasu et al 2004;Fujita et al 2007;Musielak et al 2007;Antolin & Shibata 2008).…”

Section: Model and Governing Equationsmentioning

confidence: 99%

Alfvén instability of steady state flux tubes

Taroyan

2015

A&A

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Context. MHD instabilities play an important role in the dynamics and energetics of the solar atmosphere.Aims. An open vertical magnetic flux tube is permeated by an upflow in a stratified atmosphere with variable temperature. The stability of the tube is investigated with respect to small-amplitude torsional perturbations generated at the footpoint by random convective motions. Methods. A steady state equilibrium incorporating the effects of a vertical body force, heating, and losses is derived analytically. The governing equations for torsional motions are integrated with a fourth-order Runge-Kutta method and matched with the analytical solutions in the upper regions to obtain a numerical dispersion relation. The dependence of the eigenmode frequencies on different parameters is analysed. Unstable modes are found for a range of Alfvén and flow speeds in the photosphere, as well as expansion factors of the flux tubes. Both supersonic and subsonic flows are considered. Results. It is shown that torsional perturbations are exponentially amplified in time if a section of the tube exists where the upflowing plasma decelerates and the tube expands. The flow speeds required for the instability are sub-Alfvénic. Conclusions. The instability may be important for understanding the abundance of Alfvén waves seen in recent observations and the associated heating in magnetic regions of the solar atmosphere.

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Section: Model and Governing Equationsmentioning

confidence: 99%

Alfvén instability of steady state flux tubes

Taroyan

2015

A&A

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“…These phase relations should be taken into account in the estimation of observational manifestation of torsional waves in twisted and possibly rotating plasma structures, e.g. in the gyrosynchrotron emission by the fashion similar to applied by Tapping (1983) to torsional modes and Nakariakov & Melnikov (2006) to longitudinal modes of straight non-rotating flux tubes. Also, these relations should be used in forward modelling of torsional waves observed with spectrometers.…”

Section: Compressibility Of the Torsional Modementioning

confidence: 99%

“…Ruderman 1999;Copil et al 2008). In particular, Moriyasu et al (2004) and Antolin et al (2008) paid special attention to nonlinear effects and shock formation. It was demonstrated numerically that the observed spiky intensity profiles due to impulsive energy releases could be obtained from nonlinear torsional waves.…”

Section: Introductionmentioning

confidence: 99%

Long-wavelength torsional modes of solar coronal plasma structures

Farahani¹,

Nakariakov²,

Doorsselaere³

2010

A&A

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Aims. We consider the effects of the magnetic twist and plasma rotation on the propagation of torsional m = 0 perturbations of cylindrical plasma structures (straight magnetic flux tubes) in the case when the wavelength is much longer than the cylinder diameter. Methods. The second order thin flux tube approximation is used to derive dispersion relations and phase relations in linear longwavelength axisymmetric magnetohydrodynamic waves in uniformly twisted and rotating plasma structures. Results. Asymptotic dispersion relations linking phase speeds with the plasma parameters are derived. When twist and rotation are both present, the phase speed of torsional waves depends upon the direction of the wave propagation, and also the waves are compressible. The phase relations show that in a torsional wave the density and azimuthal magnetic field perturbations are in phase with the axial magnetic field perturbations and anti-phase with tube cross-section perturbations. In a zero-β non-rotating plasma cylinder confined by the equilibrium twist, the density perturbation is found to be about 66 percent of the amplitude of the twist perturbation in torsional waves.

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“…Diffusive acceleration of particles by MHD waves was contrasted and compared to direct E-fields and shocks formed by large scale current sheets in the break-up model. Several recent articles showed that the non linear evolution of the MHD waves form small scale structures, which act also as shocks or UCS [23,22,24].…”

Section: The Loop Modelmentioning

confidence: 99%

Magnetic Complexity, Fragmentation, Particle Acceleration and Radio Emission from the Sun

Vlahos

2007

The High Energy Solar Corona: Waves, Eruptions, Particles

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Abstract. The most popular flare model used to explain the energy release, particle acceleration and radio emission is based on the following assumptions: (1) The formation of a current sheet above a magnetic loop, (2) The stochastic acceleration of particles in the current sheet at the helmet of the loop, (3) the transport and trapping of particles inside the flaring loop. We review the observational consequences of the above model and try to generalize by putting forward a new suggestion, namely assuming that a complex active region driven by the photospheric motions forms naturally a large number of stochastic current sheets that accelerate particles, which in turn can be trapped or move along complex field line structures. The emphasis will be placed on the efficiency and the observational tests of the different models proposed for a flare

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The Nonlinear Alfvn Wave Model for Solar Coronal Heating and Nanoflares

Cited by 104 publications

References 29 publications

Alfvén instability of steady state flux tubes

Alfvén instability of steady state flux tubes

Long-wavelength torsional modes of solar coronal plasma structures

Magnetic Complexity, Fragmentation, Particle Acceleration and Radio Emission from the Sun

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