Force-free thin flux tubes: Basic equations and stability

Zhugzhda, Y. D.

doi:10.1063/1.871836

Cited by 73 publications

(69 citation statements)

References 20 publications

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“…A similar (while non-rotating) model was used in the study of Erdélyi & Fedun (2007). Our governing set of equations is in terms of the second order thin flux tube approximation of Zhugzhda (1996). In its derivation, the Taylor expansion of the physical variables with respect to the radial coordinate r was used…”

Section: Model and Equilibrium Conditionsmentioning

confidence: 99%

“…Note that in Eq. (2) relation containing the internal and external pressure terms is obtained by combining the radial component of the Euler equation with the pressure balance condition (Zhugzhda 1996). Here the external plasma is taken to be non-rotating and without the magnetic twist.…”

Section: Model and Equilibrium Conditionsmentioning

confidence: 99%

“…A useful tool for the analytical study of long-wavelength axisymmetric (torsional and longitudinal, and, perhaps, sausage) perturbations of magnetic flux tubes is the second order thin flux tube approximation derived by Zhugzhda (1996). This approximation generalises the classical thin flux tube theory of Roberts & Webb (1978), accounting for the flux tube rotation and twist, and also the variation of its cross-section.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this paper is to study long-wavelength (in comparison with the transverse size of the plasma cylinder) axisymmetric torsional modes in twisted and rotating plasma structures surrounded by vacuum, developing the work of Zhugzhda (1996) and Zhugzhda & Nakariakov (1999). The paper is organised as follows.…”

Section: Introductionmentioning

confidence: 99%

“…This approximation generalises the classical thin flux tube theory of Roberts & Webb (1978), accounting for the flux tube rotation and twist, and also the variation of its cross-section. In particular, it allows to consider the effects of the long-wavelength dispersion, connected with the presence of the characteristic spatial scale, the tube diameter, on the wave propagation (Zhugzhda 1996). It has been pointed out that in twisted magnetic flux tubes, the torsional modes become compressible.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Model and Equilibrium Conditionsmentioning

confidence: 99%

Section: Model and Equilibrium Conditionsmentioning

confidence: 99%