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MHD Waves and Oscillations in
Solar Magnetic Structures
Programme and Abstract Book
Mallorca, 29 May - 1 June, 2006
Sponsored by:
Ministerio de Ciencia y Tecnologia,
Conselleria d’Economia, Hisenda i Innovació (CAIB),
Universitat de les Illes Balears
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Scientific and Social Programme
Sunday, May 28, 2006
19.30 Registration and Welcome Reception
Monday, May 29, 2006
08.30–13.00 Registration
08.55–09.00 Welcome Address
09.00–09.30 Opening Lecture. A. Hood
Session 1: Theory of MHD modes of magnetic structures
Chairman: A. Hood
09.30–10.00 Theory of MHD waves for simple equilibrium
configurations. M. Goossens
10.00–10.30 Nonlinear MHD waves in magnetically structured
plasmas. M. Ruderman
10.30–10.50 On the continuous spectrum of leaky MHD modes.
J. Andries
10.50–11.10 A mechanism for parallel electric field
generation in the MHD limit: possible
implications for coronal heating problem in
the two stage mechanism. D. Tsiklauri
11.10–11.45 Coffee Break and Poster Viewing
11.45–12.15 Solitons in Flux Tubes: from Shaping Sunspots to
Coronal Structure Formation. R. Ryutova
12.15–12.35 Finite beta wave propagation near magnetic null
points. A. Hood
12.35–12.55 Interaction of MHD Waves with Corona Magnetic
Null-Points. N. P. Young
12.55–13.15 Swing Absorption of compressional waves in
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inhomogeneous magnetized plasma. B.M.
Shergelashvili
Session 2: Magnetic Helioseismology and Waves in sunspots
Chairman: M. Goossens
15.30–16.00 Magnetic helioseismology and waves in sunspots.
R. Rutten
16.00–16.20 Responses of helioseismic f modes on
atmospheric effects in analytical MHD. B. Pinter
16.20–16.40 Local Helioseismology of Small Magnetic
Elements. A. C. Birch
16.40–17.15 Coffee Break and Poster Viewing
17.15–17.45 Effects of surface magnetic field on
Helioseismology. R. Jain
17.45–18.05 MHD waves in sunspot regions, excited by solar
flares. A. G. Kosovichev
18.05–18.25 Multi-wavelength detection of 3 minute
oscillations in and around sunspot. D. Banerjee
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Tuesday, May 30, 2006
Session 3: MHD Waves in the Lower Atmosphere
Chairman: R. Rutten
09.00–09.30 Dynamics and magnetic coupling in the lower
solar atmosphere. R. Erdélyi
09.30–09.50 Waveguiding of P-modes Into The Solar Corona.
M. Marsh
09.50–10.10 MHD waves in magnetically twisted vertical solar
flux tubes. V. Fedun
10.10–10.45 Coffee Break and Poster Viewing
10.45–11.05 Dynamics of the lower atmosphere in internetwork
regions. S. Wedemeyer-Böhm
11.05–11.25 Chromospheric oscillations from quiet Sun
millimeter observations. M. A. Loukitcheva
Session 4: Waves and Oscillations in Prominences
Chairman: R. Ryutova
15.00–15.30 Prominence Oscillations (Observations). R. Oliver
15.30–15.50 Evidence for propagating waves in a quiescent
filament. Y. Lin
15.50–16.10 Oscillations in a filament with CDS(SOHO): first
observation of long periods in the HeI 584.33 line,
modelling and diagnostic. G. Pouget
16.10–16.45 Coffee Break and Poster Viewing
16.45–17.15 Theory of small-amplitude prominence
oscillations: Historical Review. J. L. Ballester
17.15–17.35 Filling factor on prominence oscillations. A. J.
Díaz
19.00
Seven a side Football Match
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Wednesday, May 31, 2006
Session 5: Waves in the Corona. MHD Coronal Seismology
Chairman: B. Roberts
09.00–09.30 Current trends in MHD Coronal Seismology. V.
M. Nakariakov
09.30–09.50 Slow magnetoacoustic waves in curved hot coronal
loops.T. Zaqarashvili
09.50–10.10 Transverse oscillations in coronal loops: the effects
of curvature and transverse structuring. E.
Verwichte
10.10–10.45 Coffee Break and Poster Viewing
10.45–11.15 Global coronal seismology. I. Ballai
11.15–11.35 Coronal loop oscillations: Collective behaviour
and damping in a system of two coronal slabs. I.
