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Mean shear flows generated by nonlinear resonant Alfven waves  

Istvan Ballai   Submitted: 2009-07-15 09:52

In the context of resonant absorption, nonlinearity has two different manifestations. The first is the reduction in amplitude of perturbations around the resonant point (wave energy absorption). The second is the generation of mean shear flows outside the dissipative layer surrounding the resonant point. Ruderman et al. [Phys. Plasmas, 4, 75 (1997)] studied both these effects at the slow resonance in isotropic plasmas. Clack et al. [Astron. Astrophys., 494, 317 (2009)] investigated nonlinearity at the Alfven resonance, however, they did not include the generation of mean shear flow. In this present paper, we investigate the mean shear flow, analytically, and study its properties. We find that the flow generated is parallel to the magnetic surfaces and has a characteristic velocity proportional to $epsilon^{1/2}$, where $epsilon$ is the dimensionless amplitude of perturbations far away from the resonance. This is, qualitatively, similar to the flow generated at the slow resonance. The jumps in the derivatives of the parallel and perpendicular components of mean shear flow across the dissipative layer are derived. We estimate the generated mean shear flow to be of the order of 10 km s^{-1} in both the solar upper chromosphere and solar corona, however, this value strongly depends on the choice of boundary conditions. It is proposed that the generated mean shear flow can produce a Kelvin--Helmholtz instability at the dissipative layer which can create turbulent motions. This instability would be an additional effect, as a Kelvin--Helmholtz instability may already exist due to the velocity field of the resonant Alfven waves. This flow can also be superimposed onto existing large scale motions in the solar upper atmosphere.

Authors: Christopher Clack, Istvan Ballai
Projects: None

Publication Status: accepted
Last Modified: 2009-07-15 10:25
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Nonlinear resonant absorption of fast magnetoacoustic waves in strongly anisotropic and dispersive plasmas  

Istvan Ballai   Submitted: 2009-03-05 04:02

The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly anisotropic and dispersive plasmas, developed for slow resonance by Clack and Ballai [Phys. Plasmas 15(8), 2310 (2008)] and Alfven resonance by Clack et al. [A&A 494, 317 (2009)], is used to study the weakly nonlinear interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar plasma. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localized slow or Alfven dissipative layer and are partly reflected, dissipated and transmitted by this region. The nonlinearity parameter defined by Clack and Ballai (2008) is assumed to be small and a regular perturbation method is used to obtain analytical solutions in the slow dissipative layer. The effect of dispersion in the slow dissipative layer is to further decrease the coefficient of energy absorption, compared to its standard weakly nonlinear counterpart, and the generation of higher harmonics in the outgoing wave in addition to the fundamental one. The absorption of external drivers at the Alfven resonance is described within the linear MHD with great accuracy.

Authors: C.T.C. Clack, I. Ballai
Projects: None

Publication Status: Physics of Plasmas, accepted
Last Modified: 2009-03-05 07:43
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On the validity of nonlinear Alfven resonance in space plasmas  

Istvan Ballai   Submitted: 2008-12-01 06:38

In the approximation of linear dissipative magnetohydrodynamics (MHD) it can be shown that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfven (or slow) frequency of a magnetic surface. This near resonant behaviour is confined to a thin region, known as the dissipative layer, which embraces the resonant magnetic surface. Although driven MHD waves have small dimensionless amplitude far away from the resonant surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. Our aim is to study the nonlinear effects in Alfven dissipative layer. In the present paper, the method of simplified matched asymptotic expansions developed for nonlinear slow resonant waves is used to describe nonlinear effects inside the Alfven dissipative layer. The nonlinear corrections to resonant waves in the Alfven dissipative layer are derived and it is proved that at the Alfven resonance (with isotropic/anisotropic dissipation) wave dynamics can be described by the linear theory with great accuracy.

Authors: C.T.M. Clack, I. Ballai and M.S. Ruderman
Projects: None

Publication Status: Astron. & Astrophys. accepted
Last Modified: 2008-12-01 07:59
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Nonlinear theory of resonant slow waves in anisotropic and dispersive plasmas  

Istvan Ballai   Submitted: 2008-08-23 08:32

The solar corona is a typical example of a plasma with strongly anisotropic transport processes. The main dissipative mechanisms in the solar corona acting on slow magnetoacoustic waves are the anisotropic thermal conductivity and viscosity. Ballai et al. [Phys. Plasmas, 5, 252 (1998)] developed the nonlinear theory of driven slow resonant waves in such a regime. In the present paper the nonlinear behaviour of driven magnetohydrodynamic waves in the slow dissipative layer in plasmas with strongly anisotropic viscosity and thermal conductivity is expanded by considering dispersive effects due to Hall currents. The nonlinear governing equation describing the dynamics of nonlinear resonant slow waves is supplemented by a term which describes nonlinear dispersion and is of the same order of magnitude as nonlinearity and dissipation. The connection formulae are found to be similar to their non-dispersive counterparts.

