M. Goossens | KU Leuven (original) (raw)
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Papers by M. Goossens
Journal of Plasma Physics, 2000
Nonlinear resonant slow magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotrop... more Nonlinear resonant slow magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotropic plasmas for a cylindrical equilibrium model. The equilibrium magnetic field lines are unidirectional and parallel with the z axis. The nonlinear governing equations for resonant slow magnetoacoustic (SMA) waves are derived. Using the method of matched asymptotic expansions inside and outside the narrow dissipative layer, we generalize the connection formulae for the Eulerian perturbation of the total pressure and for the normal component of the velocity. These nonlinear connection formulae in dissipative cylindrical MHD are an important extention of the connection formulae obtained in linear ideal MHD [Sakurai et al., Solar Phys. 133, 227 (1991)], linear dissipative MHD [Goossens et al., Solar Phys. 175, 75 (1995); Erdélyi, Solar Phys. 171, 49 (1997)] and in nonlinear dissipative MHD derived in slab geometry [Ruderman et al., Phys. Plasmas 4, 75 (1997)]. These generalized connection formulae enable us to connect the solutions at both sides of the dissipative layer without solving the MHD equations in the dissipative layer. We also show that the nonlinear interaction of harmonics in the dissipative layer is responsible for generating a parallel mean flow outside the dissipative layer.
Astrophysics and Space Science Library, 2003
ABSTRACT
There are ubiquitous flows observed in the solar atmosphere of sub-Alfvénic speeds, however after... more There are ubiquitous flows observed in the solar atmosphere of sub-Alfvénic speeds, however after flaring and coronal mass ejection events flows can become Alfvénic. In this Letter, we derive an expression for the standing kink mode frequency due to siphon flow in coronal loops, valid for both low and high speed regimes. It is found that siphon flow introduces a linear spatially dependent phase shift along coronal loops and asymmetric eigenfunctions. We demonstrate how this theory can be used to determine the kink and flow speed of oscillating coronal loops with reference to an observational case study. It is shown that the presence of siphon flow can cause the underestimation of magnetic field strength in coronal loops using the traditional seismological methods.
ABSTRACT Alternating current in flux tubes is one of the possible contributors to the heating of ... more ABSTRACT Alternating current in flux tubes is one of the possible contributors to the heating of the solar corona. The mechanism of the generation of alternating currents in flux tubes by turbulent pressure fluctuations in convective zone is proposed. The thin-flux-tube approximation shows, that the linear and weakly nonlinear torsional waves in twisted flux tube, are accompanied by tube cross section fluctuations. Consequently, external pressure fluctuations generate not only slow MHD waves but torsional waves as well. The torsional waves are nothing else than alternating current. .
X-ray spectroscopy performed from different astronomical spacecrafts has shown that the solar cor... more X-ray spectroscopy performed from different astronomical spacecrafts has shown that the solar corona is structured by magnetic fields having the shape of loops and arcades. These structures are formed by stretching and reconnection of magnetic fields, and remain stable from days to weeks. Also, sporadic or periodic brightenings of such structures have been detected in UV and soft X-ray observations, suggesting the existence of propagating waves and plasma heating within them. In this paper, a mechanism for the deposition of Alfvén wave energy and heating of coronal arcades via resonant absorption is investigated. An analytical solution to the linear viscous, resistive MHD equations that describes the steady state of resonant shear Alfvén oscillations in coronal arcades driven by toroidal footpoint motions is obtained. General expressions for the total amount of dissipated wave energy and for its spatial distribution within the resonant magnetic surface is derived.
This paper studies the damping of slow surface MHD waves propagating along the equilibrium magnet... more This paper studies the damping of slow surface MHD waves propagating along the equilibrium magnetic field on a finite-thickness magnetic interface. The plasma is assumed to be strongly magnetised, and the full Braginskii's expressions for viscosity and the heat flux are used. The primary focus of the paper is on the competition between resonant absorption in the thin dissipative layer embracing the ideal resonant position and the bulk wave damping due to viscosity and thermal conductivity as damping mechanisms for surface MHD waves. The dependence of the wave damping decrement on the wave length and the dissipative coefficients is studied. Application of the obtained results to the surface MHD wave damping in the solar chromosphere is discussed.
The eigenfrequencies and the optimal driving frequencies for flux tubes embedded in uniform but w... more The eigenfrequencies and the optimal driving frequencies for flux tubes embedded in uniform but wave-carrying surroundings are calculated, based on matching conditions formulated in terms of the normal acoustic impedances at the flux tube boundary. The requirement of the equality of the normal acoustic impedance of the transmitted wave field with the normal acoustic impedance of the outgoing wave field selects the eigenmodes, while the equality of the ingoing and the transmitted normal acoustic impedance selects the optimal driving frequencies .
