The interaction of acoustic waves with flux tubes

Wilson, P.R.

doi:10.1086/157946

Cited by 9 publications

(6 citation statements)

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“…The total wave pressure, hydrodynamic plus magnetic, and the radial velocity must be continuous across the tube boundary. Applying these boundary conditions, Wilson (1980) showed that the total pressure wave field is…”

Section: Exact Solutionmentioning

confidence: 99%

“…For the sake of completeness, we briefly review an exact solution obtained by Wilson (1980) to equations ( 11)-( 15). We consider a plane wave incident on the magnetic tube, with pressure fluctuations of the form…”

Section: Exact Solutionmentioning

confidence: 99%

“…As a first step, in this paper, we consider the scattering of small amplitude acoustic plane waves by a magnetic cylinder embedded in a uniform medium. This simple problem has a known exact solution for arbitrary magnetic field strengths (Wilson 1980). The firstorder Born and Rytov approximations have proved useful in the context of time-distance helioseismology to model the effects of small local perturbations in sound speed and flows (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Scattering of Acoustic Waves by a Magnetic Cylinder: Accuracy of the Born Approximation

Gizon¹,

Hanasoge²,

Birch³

2006

ApJ

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With the aim of studying magnetic effects in time-distance helioseismology, we use the first-order Born approximation to compute the scattering of acoustic plane waves by a magnetic cylinder embedded in a uniform medium. We show, by comparison with the exact solution, that the travel-time shifts computed in the Born approximation are everywhere valid to first order in the ratio of the magnetic to the gas pressures. We also show that, for arbitrary magnetic field strength, the Born approximation is not valid in the limit where the radius of the magnetic cylinder tends to zero.

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Section: Exact Solutionmentioning

confidence: 99%

Section: Exact Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scattering of Acoustic Waves by a Magnetic Cylinder: Accuracy of the Born Approximation

Gizon¹,

Hanasoge²,

Birch³

2006

ApJ

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“…Unfortunately with observations at a single height they were unable to identify what mixture of m = 0, axisymmetric sausage-modes, and m = 1, kinkmodes, they were observing. Theoretical studies of the interaction of flux tubes and waves have been performed in the past, for example Roberts and Webb (1979), Wilson (1980), Spruit (1981), Spruit (1982), Bogdan and Knölker (1989), Solanki (1993), Bogdan et al (1996), Hasan and Kalkofen (1999), Tirry (2000), Gizon, Hanasoge, and Birch (2006), Jain and Gordovskyy (2008), Hanasoge et al (2008), Hanasoge and Cally (2009). It is now well established that slender magnetic flux tubes permit the propagation of the two basic types of magnetohydrodynamic waves: The longitudinal tube waves (sausage modes) with azimuthal wave number m = 0, which are axisymmetric, excited by pressure fluctuations.…”

Section: Introductionmentioning

confidence: 99%

3D Numerical Simulations of f-Mode Propagation Through Magnetic Flux Tubes

et al. 2010

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Three-dimensional numerical simulations have been used to study the scattering of a surface-gravity wave packet by vertical magnetic flux tubes, with radii from 200 km to 3 Mm, embedded in stratified polytropic atmosphere. The scattered wave was found to consist primarily of m = 0 (axisymmetric) and m = 1 modes. It was found that the ratio of the amplitude of these two modes is strongly dependant on the radius of the flux tube: The kink mode is the dominant mode excited in tubes with a small radius while the sausage mode is dominant for large tubes. Simulations of this type provide a simple, efficient and robust way to start understanding the seismic signature of flux tubes, which have recently began to be observed.

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“…Our first test reproduces the analytic result of Wilson (1980) and Gizon et al (2006) where the problem is fully described. In brief, the background state consists of a cylindrical flux tube in pressure and thermal equilibrium.…”

Section: Magnetic and Pressure Perturbationsmentioning

confidence: 61%

SLiM: a code for the simulation of wave propagation through an inhomogeneous, magnetised solar atmosphere

2007

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In this paper we describe the semi-spectral linear MHD (SLiM) code which we have written to follow the interaction of linear waves through an inhomogeneous three-dimensional solar atmosphere. The background model allows almost arbitrary perturbations of density, temperature, sound speed as well as magnetic and velocity fields. We give details of several of the tests we have used to check the code. The code will be useful in understanding the helioseismic signatures of various solar features, including sunspots.

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The interaction of acoustic waves with flux tubes

Cited by 9 publications

References 0 publications

Scattering of Acoustic Waves by a Magnetic Cylinder: Accuracy of the Born Approximation

Scattering of Acoustic Waves by a Magnetic Cylinder: Accuracy of the Born Approximation

3D Numerical Simulations of f-Mode Propagation Through Magnetic Flux Tubes

SLiM: a code for the simulation of wave propagation through an inhomogeneous, magnetised solar atmosphere

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