Arregui
11.35–11.55 Random heating excitation of waves in solar
coronal loops. C. Mendoza
11.55–12.15 Possible methods to determine if a magnetic field is
constant or varying along a coronal loop by direct
observation of fast kink standing mode oscillations.
G. Verth
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Session 5: Waves in the Corona. MHD Coronal Seismology
Chairman: V. Nakariakov
15.30–16.00 Numerical simulations of impulsively
generated waves in solar coronal loops. K.
Murawski
16.00–16.20 Detection of slow magnetoacoustic waves in open
field regions. E. O’Shea
16.20–16.40 Global Sausage Modes of Coronal Loops
D. J. Pascoe
16.40–17.15 Coffee Break and Poster Viewing
17.15–17.35 On The Period Ratio P1/2P2 in the Oscillations of
Coronal Loops. M. P. McEwan
17.35–17.55 Seismology of Dynamically Heated
Quiescent Coronal Loops. Y. Taroyan
17.55–18.15 Oscillations of solar coronal magnetic loops in
microwaves. M. Khodachenko
19.30 Conference Dinner
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Thursday, June 1, 2006
Session 6: MHD waves in Astrophysical Structures
Chairman: R. Erdélyi
09.00–09.30 Magnetoseismology of accretion disks. R.
Keppens
09.30–09.50 The periodic variations of stellar flares M.
Mathioudakis
09.50-10.10 Damping of hydromagnetic waves by bulk
viscosity. M. H. Ibañez
10.10-10.30 Slow nonlinear and shock waves in flux
tubes. Y.D.Zhugzhda
10.30–11.00 Coffee Break
Session 7: Modern Data Analysis Methods for Wave and
Oscillation Phenomena
Chairman: R. Oliver
11.00–11.30 Modern Data Analysis Methods for Wave and
Oscillation Phenomena. B. Fleck
11.30–11.50 Application of statistical techniques to the analysis
of solar coronal oscillations. J. Terradas
11.50–12.10 High frequency oscillations in active regions and
sunspots. K. Muglach
12.10–12.30 Application of the POD in the study of the solar
atmospheric dynamics. A. Vecchio
12.30–13.00 Closing Summary Review. B. Roberts
End of the Scientific Programme
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Friday, June 2, 2006
09.30 Excursion
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Session 1: Theory of MHD Modes of Magnetic Structures
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Invited Review: Theory of MHD waves for simple
equilibrium configurations
M. Goossens
Centrum Plasma Astrofysica, K.U.Leuven
Abstract
The magnetic field in the solar atmosphere is not uniformly
distributed but organized in typical configurations. Each of these
magnetic configurations can support MHD waves and
observations show that this is indeed the case. The solar magnetic
plasma configurations are often characterized by non-uniformity.
In addition, they are not bounded by rigid walls but embedded in a
surrounding plasma environment. This review concentrates on
basic properties that are independent of specific equilibrium
models but are rather related to non-uniformity of the plasma and
the fact that the equilibrium configuration is embedded in a
surrounding plasma environment. The discussion is confined to
MHD waves in 1-d equilibrium models. These models contain
sufficient physics for understanding basic properties of MHD
waves and still allow for a relatively straightforward mathematical
analysis. The non-uniformity enables local slow and Alfvén waves
to exist on individual magnetic surfaces. In ideal MHD these local
slow and Alfvén waves are confined to their resonant magnetic
surfaces on which their dispersion relations are satisfied locally.
Dissipative effects produce coupling to the neighbouring surfaces,
but the local slow and Alfvén waves still have steep gradients
across the magnetic surfaces. These local resonant MHD modes
exist in addition to the discrete MHD modes. Non-uniformity can
produce discrete modes with mixed character and can couple
discrete eigenmodes to local slow or Alfvén waves producing
quasi-modes. These quasi-modes are the natural wave modes of
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the system. They are important for wave damping and wave
heating. The fact that the magnetic plasma configuration is not
bounded means that the system can support both non-leaky and
leaky modes. In turn both non-leaky and leaky modes can have a
non-resonant or resonant behaviour. These various cases and
possible applications are discussed for 1-d equilibrium
configurations.
