Marcel Goossens

Coronal loop oscillations - An interpretation in terms of resonant absorption of quasi-mode kink oscillations

Damped quasi-mode kink oscillations in cylindrical flux tubes are capable of explaining the observed rapid damping of the coronal loop oscillations when the ratio of the inhomogeneity length scale to the radius of the loop is allowed to vary from loop to loop, without the need to invoke anomalously low Reynolds numbers. The theoretical expressions for the decay time by Hollweg & Yang ([CITE]) and Ruderman & Roberts ([CITE]) are used to estimate the ratio of the length scale of inhomogeneity compared to the loop radius for a collection of loop oscillations.

Determination of the Coronal Density Stratification from the Observation of Harmonic Coronal Loop Oscillations

The recent detection of multiple harmonic standing transverse oscillations in coronal loops by Verwichte et al. is of special importance, as it allows one to obtain information on the longitudinal density variation in loops. Verwichte et al. detected the simultaneous presence of both the fundamental and the first-overtone mode in two coronal loops. Here we point out that the ratio of the period of the fundamental mode to the period of the overtone mode differs from 2 in loops with longitudinal density stratification. Conversely, the difference between this ratio and 2 can be used as a seismological tool to obtain information about the density scale height in loops.

Resonant behaviour of MHD waves on magnetic flux tubes

A basic procedure is presented for dealing with the resonance problems that appear in MHD of which resonant absorption of waves at the Alfvén resonance point is the best known example in solar physics. The procedure avoids solving the full fourth-order differential equation of dissipative MHD by using connection formulae across the dissipation layer.

Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

AbstractThe present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfvén waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfvén waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions forξr, andP′ across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg forξr, andP′ in terms of double integrals of Hankel functions of complex argument of order

On the nature of kink MHD waves in magnetic flux tubes

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Numerical-simulation of coronal heating by resonant absorption of alfven waves

with compact analytical solutions that allow a straightforward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpendicular to the magnetic field linesξ⊥ which enables us to determine the dominant dynamics of resonant Alfvén waves in dissipative MHD.

Cross-Field Heating of Coronal Ions by Low-Frequency Kinetic Alfvén Waves

The analytic study of coronal loop oscillations in equilibrium states with thin nonuniform boundary layers is extended by a numerical investigation for one-dimensional nonuniform equilibrium states. The frequency and the damping time of the ideal kink quasi mode are calculated in fully resistive MHD. In this numerical investigation there is no need to adopt the assumption of a thin nonuniform boundary layer, which is essential for analytic theory. An important realization is that analytical expressions for the damping rate that are equivalent for thin nonuniform layers give results differing by a factor of 2 when they are used for thick nonuniform layers. Analytical theory for thin nonuniform layers does not allow us to discriminate between these analytical expressions. The dependence of the complex frequency of the kink mode on the width of the nonuniform layer, on the length of the loop, and on the density contrast between the internal and the external region is studied and is compared with analytical theory, which is valid only for thin boundaries. Our numerical results enable us to show that there exists an analytical expression for thin nonuniform layers that might be used as a qualitative tool for extrapolation into the regime of thick nonuniform layers. However, when the width of the nonuniform layer is varied, the differences between our numerical results and the results obtained with the version of the analytical approximation that can be extended into the regime of thick nonuniform layers are still as large as 25%.

Selective spatial damping of propagating kink waves due to resonant absorption

Context. Magnetohydrodynamic (MHD) waves are often reported in the solar atmosphere and usually classified as slow, fast, or Alfven. The possibility that these waves have mixed properties is often ignored. Aims. The goal of this work is to study and determine the nature of MHD kink waves. Methods. This is done by calculating the frequency, the damping rate and the eigenfunctions of MHD kink waves for three widely different MHD waves cases: a compressible pressure-less plasma, an incompressible plasma and a compressible plasma which allows for MHD radiation. Results. In all three cases the frequency and the damping rate are for practical purposes the same as they differ at most by terms proportional to (kzR) 2 . In the magnetic flux tube the kink waves are in all three cases, to a high degree of accuracy incompressible waves with negligible pressure perturbations and with mainly horizontal motions. The main restoring force of kink waves in the magnetised flux tube is the magnetic tension force. The total pressure gradient force cannot be neglected except when the frequency of the kink wave is equal or slightly differs from the local Alfven frequency, i.e. in the resonant layer. Conclusions. Kink waves are very robust and do not care about the details of the MHD wave environment. The adjective fast is not the correct adjective to characterise kink waves. If an adjective is to be used it should be Alfvenic. However, it is better to realize that kink waves have mixed properties and cannot be put in one single box.