Abstract
Magnetohydrodynamic (MHD) sausage waves in a coronal loop consisting of a core with longitudinal magnetic field and a current-carrying annulus with azimuthal magnetic field in the presence of plasma pressure are studied. As the plasma pressure is introduced to the loop a narrow band of infinite slow waves appear in the dispersion diagram, and the oscillation frequency of the fast sausage waves increases. In the loops with thinner annulus, more fast sausage waves with higher radial mode numbers are supported by the loop, and the fast sausage waves have smaller cut off wave numbers. The eigenfunction of the long wavelength fast sausage wave supported by the current-carrying loop, in the case of low density contrast, is similar to the eigenfunction of the slow sausage wave in a straight homogeneous loop with the maximum frequency of the frequency band. Other slow sausage waves both in a straight homogeneous loop and a current-carrying loop do not perturb the surrounding environment substantially.
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Andries, J., Goossens, M., Hollweg, J.V., Arregui, I., Van Doorsselaere, T.: Coronal loop oscillations, calculation of resonantly damped MHD quasi-mode kink oscillations of longitudinally stratified loops. Astron. Astrophys. 430, 1109 (2005)
Aschwanden, M.J.: Physics of the Solar Corona. Springer, Berlin (2005). ISBN 3-540-30765-6.
Aschwanden, M.J., Fletcher, L., Schrijver, C.J., Alexander, D.: Coronal loop oscillations observed with the transition region and coronal explorer. Astrophys. J. 520, 880 (1999)
Barbulescu, M., Erdélyi, R.: Propagation of long-wavelength nonlinear slow sausage waves in stratified magnetic flux tubes. Sol. Phys. 291, 1369B (2016)
Cally, P.S.: Leaky and non-leaky oscillations in magnetic flux tubes. Sol. Phys. 103, 227c (1986)
Chen, S.X., Li, B., Xia, L.D., Yu, H.: Periods and damping rates of fast sausage oscillations in multishelled coronal loops. Sol. Phys. 290, 2231 (2015a)
Chen, S.X., Li, B., Xiong, M., Yu, H., Guo, M.Z.: Standing sausage modes in nonuniform magnetic tubes: an inversion scheme for inferring flare loop parameters. Astrophys. J. 812, 22 (2015b)
Chen, S.X., Li, B., Xiong, M., Yu, H., Guo, M.Z.: Fast sausage modes in magnetic tubes with continuous transverse profiles: effect of a finite plasma beta. Astrophys. J. 833, 114 (2016)
Edwin, P.M., Roberts, B.: Wave propagation in a magnetic cylinder. Sol. Phys. 88, 179 (1983)
Erdélyi, R., Carter, B.K.: Wave propagation in incompressible MHD wave guides: the twisted magnetic annulus. Astron. Astrophys. 455, 361 (2006)
Erdélyi, R., Fedun, V.: Sausage MHD waves in incompressible flux tubes with twisted magnetic fields. Sol. Phys. 238, 41 (2006)
Erdélyi, R., Fedun, V.: Linear MHD sausage waves in compressible magnetically twisted flux tubes. Sol. Phys. 246, 101 (2007)
Erdélyi, R., Verth, G.: The effect of density stratification on the amplitude profile of transversal coronal loop oscillations. Astron. Astrophys. 462, 743 (2007)
Foullon, C., Fletcher, L., Hannah, I.G., Nakariakov, V.M.: From large-scale loops to the sites of dense flaring loops: preferential conditions for long-period pulsations in solar flares. Astrophys. J. 719, 151 (2010)
Giagkiozis, I., Goossens, M., Verth, G., Fedun, V., Van Doorsselaere, T.: Resonant absorption of axisymmetric modes in twisted magnetic flux tubes. Astrophys. J. 823, 71 (2016)
Karami, K., Bahari, K.: The effect of a twisted magnetic field on the period ratio \(P_{1}/P_{2}\) of nonaxisymmetric waves. Astrophys. J. 757, 186 (2012)
Khongorova, O.V., Mikhalyaev, B.B., Ruderman, M.S.: Fast sausage waves in current-carrying coronal loops. Sol. Phys. 280, 153 (2012)
Kopylova, Y.G., Melnikov, A.V., Stepanov, A.V., Tsap, Y.T., Goldvarg, T.B.: Oscillations of coronal loops and second pulsations of solar radio emission. Astron. Lett. 33, 706 (2007)
Kupriyanova, E.G., Melnikov, V.F., Nakariakov, V.M., Shibasaki, K.: Types of microwave quasi-periodic pulsations in single flaring loops. Sol. Phys. 267, 329 (2010)
Li, B., Chen, S.X., Xia, L.D., Yu, H.: Standing sausage modes in coronal loops with plasma flow. Astron. Astrophys. 568, A31 (2014)
Lopin, I., Nagorny, I.: Sausage waves in transversely nonuniform monolithic coronal tubes. Astrophys. J. 810, 87 (2015)
Nakariakov, V.M., Melnikov, V.F.: Modulation of gyrosynchrotron emission in solar and stellar flares by slow magnetoacoustic oscillations. Astron. Astrophys. 446, 1151 (2006)
Nakariakov, V.M., Ofman, L.: Determination of the coronal magnetic field by coronal loop oscillations. Astron. Astrophys. 372, L53 (2001)
Nakariakov, V.M., Ofrnangz, L., DeLuca, E.E., Roberts, B., Davila, J.M.: TRACE observation of damped coronal loop oscillations: implications for coronal heating. Science 285, 862 (1999)
Nakariakov, V.M., Hornsey, C., Melnikov, V.F.: Sausage oscillations of coronal plasma structures. Astrophys. J. 761, 134 (2012)
Roberts, B.: Waves and oscillations in the solar corona. Sol. Phys. 193, 139 (2000)
Roberts, B., Edwin, P.M., Benz, A.O.: On coronal oscillations. Astrophys. J. 279, 857 (1984)
Rosenberg, H.: Evidence for MHD pulsations in the solar corona. Astron. Astrophys. 9, 159 (1970)
Sakurai, T., Goossens, M., Hollweg, J.V.: Resonant behaviour of MHD waves on magnetic flux tubes. Sol. Phys. 133, 227 (1991)
Spruit, H.C.: Propagation speeds and acoustic damping of waves in magnetic flux tubes. Sol. Phys. 75, 3 (1982)
Uchida, Y.: Diagnosis of coronal magnetic structure by flare-associated hydromagnetic disturbances. Publ. Astron. Soc. Jpn. 22, 341 (1970)
Verth, G., Erdélyi, R., Jess, D.B.: Refined magnetoseismological technique for the solar corona. Astrophys. J. 687, L45 (2008)
Wang, T., Innes, D.E., Qiu, J.: Determination of the coronal magnetic field from hot-loop oscillations observed by SUMER and SXT. Astrophys. J. 656, 598 (2007)
Zaitsev, V.V., Stepanov, A.V.: On the origin of pulsations of type IV solar radio emission. Plasma cylinder oscillations (I). Issled. Geomagn. Aeron. Fiz. Solntsa 37, 3 (1975)
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The author thanks the anonymous referee for his/her valuable suggestions and comments, and also thanks M.S. Ruderman for a number of useful comments.
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Bahari, K. Magnetohydrodynamic sausage waves in current-carrying coronal tubes. Astrophys Space Sci 362, 177 (2017). https://doi.org/10.1007/s10509-017-3160-6
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DOI: https://doi.org/10.1007/s10509-017-3160-6