Journal of Plasma Physics, 2000
Nonlinear resonant slow magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotrop... more Nonlinear resonant slow magnetohydrodynamic (MHD) waves are studied in weakly dissipative isotropic plasmas for a cylindrical equilibrium model. The equilibrium magnetic field lines are unidirectional and parallel with the z axis. The nonlinear governing equations for resonant slow magnetoacoustic (SMA) waves are derived. Using the method of matched asymptotic expansions inside and outside the narrow dissipative layer, we generalize the connection formulae for the Eulerian perturbation of the total pressure and for the normal component of the velocity. These nonlinear connection formulae in dissipative cylindrical MHD are an important extention of the connection formulae obtained in linear ideal MHD [Sakurai et al., Solar Phys. 133, 227 (1991)], linear dissipative MHD [Goossens et al., Solar Phys. 175, 75 (1995); Erdélyi, Solar Phys. 171, 49 (1997)] and in nonlinear dissipative MHD derived in slab geometry [Ruderman et al., Phys. Plasmas 4, 75 (1997)]. These generalized connection formulae enable us to connect the solutions at both sides of the dissipative layer without solving the MHD equations in the dissipative layer. We also show that the nonlinear interaction of harmonics in the dissipative layer is responsible for generating a parallel mean flow outside the dissipative layer.
Astrophysics and Space Science Library, 2003
ABSTRACT
There are ubiquitous flows observed in the solar atmosphere of sub-Alfvénic speeds, however after... more There are ubiquitous flows observed in the solar atmosphere of sub-Alfvénic speeds, however after flaring and coronal mass ejection events flows can become Alfvénic. In this Letter, we derive an expression for the standing kink mode frequency due to siphon flow in coronal loops, valid for both low and high speed regimes. It is found that siphon flow introduces a linear spatially dependent phase shift along coronal loops and asymmetric eigenfunctions. We demonstrate how this theory can be used to determine the kink and flow speed of oscillating coronal loops with reference to an observational case study. It is shown that the presence of siphon flow can cause the underestimation of magnetic field strength in coronal loops using the traditional seismological methods.
ABSTRACT Alternating current in flux tubes is one of the possible contributors to the heating of ... more ABSTRACT Alternating current in flux tubes is one of the possible contributors to the heating of the solar corona. The mechanism of the generation of alternating currents in flux tubes by turbulent pressure fluctuations in convective zone is proposed. The thin-flux-tube approximation shows, that the linear and weakly nonlinear torsional waves in twisted flux tube, are accompanied by tube cross section fluctuations. Consequently, external pressure fluctuations generate not only slow MHD waves but torsional waves as well. The torsional waves are nothing else than alternating current. .
X-ray spectroscopy performed from different astronomical spacecrafts has shown that the solar cor... more X-ray spectroscopy performed from different astronomical spacecrafts has shown that the solar corona is structured by magnetic fields having the shape of loops and arcades. These structures are formed by stretching and reconnection of magnetic fields, and remain stable from days to weeks. Also, sporadic or periodic brightenings of such structures have been detected in UV and soft X-ray observations, suggesting the existence of propagating waves and plasma heating within them. In this paper, a mechanism for the deposition of Alfvén wave energy and heating of coronal arcades via resonant absorption is investigated. An analytical solution to the linear viscous, resistive MHD equations that describes the steady state of resonant shear Alfvén oscillations in coronal arcades driven by toroidal footpoint motions is obtained. General expressions for the total amount of dissipated wave energy and for its spatial distribution within the resonant magnetic surface is derived.
This paper studies the damping of slow surface MHD waves propagating along the equilibrium magnet... more This paper studies the damping of slow surface MHD waves propagating along the equilibrium magnetic field on a finite-thickness magnetic interface. The plasma is assumed to be strongly magnetised, and the full Braginskii's expressions for viscosity and the heat flux are used. The primary focus of the paper is on the competition between resonant absorption in the thin dissipative layer embracing the ideal resonant position and the bulk wave damping due to viscosity and thermal conductivity as damping mechanisms for surface MHD waves. The dependence of the wave damping decrement on the wave length and the dissipative coefficients is studied. Application of the obtained results to the surface MHD wave damping in the solar chromosphere is discussed.
The eigenfrequencies and the optimal driving frequencies for flux tubes embedded in uniform but w... more The eigenfrequencies and the optimal driving frequencies for flux tubes embedded in uniform but wave-carrying surroundings are calculated, based on matching conditions formulated in terms of the normal acoustic impedances at the flux tube boundary. The requirement of the equality of the normal acoustic impedance of the transmitted wave field with the normal acoustic impedance of the outgoing wave field selects the eigenmodes, while the equality of the ingoing and the transmitted normal acoustic impedance selects the optimal driving frequencies .