53 research outputs found
Resonant Absorption as Mode Conversion? II. Temporal Ray Bundle
A fast-wave pulse in a simple, cold, inhomogeneous MHD model plasma is
constructed by Fourier superposition over frequency of harmonic waves that are
singular at their respective Alfven resonances. The pulse partially reflects
before reaching the resonance layer, but also partially tunnels through to it
to mode convert to an Alfven wave. The exact absorption/conversion coefficient
for the pulse is shown to be given precisely by a function of transverse
wavenumber tabulated in Paper I of this sequence, and to be independent of
frequency and pulse width.Comment: 6 pages, 4 figures, accepted (15 Nov 2010) by Solar Physics.
Ancillary file (animation) attache
Sensitivity of helioseismic travel-times to the imposition of a Lorentz force limiter in computational helioseismology
The rapid exponential increase in the Alfv\'en wave speed with height above
the solar surface presents a serious challenge to physical modelling of the
effects of magnetic fields on solar oscillations, as it introduces a
significant CFL time-step constraint for explicit numerical codes. A common
approach adopted in computational helioseismology, where long simulations in
excess of 10 hours (hundreds of wave periods) are often required, is to cap the
Alfv\'en wave speed by artificially modifying the momentum equation when the
ratio between Lorentz and hydrodynamic forces becomes too large. However,
recent studies have demonstrated that the Alfv\'en wave speed plays a critical
role in the MHD mode conversion process, particularly in determining the
reflection height of the upward propagating helioseismic fast wave. Using
numerical simulations of helioseismic wave propagation in constant inclined
(relative to the vertical) magnetic fields we demonstrate that the imposition
of such artificial limiters significantly affects time-distance travel times
unless the Alfv\'en wave-speed cap is chosen comfortably in excess of the
horizontal phase speeds under investigation.Comment: 8 pages, 5 figures, accepted by ApJ
Multiple Scattering of Seismic Waves from Ensembles of Upwardly Lossy Thin Flux Tubes
Our previous semi-analytic treatment of f- and p-mode multiple scattering
from ensembles of thin flux tubes (Hanson and Cally, Astrophys. J. 781, 125;
791, 129, 2014) is extended by allowing both sausage and kink waves to freely
escape at the top of the model using a radiative boundary condition there. As
expected, this additional avenue of escape, supplementing downward loss into
the deep solar interior, results in substantially greater absorption of
incident f- and p-modes. However, less intuitively, it also yields mildly to
substantially smaller phase shifts in waves emerging from the ensemble. This
may have implications for the interpretation of seismic data for solar plage
regions, and in particular their small measured phase shifts.Comment: 9 Pages, 5 Figures. Accepted by Solar Physic
Sensitivity of Coronal Loop Sausage Mode Frequencies and Decay Rates to Radial and Longitudinal Density Inhomogeneities: A Spectral Approach
Fast sausage modes in solar magnetic coronal loops are only fully contained
in unrealistically short dense loops. Otherwise they are leaky, losing energy
to their surrounds as outgoing waves. This causes any oscillation to decay
exponentially in time. Simultaneous observations of both period and decay rate
therefore reveal the eigenfrequency of the observed mode, and potentially
insight into the tubes' nonuniform internal structure. In this article, a
global spectral description of the oscillations is presented that results in an
implicit matrix eigenvalue equation where the eigenvalues are associated
predominantly with the diagonal terms of the matrix. The off-diagonal terms
vanish identically if the tube is uniform. A linearized perturbation approach,
applied with respect to a uniform reference model, is developed that makes the
eigenvalues explicit. The implicit eigenvalue problem is easily solved
numerically though, and it is shown that knowledge of the real and imaginary
parts of the eigenfrequency is sufficient to determine the width and density
contrast of a boundary layer over which the tubes' enhanced internal densities
drop to ambient values. Linearized density kernels are developed that show
sensitivity only to the extreme outside of the loops for radial fundamental
modes, especially for small density enhancements, with no sensitivity to the
core. Higher radial harmonics do show some internal sensitivity, but these will
be more difficult to observe. Only kink modes are sensitive to the tube
centres. {Variation in internal and external Alfv\'en speed along the loop is
shown to have little effect on the fundamental dimensionless eigenfrequency,
though the associated eigenfunction becomes more compact at the loop apex as
stratification increases, or may even displace from the apex.Comment: Accepted J. Phys. A: Math. Theor. (Oct 31 2017). 20 pages, 12 figure
The scattering of - and -modes from ensembles of thin magnetic flux tubes - An analytical approach
Motivated by the observational results of Braun (1995), we extend the model
of Hanson & Cally (2014) to address the effect of multiple scattering of f and
p-modes by an ensemble of thin vertical magnetic flux tubes in the surface
layers of the Sun. As in observational Hankel analysis we measure the scatter
and phase shift from an incident cylindrical wave in a coordinate system
roughly centred in the core of the ensemble. It is demonstrated that, although
thin flux tubes are unable to interact with high order fluting modes
individually, they can indirectly absorb energy from these waves through the
scatters of kink and sausage components. It is also shown how the distribution
of absorption and phase shift across the azimuthal order m depends strongly on
the tube position, as well as on the individual tube characteristics. This is
the first analytical study into an ensembles multiple scattering regime, that
is embedded within a stratified atmosphere.Comment: 20 pages, 8 Figure
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