Authors: Christopher Clack, Istvan Ballai
Projects: None

Publication Status: Physics of Plasmas, in press
Last Modified: 2008-08-23 09:20
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Forced oscillations of coronal loops driven by EIT waves  

Istvan Ballai   Submitted: 2008-07-08 09:46

We study the generation of transversal oscillations in coronal loops represented as a straight thin flux tube under the effect of an external driver modeling the global coronal EIT wave. We investigate how the generated oscillations depend on the nature of the driver, and the type of interaction between the two systems. We consider the oscillations of a magnetic straight cylinder with fixed-ends under the influence of an external driver modeling the force due to the global EIT wave. Given the uncertainties related to the nature of EIT waves, we first approximate the driver by an oscillatory force in time and later by a shock with a finite width. Results show that for a harmonic driver the dominant period in the generated oscillation belongs to the driver. Depending on the period of driver, compared to the natural periods of the loop, a mixture of standing modes harmonics can be initiated. In the case of a non-harmonic driver (modeling a shock wave), the generated oscillations in the loop are the natural periods only. The amplitude of oscillations is determined by the position of the driver along the tube. The full diagnosis of generated oscillations is achieved using simple numerical methods.

Authors: I. Ballai, M. Douglas, A. Marcu
Projects: None

Publication Status: A&A accepted
Last Modified: 2008-09-23 20:57
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Global coronal seismology  

Istvan Ballai   Submitted: 2007-03-20 11:59

Following the observation and analysis of large-scale coronal wave-like disturbances, we discuss the theoretical progress made in the field of global coronal seismology. Using simple mathematical techniques we determine average values for magnetic field together with a magnetic map of the quiet Sun. The interaction between global coronal waves and coronal loops allows us to study loop oscillations in a much wider context, i.e. we connect global and local coronal oscillations.

Authors: Istvan Ballai
Projects:

Publication Status: Solar Physics (in press)
Last Modified: 2007-04-12 02:57
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Slow magnetohydrodynamic waves in stratified and viscous plasmas  

Istvan Ballai   Submitted: 2006-04-06 04:43

The propagation of slow magnetohydrodynamic waves in vertical thin flux tubes embedded in a vertically stratified plasma in the presence of viscosity is shown here to be governed by the Klein-Gordon-Burgers (KGB) equation which is solved in two limiting cases assuming an isothermal medium in hydrostatic equilibrium surrounded by a quiescent environment. The results presented here can be applied to, e.g. study the propagation of slow magnetohydrodynamic waves generated by the granular buffeting motion in thin magnetic photospheric tubes. When the variation in the reduced velocity occurs over typical lengths much larger than the gravitational scale height, the KGB equation can be reduced to a Klein-Gordon equation describing the propagation of an impulse followed by a wake oscillating with the frequency reduced by viscosity and the solution has no spatial or temporal decay. However, in the other limiting case, i.e. typical variations in the reduced velocity occur over characteristic lengths much smaller than the gravitational scale height, waves have a temporal and spatial decay.

Authors: Ballai, I., Erdelyi, R. and Hargreaves, J.
Projects: None

Publication Status: Physics of Plasmas (in press)
Last Modified: 2006-04-10 15:51
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On the nature of coronal EIT waves  

Istvan Ballai   Submitted: 2005-11-01 10:32

Large-scale eruption events in the solar atmosphere can generate global waves, i.e., waves that propagate over distances comparable to the solar radius. In the low solar corona, global waves observed by SOHO EIT, generated by coronal mass ejections or flares, are usually referred to as “EIT waves.” The nature of these global waves is the subject of strong debate, and opinions are divided between different interpretations (e.g., fast magnetohydrodynamic waves, shock waves, nonwave feature, etc.). In the present Letter, we studied TRACE EUV data to show that these global coronal disturbances are indeed waves with a well-defined period. Supposing that the EIT waves transfer all their energy to interacting loops, we also estimate the minimum energy threshold carried by EIT waves.

Authors: I. Ballai, R. Erdelyi and B. Pinter
Projects: TRACE

Publication Status: ApJL (in press)
Last Modified: 2005-11-01 10:32
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On dissipative effects in solar prominences  

Istvan Ballai   Submitted: 2003-12-03 04:01

The present paper aims to discuss the possible dissipative mechanisms acting in a coronal prominence. These mechanism are discussed within the context of spatial damping of linear compressional waves. The obtained results show that the dominant mechanism is thermal radiation provided the supposition of optically thin prominence is valid. Damping due to thermal conduction is a viable attenuation mechanism provided the wavelength of the waves is small.

Authors: Istvan Ballai
Projects: None

Publication Status: A&A, 410, L17, 2003
Last Modified: 2003-12-03 04:01
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Abstracts by Author
Mean shear flows generated by nonlinear resonant Alfven waves
Nonlinear resonant absorption of fast magnetoacoustic waves in strongly anisotropic and dispersive plasmas
On the validity of nonlinear Alfven resonance in space plasmas
Nonlinear theory of resonant slow waves in anisotropic and dispersive plasmas
Forced oscillations of coronal loops driven by EIT waves
Global coronal seismology
Slow magnetohydrodynamic waves in stratified and viscous plasmas
On the nature of coronal EIT waves
On dissipative effects in solar prominences

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