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Invited Review: Nonlinear MHD waves in magnetically
structured plasmas
M. Ruderman
Solar Physics and Upper-Atmosphere Research Group,
Department of Applied Mathematics, University of Sheffield,
Hicks Building, Hounsfield Road, S3 7RH, England, UK,
Abstract
It is well known that the solar atmosphere is strongly magnetically
structured. The simples examples of magnetic structures are single
magnetic interfaces, magnetic slabs and magnetic tubes. We
consider the nonlinear waves propagation in magnetically
structured plasmas. We start from studying nonlinear surface
waves on magnetic interfaces and discuss the equation governing
the propagation of these waves. We present the results of a
numerical solution of this equation. Then we discuss various
generalizations of the governing equation. We proceed to studying
slow nonlinear waves in magnetic slabs. We present the
Benjamin-Ono equation describing nonlinear slow sausage surface
waves in magnetic slabs, and discuss its solutions in the form of
algebraic solitons. We also briefly describe the extension of the
Benjamin-Ono equation for more complicated slab-like magnetic
structures. Finally, we consider nonlinear slow sausage waves in
magnetic tubes. We briefly discuss the derivation of the
Leibovich-Roberts equation for slow sausage waves and present
the results of its numerical study. We complete the review with
presenting the governing equation for non-axisymmetric surface
waves in a thin magnetic tube in an incompressible plasma.
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On the continuous spectrum of leaky MHD modes
m
Jesse Andries* and Marcel Goossens
Centrum voor Plasma Astrofysica, KULeuven, Belgium
Abstract
When the MHD operator is considered on an unbounded spatial
domain the self-adjointness of the operator can still be established,
resulting in the fact that eigenfrequencies are necessarily either
real or imaginary, and that a complete spectral representation can
be constructed. Nevertheless, considering an unbounded domain
removes one of the boundary conditions (at the boundary which is
moved to infinity) resulting in the appearance of additional
continuous spectra as infinity becomes a singular point in the
equations. These additional leaky continuous spectra are the MHD
analog of the free electrons in the quantum mechanical model of
the hydrogen atom. As soon as the spatial domain is unbounded
the continuous spectrum does not only consist of the classical
Alfvén and slow continuous spectrum, but is to be extended with a
fast and slow leaky continuous spectrum. The eigenmodes that are
associated with the leaky MHD continuum are shown to be
improper in the sense that they carry an infinite amount of energy
(just like the Alfv´en continuum modes, or the Case – van
Kampen modes in Vlasov plasmas), and are therefor not contained
in the Hilbert space of square integrable functions. The unstable
leaky modes found by Wilson (1981), Spruit(1982) and Cally
(1986) are quasi-modes and are found by continuation of the
Green’s function into the lower half of the complex frequency
plane. The physical relevance of these modes in the context of the
observed damping of oscillations in the solar corona is subject of a
debate by Ruderman and Roberts (2006) and Cally (2006). The
present discussion is intended to shed light on the debate and to
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clarify at least the mathematical status of the unstable leaky quasimodes in terms of the mathematical process of continuum
damping.
*Postdoctoral Fellow of the National Fund for Scientific Research
- Flanders (Belgium) (F.W.O.-Vlaanderen)
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A mechanism for parallel electric field generation in the MHD
limit: possible implications for coronal heating
problem in the two stage mechanism
David Tsiklauri
Institute for Materials Research, University of Salford,
Greater Manchester, M5 4WT, United Kingdom
Abstract
Using Particle-In-Cell simulations i.e. in the kinetic plasma
description Tsiklauri et al. and Genot et al. recently reported on a
discovery of a new mechanism of parallel (to the ambient uniform
magnetic field) electric field generation, which results in electron
acceleration. This new effect takes place when an Alfvén wave
moves along the field in the plasma which has transverse density
inhomogeneity. The progressive distortion of the Alfvén wave
front due to differences of local Alfvén speed then generates the
parallel electric field. In this work we show that the parallel (to the
uniform unperturbed magnetic field) electric field generation can
be obtained in much simpler framework using ideal MHD
description, i.e. without resorting to complicated wave particle
interaction effects such as ion polarisation drift and resulting space
charge separation which is the ultimate cause of electron
acceleration. Within ideal MHD the parallel electric field appears
due to fast magnetosonic waves which are generated by the
interaction of weakly non-linear Alfvén waves with the transverse
density inhomogeneity. Further, in the context of the coronal
heating problem a new two stage mechanism of the plasma
heating is presented by putting emphasis, fi rst, on the generation
of parallel electric fields within ideal MHD description directly,
rather than focusing on the enhanced dissipation mechanisms of
the Alfvén waves and, second, dissipation of these parallel electric
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fields via kinetic effects. It is shown that a single Alfvén wave
harmonic with frequency (υ = 7 Hz), (which has longitudinal
wavelength λA= 0.63 Mm for putative Alfvén speed of 4328
km/s) the generated parallel electric field could account for the
10% of the necessary coronal heating requirement. We conjecture
that wide spectrum (10-4 – 103 Hz) Alfvén waves, based on
observationally constrained spectrum, could provide necessary
coronal heating requirement. Exact amount of energy that could be
deposited by such waves under our mechanism of parallel electric
field generation could only be calculated once fuller parametric
study is done. In other words "theoretical spectrum" of the energy
stored in parallel electric fields versus frequency needs to be yet
obtained. It is also shown that the amplitude of generated parallel
electric field exceeds the Dreicer electric field by about four
orders of magnitude, which implies realisation of the run-away
regime with the associated electron acceleration.
