Solar Physics

, Volume 289, Issue 6, pp 1999–2020 | Cite as

Nonlinear Kink Oscillations of Coronal Magnetic Loops



We studied nonlinear kink oscillations of a thin magnetic tube using the cold-plasma approximation. We assumed that the plasma density varies along the tube but does not vary in the radial direction. Using the regular perturbation method, we show that the nonlinearity does not affect the oscillation amplitude. We also calculated the nonlinear correction to the oscillation frequency, which is proportional to the oscillation amplitude squared. As an example, we considered nonlinear oscillations of a coronal magnetic loop of half-circle shape in an isothermal atmosphere with equal plasma temperatures inside and outside the loop.


Sun Corona Magnetic fields Oscillations 



MSR acknowledges the support by a Royal Society Leverhulme Trust Senior Research Fellowship. He is also grateful to the STFC for financial support. A part of this work has been carried out when MSR was a guest at the Centre for Mathematical Plasma Astrophysics of K.U. Leuven. He acknowledges the warm hospitality of the Centre.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Solar Physics and Space Plasma Research Centre (SP²RC), School of Mathematics and StatisticsUniversity of SheffieldSheffieldUK
  2. 2.Space Research Institute (IKI)Russian Academy of SciencesMoscowRussia
  3. 3.Centre for Mathematical Plasma Astrophysics, Department of MathematicsKatholieke Universiteit LeuvenLeuvenBelgium

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