Transverse Oscillations of Coronal Loops

Рудерман, М. С.; Erdélyi, R.

doi:10.1007/s11214-009-9535-4

Cited by 180 publications

(157 citation statements)

References 67 publications

Supporting

Mentioning

148

Contrasting

Order By: Relevance

“…which coincides with the expression used by Goossens et al (2002; see also the review papers by Goossens et al 2006;and Ruderman & Erdélyi 2009). For the sinusoidal density profile determined by…”

Section: Kink Oscillations Of Static Coronal Loopssupporting

confidence: 80%

Resonant damping of kink oscillations of cooling coronal magnetic loops

Ruderman

2011

A&A

View full text Add to dashboard Cite

The simultaneous effect of amplification due to cooling and damping due to resonant absorption on the kink oscillations of coronal loops is studied. The governing equation describing the kink oscillations is derived in the thin tube thin boundary layer approximation. The cooling time is assumed to be much larger than the oscillation period, and the Wentzel-Kramers-Brillouin (WKB) method is used to obtain the equation describing the dependence of the oscillation amplitude on time. This equation is solved numerically for various values of determining parameters. In particular, the question if the amplification due to cooling can balance the resonant damping and produce undamped oscillation is addressed. The conclusion is that the amplification due to cooling is not very efficient and can balance the resonant damping only when the density contrast is not very large and the cooling is very fast with the characteristic cooling time of the order of the oscillation period.

show abstract

Section: Kink Oscillations Of Static Coronal Loopssupporting

confidence: 80%

Resonant damping of kink oscillations of cooling coronal magnetic loops

Ruderman

2011

A&A

View full text Add to dashboard Cite

show abstract

“…which corresponds to the fundamental mode of kink oscillations, in complete agreement with the general theory of kink oscillations (e.g., Ruderman & Erdélyi 2009). In the first-order approximation, after some algebra, we obtain from Eq.…”

Section: It Follows From Eqs (54) and (56) That Both H(s) + H(−s) Ansupporting

confidence: 88%

“…Later, more sophisticated models have been developed. For a review of the theory of coronal loop oscillations, see for example Ruderman & Erdélyi (2009).…”

Section: Introductionmentioning

confidence: 99%

Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

Terradas

2015

A&A

View full text Add to dashboard Cite

In this article we study standing kink waves in twisted magnetic tubes. We use the cold plasma and thin tube approximation. We assume that the plasma density is constant inside and outside the tube. We also assume that the magnetic twist is weak and take the ratio of the azimuthal and axial component of the magnetic field to be of the order of ratio of the tube radius and tube length. The azimuthal component of the magnetic field is proportional to the distance from the tube axis inside the tube, and inversely proportional to this distance outside the tube. Using the method of asymptotic expansions we derived the governing integral equation that determines the eigenfrequencies and eigenmodes of the tube kink oscillations. In the approximation of a very weak twist, we calculated analytically the corrections to the frequencies of the fundamental mode and first overtone of a straight magnetic tube related to the presence of twist. The analytical results are compared with the numerical results obtained using the full set of linear ideal magnetohydrodynamic equations. We also calculated the ratio of frequencies of the fist overtone and fundamental mode. We found that the magnetic twist enhances this ratio for moderate values of the density ratio, and reduces this ratio for large values of the density ratio. In general, the deviation of the frequency ratio from 2 caused by the magnetic twist is comparable to that found in simultaneous observations of the fundamental mode and first overtone of the coronal loop kink oscillations. Finally, we studied the eigenmode polarization. We found that, in a particular case of linear polarization, the polarization direction rotates along the tube.

show abstract

“…Later theorists started to develop more sophisticated models that took such effects as the loop curvature, non-circular cross-section and magnetic twist into account. For the review of the recent progress in the theory of the transverse coronal loop oscillations see, e.g., a review by Ruderman & Erdélyi (2009).…”

Section: Introductionmentioning

confidence: 99%

The effect of density stratification on the transverse oscillations of two parallel coronal loops

Robertson

Taroyan

2010

A&A

View full text Add to dashboard Cite

Transverse oscillations of coronal magnetic loops are routinely observed during the space missions. Since the first observation these oscillations were interpreted in terms of kink oscillations of magnetic tubes. Sometimes collective oscillations of two or more coronal loops are observed. This makes the development of theory of collective oscillations of a few parallel magnetic tubes desirable. Another reason for the development of this theory is that there are evidences that at least some coronal loops are not monolithic but consist of many thin magnetic threads. In this paper the linear theory of kink oscillations of two parallel magnetic tubes with the density varying along the tubes is developed. The asymptotic method is used to derive the system of equations governing the collective kink oscillations of two tubes. This system is used to study the effect of density variation on the eigenfrequencies of collective oscillations. The implication of the obtained results on coronal seismology is discussed.

show abstract

Transverse Oscillations of Coronal Loops

Cited by 180 publications

References 67 publications

Resonant damping of kink oscillations of cooling coronal magnetic loops

Resonant damping of kink oscillations of cooling coronal magnetic loops

Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

The effect of density stratification on the transverse oscillations of two parallel coronal loops

Contact Info

Product

Resources

About