Sausage oscillations of coronal loops

Pascoe, D. J.; Nakariakov, V. M.; Arber, T. D.

doi:10.1051/0004-6361:20065986

Cited by 75 publications

(67 citation statements)

References 15 publications

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“…A further increase in L leads the sausage oscillations into the leaky regime, where P turns out to increase with L as well and shows saturation in the thin-tube limit (L/a 1). This behavior of sausage mode periods was analytically shown by Zaitsev & Stepanov (1975);Vasheghani Farahani et al (2014), and numerically demonstrated both via analysing the relevant dispersion diagrams (Kopylova et al 2007) and by solving the problem as an initial-boundary value one (Pascoe et al 2007a;Inglis et al 2009;Nakariakov et al 2012).…”

Section: Introductionsupporting

confidence: 52%

Standing sausage modes in coronal loops with plasma flow

Chen

Xia

et al. 2014

A&A

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Context. Magnetohydrodynamic waves are important for diagnosing the physical parameters of coronal plasmas. Field-aligned flows appear frequently in coronal loops. Aims. We examine the effects of transverse density and plasma flow structuring on standing sausage modes trapped in coronal loops, and examine their observational implications in the context of coronal seismology. Methods. We model coronal loops as straight cold cylinders with plasma flow embedded in a static corona. An eigen-value problem governing propagating sausage waves is formulated and its solutions are employed to construct standing modes. Two transverse profiles are distinguished, and are called profiles E and N. A parameter study is performed on the dependence of the maximum period P max and cutoff length-to-radius ratio (L/a) cutoff in the trapped regime on the density parameters (ρ 0 /ρ ∞ and profile steepness p) and the flow parameters (its magnitude U 0 and profile steepness u). Results. For either profile, introducing a flow reduces P max obtainable in the trapped regime relative to the static case. The value of P max is sensitive to p for profile N, but is insensitive to p for profile E. By far the most important effect a flow introduces is to reduce the capability for loops to trap standing sausage modes: (L/a) cutoff may be substantially reduced in the case with flow relative to the static one. In addition, (L/a) cutoff is smaller for a stronger flow, and for a steeper flow profile when the flow magnitude is fixed. Conclusions. If the density distribution can be described by profile N, then measuring the sausage mode period can help deduce the density profile steepness. However, this practice is not feasible if profile E more accurately describes the density distribution. Furthermore, even field-aligned flows with magnitudes substantially smaller than the ambient Alfvén speed can make coronal loops considerably less likely to support trapped standing sausage modes.

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Section: Introductionsupporting

confidence: 52%

Standing sausage modes in coronal loops with plasma flow

Chen

Xia

et al. 2014

A&A

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“…However, the excitation we choose is always sufficiently close to the eigenmode that the amplitude of these harmonics is very small with respect to the fundamental oscillation, and they are quickly damped. Thus, by running the simulation for sufficient time, the dominance of the desired mode is ensured (Pascoe et al 2007b).…”

Section: Numerical Modelmentioning

confidence: 99%

“…It is unclear whether or not a significant value of β 0 would have a strong effect on the period of the mode. As a first step therefore, we reproduce the result of Pascoe et al (2007b) showing the dependence of the period on the loop length L, but this time for a variety of β 0 values. This is achieved by simulating sausage oscillations in a loop with an Epstein density profile and a density contrast ratio of 10.…”

Section: The Period Of the Sausage Modementioning

confidence: 99%

“…However, the high temperatures and densities of flaring loops also lead to the increase in the plasma-β inside the loops (Shibasaki 2001). This can cause a significant deviation of the resonant periods and cut-offs from the results obtained in the zero-β approximation studied in Cooper et al (2003); Pascoe et al (2007b).…”

Section: Introductionmentioning

confidence: 95%

“…Long wavelength (in comparison with the minor radius of the oscillating loop) sausage modes are subject to a cut-off, in contrast with all other (kink and various fluting or ballooning) magnetoacoustic modes. Modes with wavelengths longer than the cut-off are leaky, and their phase speed is slightly higher than the external Alfvén speed (Pascoe et al 2007b). For shorter wavelengths, sausage modes are trapped in the guiding structure, and have phase speeds in the range between the internal and external Alfvén speeds.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Characteristics of magnetoacoustic sausage modes

Inglis¹,

Doorsselaere²,

Brady³

et al. 2009

A&A

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Aims. We perform an advanced study of the fast magnetoacoustic sausage oscillations of coronal loops in the context of MHD coronal seismology to establish the dependence of the sausage mode period and cut-off wavenumber on the plasma-β of the loopfilling plasma. A parametric study of the ratios for different harmonics of the mode is also carried out. Methods. Full magnetohydrodynamic numerical simulations were performed using Lare2d, simulating hot, dense loops in a magnetic slab environment. The symmetric Epstein profile and a simple step-function profile were both used to model the density structure of the simulated loops. Analytical expressions for the cut-off wavenumber and the harmonic ratio between the second longitudinal harmonic and the fundamental were also examined. Results. It was established that the period of the global sausage mode is only very weakly dependent on the value of the plasma-β inside a coronal loop, which justifies the application of this model to hot flaring loops. The cut-off wavenumber k c for the global mode was found to be dependent on both internal and external values of the plasma-β, again only weakly. By far the most important factor in this case was the value of the density contrast ratio between the loop and the surroundings. Finally, the deviation of the harmonic ratio P 1 /2P 2 from the ideal non-dispersive case was shown to be considerable at low k, again strongly dependent on plasma density. Quantifying the behaviour of the cut-off wavenumber and the harmonic ratio has significant applications to the field of coronal seismology.

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Waves in Solar Coronal Loops

Wang

2016

Low‐Frequency Waves in Space Plasmas

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Recent observations have revealed the ubiquitous presence of magnetohydrodynamic (MHD) waves and oscillations in the solar corona. The aim of this review is to present recent progress in the observational study of four types of wave (or oscillation) phenomena mainly occurring in active region coronal loops, including (i) flare-induced slow mode oscillations, (ii) fast kink mode oscillations, (iii) propa-gating slow magnetoacoustic waves, and (iv) ubiquitous propagating kink (Alfvenic) waves. This review not only comprehensively outlines various aspects of these waves and coronal seismology, but also highlights the topics that are newly emerging or hotly debated, thus can provide readers a useful guidance on further studies of their interested topics.

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Sausage oscillations of coronal loops

Cited by 75 publications

References 15 publications

Standing sausage modes in coronal loops with plasma flow

Standing sausage modes in coronal loops with plasma flow

Characteristics of magnetoacoustic sausage modes

Waves in Solar Coronal Loops

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