Topological Formation of Small Scales in Magnetohydrodynamics: A Fast Dissipation Mechanism

Petkaki, P.; Malara, F.; Veltri, P.

doi:10.1086/305707

Cited by 29 publications

(40 citation statements)

References 22 publications

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“…2D and 3D structuring can dramatically affect properties of MHD waves. In particular, as it was shown in the incompressible regime by Similon & Sudan (1989) and confirmed in numerical experiments performed by Petkaki et al (1998) and Malara et al (2000), the structuring dramatically increases the efficiency of wave dissipation. However, in those studies, the compressible effects were not taken into account.…”

Section: Introductionsupporting

confidence: 59%

A Three Dimensional Magnetohydrodynamic Pulse in a Transversely Inhomogeneous Medium

Tsiklauri

Nakariakov

2003

AIP Conference Proceedings

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Interaction of impulsively generated MHD waves with a one-dimensional plasma inhomogeneity, transverse to the magnetic field, is considered in the three-dimensional regime. Because of the transverse inhomogeneity, MHD fluctuations, even if they do not include initially any density perturbation, evolve toward states where the compressible components tend to become predominant. The propagating MHD pulse asymptotically reaches a quasi-steady state with the final levels of density perturbation weakly depending on the degree of non-planeness of the pulse in the homogeneous transverse direction and somewhat stronger depending on plasma β. Our study demonstrates the necessity of incorporation of compressible and 3D effects in theory of Alfvén wave phase mixing. However, as far as the dynamics of weakly non-plane Alfvén waves is concerned it can still be qualitatively understood in terms of the previous 2.5D models.

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Section: Introductionsupporting

confidence: 59%

A Three Dimensional Magnetohydrodynamic Pulse in a Transversely Inhomogeneous Medium

Tsiklauri

Nakariakov

2003

AIP Conference Proceedings

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“…Another assumption is that the wavelength λ of the perturbation stays much smaller than the scale length L 0 of the equilibrium structure (λ L 0 ). During the evolution, the wavelength λ tends to decrease in time (Petkaki et al 1998). Thus, the above condition is always fulfilled, provided that it is satisfied at the initial time.…”

Section: Alfvén Waves In An Inhomogeneous Magnetic Fieldmentioning

confidence: 90%

“…In this paper we have characterized the property of small-scale generation in small-amplitude Alfvénic perturbations propagating in an inhomogeneous equilibrium magnetic structure, within the framework of a WKB approximation (Petkaki et al 1998;Malara et al 2003). The growth of the wavevector k in the perturbation is intimately related to the property that nearby field lines of the c (0) A field move apart.…”

Section: Discussionmentioning

confidence: 99%

“…Thus, t d remains relatively small even for high values of S , as in the coronal plasma. This mechanism has been investigated by Petkaki et al (1998) and by Malara et al (2000), who built up a model describing propagation and dissipation of Alfvénic wave packets in 3D magnetic structures, both in the incompressible and in the compressible low-β case (Malara et al 2003). These authors show that the scaling law (1) is recovered in regions of chaotic magnetic lines, while a slower dissipation related to phase-mixing takes place in regions where the topology of magnetic lines is quasi-2D.…”

Section: Introductionmentioning

confidence: 99%

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Alfvén wave dissipation and topological properties of 3D coronal force-free magnetic fields

Malara¹,

Veltri²,

Franceschis³

2007

A&A

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We study the propagation and dissipation of Alfvénic perturbation in a 3D equilibrium structure within a WKB model. We assume small amplitude and small wavelength of the perturbation. The generation of small scales in the perturbation is related to the property that nearby magnetic lines move apart from each other locally. This property is quantified by means of the Kolmogorov entropy H of magnetic lines. We numerically calculate the distribution of H for a 3D complex force-free equilibrium, which models the magnetic field above a quiet-Sun region, both for nonvanishing current and for a potential field. It is found that H decreases slightly with the altitude due to the decreasing complexity of the field, but it is relatively uniform except for the presence of sharp peaks, where H reaches much higher values than the average. These locations are those where Alfvén waves are preferentially dissipated. By analyzing the magnetic topology at these locations, we find that they correspond to separator lines which are intersections of separatrix surfaces. Then, in a high-Reynolds number plasma, such as in the solar corona, heating due to Alfvén wave dissipation takes place mainly at magnetic separatrices.

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“…More recent studies have shown that the creation of a dissipative scale can be made exponentially fast (dk/dt ∝ const.·k), with the associated time scale being proportional to ln S S 1/3 S (Similon & Sudan 1989;Petkaki et al 1998;Malara et al 2007). The latter improved efficiency of the dissipation results by essentially considering a more complex magnetic geometry, with the property of local exponential separation or divergence of neighboring magnetic field lines.…”

Section: Introductionmentioning

confidence: 99%

Mixing of shear Alfven wave packets

Bian¹,

Tsiklauri

2008

A&A

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Aims. We consider the propagation of shear Alfven wave packets in inhomogeneous magnetic fields which is at the origin of their distortion regardless of any non-linear coupling. It is shown that this can be regarded as a mixing process and hence, standard phase mixing corresponds to the effect of an Alfvenic shear flow, while enhanced dissipation at a magnetic X-point corresponds to mixing by an Alfvenic strain flow. Methods. The evolution of the wave field is supposed to result from the dynamics of a superposition of wave packets, and a kinetic equation for the wave energy is obtained following this eikonal (WKB) description. Results. Since shear Alfven wave packets experience continuous shearing/straining, while transported by an inhomogeneous Alfvenic flow V A , their mixing process in physical space is also a cascade of wave energy in k-space. The wave energy spectrum resulting from this linear mechanism of energy transfer is determined for the special case of waves propagating along chaotic magnetic field lines, the analog of a chaotic mixing process. The latter follows a k −1 power law in the energy conserving range in k space.

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Topological Formation of Small Scales in Magnetohydrodynamics: A Fast Dissipation Mechanism

Cited by 29 publications

References 22 publications

A Three Dimensional Magnetohydrodynamic Pulse in a Transversely Inhomogeneous Medium

A Three Dimensional Magnetohydrodynamic Pulse in a Transversely Inhomogeneous Medium

Alfvén wave dissipation and topological properties of 3D coronal force-free magnetic fields

Mixing of shear Alfven wave packets

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