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Invited Review: Solitons in Flux Tubes: from Shaping
Sunspots to Coronal Structure Formation
M. Ryutova
Lawrence Livermore National Laboratory/IGPP
L-413, CA 94550, USA
Abstract
Flux tubes in highly dynamic environment with source and sink of
energy do not obey the local conservation laws; far less the
ensembles of flux tubes that exhibit collective wave phenomena.
Seemingly complex approach of energetically open nonlinear
dissipative systems makes the explanation of many observed
phenomena simple and easy. I'll discuss two problems associated
with nonlinear waves in flux tubes: (1) the origin of moving
magnetic features (MMFs) around sunspots and their impact on
dynamics of overlying atmosphere, and (2) soliton gas above the
``unipolar'' plages providing generation of the amorphous
emission at coronal temperatures. In the first part I'll describe all
types of MMFs (for now at least 5 different types of MMFs are
discussed in literature) on basis of evolutionary soliton- and
shock-like formations, and corresponding response of overlying
atmosphere that depends on their type. Several multi-wavelength
datasets allowed us to study hundreds of MMFs and their
signatures in the overlying atmosphere, and bring the theory to
numbers. I'll also mention a new phenomenon discovered during
these observations, consisting in fact that as an ensemble, MMFs
seem to suppress the formation of large scale ``stable'' coronal
loops; in other words, such loops avoid regions of penumbra
highly populated by MMFs. This fact still needs to be explained,
although some hypothesis have been proposed. In the second part
I'll describe the observed properties of the amorphous coronal
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emission evolving in space and time, and show how well these
properties fit the behavior of a soliton gas produced by the
ensemble of non-collinear oscillating flux tubes distributed over
the space with the filling factor corresponding to plage regions.
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Finite beta wave propagation near magnetic null points
James Mclaughlin and Alan Hood
Mathematical Institute, University of St
Andrews, St. Andrews (Scotland)
Abstract
Previous work has looked at the propagation of fast waves near a
magnetic null point in the cold plasma limit. The inclusion of a
small uniform gas pressure means that the plasma beta varies from
smaller than unity away from the null point to extremely large at
the null point. There is a circle (defined by beta approximately
unity) at which the small beta fast wave is converted into a high
beta fast and slow wave. The implications for wave dissipation are
considered.
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Interaction of MHD Waves with Corona Magnetic Null-Points
N.P. Young (1), V.M. Nakariakov (1), C. Foullon (2),
E. Verwichte(1)
(1) University of Warwick, Coventry, UK
(2) MSSL, University College London, UK
Abstract
In recent work we have proposed a model for production of
quasiperiodic pulsations in flaring light curves through the
triggering
of
reconnection
by
small-amplitude
fast
magnetoacoustic waves via current driven microinstabilities
(Nakariakov et al. 2006). Using a 2D numerical simulation (the
Lare2d code) with finite plasma-beta and resistivity, we model the
interaction of a periodic fast wave with a coronal magnetic null
point. We observe the incoming wavefront wrap around the
neutral point (similar to the zero-beta simulations of McLauglin&
Hood 2004), producing a current density spike at the null point
and current sheets along the separatrices. Finite plasma-beta and
resistivity allow the wavefront to both pass through the null point
and to dissipate. As a result, if the wave period is sufficiently long,
each incoming wavefront results in a distinct peak in the
maximum current density. A sufficiently long-period harmonic
fast wave produces quasi-periodic aharmonic variation of the
current in the vicinity of the null point. The modelling
demonstrates that the modulation depth of the current is much
greater than the initial amplitude of the wave and could be
sufficiently large to trigger microinstabilities and hence
anomalous resistivity. This would result in periodic triggering of
magnetic reconnection and thus the observed quasi-periodic
pulsations in flaring light curves. This effect can easily explain the
observed patchy spatial structure of the quasi-periodic energy
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releases in two-ribbon solar flares.
