Nonlinear fast sausage waves in homogeneous magnetic flux tubes

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
Badma B. Mikhalyaev ◽  
Michael S. Ruderman
Keyword(s):  
Bessel Functions ◽  
Nonlinear Evolution ◽  
Solar Physics ◽  
Modified Bessel Functions ◽  
Magnetohydrodynamic Equations ◽  
Carrier Wave ◽  
Flux Tubes ◽  
Magnetic Flux Tubes ◽  
Ideal Magnetohydrodynamic ◽  
The Ideal

We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin–Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.

scholarly journals Observational Study of Large Amplitude Longitudinal Oscillations in a Solar Filament

2013 ◽  
Vol 8 (S300) ◽  
pp. 428-429
Author(s):  
Kalman Knizhnik ◽  
Manuel Luna ◽  
Karin Muglach ◽  
Holly Gilbert ◽  
Therese Kucera ◽  
...  
Keyword(s):  
Large Amplitude ◽  
Bessel Functions ◽  
Accretion Rate ◽  
Equations Of Motion ◽  
Radius Of Curvature ◽  
Oscillation Pattern ◽  
Restoring Force ◽  
Flux Tubes ◽  
Solar Filament ◽  
Magnetic Flux Tubes

AbstractOn 20 August 2010 an energetic disturbance triggered damped large-amplitude longitudinal (LAL) oscillations in almost an entire filament. In the present work we analyze this periodic motion in the filament to characterize the damping and restoring mechanism of the oscillation. Our method involves placing slits along the axis of the filament at different angles with respect to the spine of the filament, finding the angle at which the oscillation is clearest, and fitting the resulting oscillation pattern to decaying sinusoidal and Bessel functions. These functions represent the equations of motion of a pendulum damped by mass accretion. With this method we determine the period and the decaying time of the oscillation. Our preliminary results support the theory presented by Luna and Karpen (2012) that the restoring force of LAL oscillations is solar gravity in the tubes where the threads oscillate, and the damping mechanism is the ongoing accumulation of mass onto the oscillating threads. Following an earlier paper, we have determined the magnitude and radius of curvature of the dipped magnetic flux tubes hosting a thread along the filament, as well as the mass accretion rate of the filament threads, via the fitted parameters.

Structures of reconnection layers based on the ideal magnetohydrodynamic equations

1994 ◽  
Vol 51 (3) ◽  
pp. 381-398
Author(s):  
Wenlong Dai ◽  
Paul R. Woodward
Keyword(s):  
Numerical Simulations ◽  
Quantitative Agreement ◽  
Mhd Equations ◽  
Riemann Solver ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
Ideal Mhd ◽  
Ideal Magnetohydrodynamic ◽  
The One ◽  
The Ideal

A Riemann solver is used, and a set of numerical simulations are performed, to study the structures of reconnection layers in the approximation of the one- dimensional ideal MHD equations. Since the Riemann solver may solve general Riemarin problems, the model used in this paper is more general than those in previous investigations on this problem. Under the conditions used in the previous investigations, the structures we obtained are the same. Our numerical simulations show quantitative agreement with those obtained through the Riemann solver.

scholarly journals Are the umbral dots, penumbral grains, and G band bright points formed by the same type of magnetic flux tubes?

2010 ◽  
Vol 6 (S273) ◽  
pp. 426-429
Author(s):  
Isroil Sattarov
Keyword(s):  
Magnetic Flux ◽  
Solar Atmosphere ◽  
Solar Physics ◽  
Common Type ◽  
Present Evidence ◽  
Flux Tubes ◽  
Quiet Sun ◽  
Magnetic Flux Tubes ◽  
Fine Structures ◽  
Umbral Dots

AbstractToday's Solar Physics comes across of different type of fine structures in solar atmosphere including umbral dots and penumbral grains in sunspots, and G-band bright points in quiet Sun. In this report, we present evidence that umbral dots, penumbral grains, and, possibly, G band bright points are related to a common type of features in solar atmosphere magnetic flux tubes.

Nonlinear Evolution of Kink‐unstable Magnetic Flux Tubes and Solar δ‐Spot Active Regions

1998 ◽  
Vol 507 (1) ◽  
pp. 404-416 ◽  
Author(s):  
M. G. Linton ◽  
R. B. Dahlburg ◽  
G. H. Fisher ◽  
D. W. Longcope
Keyword(s):  
Magnetic Flux ◽  
Nonlinear Evolution ◽  
Active Regions ◽  
Flux Tubes ◽  
Magnetic Flux Tubes

Linear Visco-Resistive Computations of Magnetohydrodynamic Waves: I. The Code and Test Cases

1994 ◽  
Vol 144 ◽  
pp. 503-505
Author(s):  
R. Erdélyi ◽  
M. Goossens ◽  
S. Poedts
Keyword(s):  
Resonant Absorption ◽  
Numerical Code ◽  
Mhd Waves ◽  
Test Cases ◽  
Numerical Accuracy ◽  
Element Discretization ◽  
Flux Tubes ◽  
Magnetohydrodynamic Waves ◽  
Viscosity Coefficients ◽  
Magnetic Flux Tubes

AbstractThe stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. Our computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code.

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