In this paper we present and discuss results of 2D simulations of linear and non-linear magneto-acoustic wave propagation through
an open magnetic flux tube embedded in the solar atmosphere expanding from the photosphere through to the
transition region and into the low corona. Our aim is to model and analyse the response of such a magnetic structure
to vertical and horizontal periodic motions originating in the
photosphere. To carry out the simulations we employed our MHD code SAC (Sheffield Advanced Code). A combination
of the VALIIIC and McWhirter solar atmospheres and coronal density profiles were used as the background equilibrium
model in the simulations. Vertical and horizontal harmonic sources, located at the footpoint region of
the open magnetic flux tube, are incorporated in the calculations, to excite oscillations in the domain of interest.
To perform the analysis we have constructed a series of time-distance diagrams of the vertical and perpendicular components
of the velocity with respect to the magnetic field lines at each height of the computational domain. These time-distance
diagrams are subject to spatio-temporal Fourier transforms allowing us to build omega-k dispersion diagrams for all
of the simulated regions in the solar atmosphere.
This approach makes it possible to compute the phase speeds of waves propagating throughout the various regions
of the solar atmosphere model.
We demonstrate the transformation of linear slow and fast magneto-acoustic wave modes into nonlinear ones,
i.e. shock waves, and also show that magneto-acoustic waves with a range of frequencies efficiently leak
through the transition region into the solar corona. It is found that the waves interact with the transition
region and excite horizontally propagating surface waves along the transition region for both types of drivers.
Finally, we estimate the phase speed of the oscillations in the solar corona and compare it with the phase speed
derived from observations.

Authors: Fedun V., Shelyag S., Erdelyi R.
Projects: None

Publication Status: ApJ (accepted)
Last Modified: 2010-11-11 10:59

Large-amplitude MHD waves are routinely observed in space plasmas. We suggest that dispersive focusing, previously proposed for the excitation of freak waves in the ocean, can be also responsible for the excitation of short-lived large-amplitude MHD waves in space plasmas. The DNLS equation describes MHD waves propagating in plasmas at moderate angles with respect to the equilibrium magnetic field. We obtained an analytical solution of the linearised DNLS equation governing the generation of large-amplitude MHD waves from small-amplitude wave trains due to the dispersive focusing. Our numerical solutions of the full DNLS equation confirm this result.

Authors: Fedun, V. Ruderman, M. S. Erdélyi, R.
Projects: None

Publication Status: published
Last Modified: 2008-09-22 07:47

Generation of short-lived large-amplitude magnetohydrodynamic pulses by dispersive focusing

Large-amplitude MHD waves are routinely observed in space plasmas. We suggest that dispersive focusing, previously proposed for the excitation of freak waves in the ocean, can be also responsible for the excitation of short-lived large-amplitude MHD waves in space plasmas. The DNLS equation describes MHD waves propagating in plasmas at moderate angles with respect to the equilibrium magnetic field. We obtained an analytical solution of the linearised DNLS equation governing the generation of large-amplitude MHD waves from small-amplitude wave trains due to the dispersive focusing. Our numerical solutions of the full DNLS equation confirm this result.

Authors: Fedun, V.; Ruderman, M. S.; Erdélyi, R.
Projects: None

Publication Status: published
Last Modified: 2008-09-23 18:09

Large-amplitude MHD waves are routinely observed in space plasmas. We suggest that dispersive focusing, previously proposed for the excitation of freak waves in the ocean, can be also responsible for the excitation of short-lived large-amplitude MHD waves in space plasmas. The DNLS equation describes MHD waves propagating in plasmas at moderate angles with respect to the equilibrium magnetic field. We obtained an analytical solution of the linearised DNLS equation governing the generation of large-amplitude MHD waves from small-amplitude wave trains due to the dispersive focusing. Our numerical solutions of the full DNLS equation confirm this result.

Authors: Fedun, V.; Ruderman, M. S.; Erdélyi, R.
Projects: None

Publication Status: published
Last Modified: 2008-09-22 07:46

MHD waves in magnetically twisted flux tubes in twisted magnetic environment

Twisted magnetic flux tubes are of considerable interest because of their natural occurrence
from the Sun's interior, throughout the solar atmosphere and interplanetary space up to
a wide range of applicabilities to astrophysical plasmas.
The aim of the present work is to obtain analytically a dispersion
equation of linear wave propagation in twisted incompressible cylindrical magnetic waveguides and find appropriate
solutions for surface,
body and pseudobody sausage modes (i.e. m=0) of
a twisted magnetic flux tube embedded in an incompressible but also magnetically twisted plasma.
Asymptotic solutions are
derived in long- and short- wavelength approximations. General solutions of the dispersion
equation for intermediate wavelengths
are obtained numerically. We found, that in case of a constant, but non-zero azimuthal
component of the equilibrium magnetic field
outside the flux tube the index nu of Bessel functions in the dispersion relation is not integer
any more in general.
This gives rise to a reach mode-structure of degenerated magneto-acoustic waves in solar flux tubes. In the particular
case of a homogen magnetic twist the total pressure is found to be constant across the boundary of the flux tube.
Finally, the effect of magnetic twist on oscillation periods is estimated under solar atmospheric conditions. It was
found that a magnetic twist will
increase, in general, the periods of waves approximately by a few per cent when compared to their untwisted counterparts.

Authors: Robert Erdelyi and Viktor Fedun
Projects: None

Publication Status: Under review
Last Modified: 2006-06-08 15:54