Zur Stabilität zylindersymmetrischer Plasmakonfigurationen mit Volumenströmen

Hain, K.; Lüst, Reimar

doi:10.1515/zna-1958-1103

Cited by 164 publications

(70 citation statements)

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“…In fact, Eq. (33) is similar to the Hain-Lüst equation (Hain & Lüst 1958) for twisted tubes without flow, but instead Eq. (33) is valid in a tube filled with uniform twist, low-beta plasma and a field aligned flow.…”

Section: Wave Equation Inside the Magnetic Tube For Uniform Twistmentioning

confidence: 92%

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Twisted magnetic tubes with field aligned flow

Díaz

Oliver

Ballester

et al. 2011

A&A

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Aims. We study the equilibrium and stability of twisted magnetic flux tubes with mass flows along the field lines. Then, we focus on the stability and oscillatory modes of magnetic tubes with uniform twist B 0 = B 0 (r/p e ϕ + e z ) in a zero-β plasma, surrounded by a uniform, purely longitudinal field. Methods. First we investigate the possible equilibriums, and then consider the linearised MHD equations and obtain a system of two first-order differential equations. These are solved numerically, while analytical approximations involving confluent hypergeometric functions are found in the thin tube limit. Finally, new appropriate boundary conditions are deduced and the outer solution considered (with the apparition of cut-off frequencies). We use this to derive a dispersion relation, from which the frequencies of the normal modes can be obtained. Results. Regarding the equilibrium, the only value of the flow that satisfies the equations for this magnetic field configuration is a super-Alfvénic one. Then, we consider the normal modes of this configuration. The thin-tube approximation proves accurate for typical values, and it is used to prove that the equilibrium is unstable, unless the pitch is large. The stability criteria for twisted tubes are significantly lowered. Conclusions. The twisted tube is subject to the kink instability unless the pitch is very high, since the Lundquist criterion is significantly lowered. This is caused by the requirement of having a magnetic Mach number greater than 1, so the magnetic pressure balances the magnetic tension and fluid inertia. This type of instability might be observed in some solar atmospheric structures, like surges.

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Section: Wave Equation Inside the Magnetic Tube For Uniform Twistmentioning

confidence: 92%

“…(12)−(15) are a generalisation for field-aligned flows of the well-known equations for twisted tubes, which are recovered if we set u 0 = 0 (Hain & Lüst 1958;Appert et al 1974). The equation for the perturbed density (Eq.…”

Section: Wave Equation Inside the Magnetic Tube For Uniform Twistmentioning

confidence: 96%

Twisted magnetic tubes with field aligned flow

Díaz

Oliver

Ballester

et al. 2011

A&A

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“…Hain and Lüst, 1958). At this point we can, once again, solve the two governing equations for the perturbed total pressure and the radial displacement.…”

Section: Governing Equationsmentioning

confidence: 99%

Linear MHD Wave Propagation in Time-Dependent Flux Tube

Williamson

Erdélyi

2015

Sol Phys

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In this article, we evaluate the time-dependent wave properties and the damping rate of propagating fast magneto-hydrodynamic (MHD) waves when energy leakage into a magnetised atmosphere is considered. By considering a cold plasma, initial investigations into the evolution of MHD wave damping through this energy leakage will take place. The time-dependent governing equations have been derived previously in Williamson and Erdé-lyi (2014a, Solar Phys. 289, 899 -909) and are now solved when the assumption of evanescent wave propagation in the outside of the waveguide is relaxed. The dispersion relation for leaky waves applicable to a straight magnetic field is determined in both an arbitrary tube and a thin-tube approximation. By analytically solving the dispersion relation in the thin-tube approximation, the explicit expressions for the temporal evolution of the dynamic frequency and wavenumber are determined. The damping rate is, then, obtained from the dispersion relation and is shown to decrease as the density ratio increases. By comparing the decrease in damping rate to the increase in damping for a stationary system, as shown, we aim to point out that energy leakage may not be as efficient a damping mechanism as previously thought.

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“…Most of the general results on pressure-driven instabilities were obtained in the fusion literature either from the use of the Energy Principle, or from the so-called Hain-Lüst equation (a reduced perturbation equation for the radial displacement [19] [17]). These approaches are quite powerful, but not familiar to the astrophysics community, and involve a lot of prerequisite.…”

Section: Dispersion Relation In the Large Azimuthal Field Limitmentioning

confidence: 99%

Pressure-Driven Instabilities in Astrophysical Jets

Longaretti

2008

Lecture Notes in Physics

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Zur Stabilität zylindersymmetrischer Plasmakonfigurationen mit Volumenströmen

Cited by 164 publications

References 0 publications

Twisted magnetic tubes with field aligned flow

Twisted magnetic tubes with field aligned flow

Linear MHD Wave Propagation in Time-Dependent Flux Tube

Pressure-Driven Instabilities in Astrophysical Jets

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