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Swing Absorption of compressional waves in inhomogeneous
magnetized plasma
B.M. Shergelashvili, T.V. Zaqarashvili, S. Poedts and B. Roberts
Abstract
The recently suggested swing interaction between fast
magnetosonic and Alfvén waves is generalized to inhomogeneous
media. We show that the fast magnetosonic waves propagating
across an applied non-uniform magnetic field can parametrically
amplify the Alfvén waves propagating along the field through the
periodical variation of the Alfvén speed. The resonant Alfvén
waves have half the frequency and the perpendicular velocity
polarization of the fast waves. The wavelengths of the resonant
waves have different values across the magnetic field, due to the
inhomogeneity in the Alfvén speed. Therefore, if the medium is
bounded along the magnetic field, then the harmonics of the
Alfvén waves, which satisfy the condition for onset of a standing
pattern, have stronger growth rates. In these regions the fast
magnetosonic waves can be strongly absorbed, their energy going
in transversal Alfvén waves. We refer to this phenomenon as
Swing Absorption. This mechanism can be of importance in
various astrophysical situations.
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Session 2: Magnetic Helioseismology and Waves in Sunspots
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Invited Review: Magnetic helioseismology and waves in
sunspots
R. J. Rutten
Sterrenkundig Instituut, Universiteit Utrecht, P.O. Box 80000,
NL-3508 TA Utrecht, The Netherlands.
Abstract
I will review sunspot waves emphasizing observations of umbral
flashes and running penumbral waves. I believe these to be closely
similar to acoustic internetwork waves, but field guided, and ripe
for full explanation through MHD simulation.
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Responses of helioseismic f modes on atmospheric effects in
analytical MHD models
Balázs Pintér and Róbert Erdélyi
Department of Applied Mathematics, The University of Sheffield
Abstract
The helioseismic fundamental (f) mode is investigated in plane
parallel hydrodynamic (HD) and magnetohydrodynamic (MHD)
solar models, which consist of three layers of incompressible
plasma. The lower, semi-infinite layer is the solar interior with
constant density and plasma pressure decaying linearly with
height. Two overlaying upper layers, representing the solar
atmosphere, are embedded in a horizontal canopy-like magnetic
field. The top semi-infinite layer is the corona with exponentially
decaying density, plasma pressure and magnetic field strength. In
the intermediate (transitional) layer, the plasma density is constant
while the magnetic field increases with height continuously from
zero to its maximum value. It is shown, that the f mode can be
coupled resonantly to a local incompressible Alfvén wave in the
transitional layer, which results in damping of the f mode, due to
resonant absorption. Solutions (both analytic and numerical) of the
dispersion relation are obtained for a magnetic-field-free (HD)
model with a transitional layer of non-zero thickness and also for a
magnetic (MHD) model in the thin-transitional-layer
approximation. We focus on the shifts of the f mode frequency
caused by the atmospheric magnetic field and the line width
variation due to resonant absorption.
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Local Helioseismology of Small Magnetic Elements
A.C. Birch (1), T.L. Duvall, Jr. (2), L. Gizon (3),
S. Hanasoge (4)
(1) NWRA/CoRA, Boulder, CO USA
(2) Laboratory for Solar and Space Physics NASA/Goddard Space
Flight Center Greenbelt, MD USA
(3) Max-Planck-Institut fuer Sonnensystemforschung
Katlenburg-Lindau, Germany
(4) W.W. Hansen Experimental Physics Laboratory
Stanford University USA
Abstract
We show helioseismic observations of the scattering of f modes
from small quiet-Sun magnetic elements. These measurements are
approximately consistent with a toy model in which small
magnetic elements act as monopole and dipole scatterers. We
show that in a simple model for the scattering of acoustic waves
by a magnetic cylinder the Born approximation can be used when
the magnetic field strength is sufficiently weak, but is not always
valid in the limit of small tube radius. We discuss progress in
modeling the scattering of waves by thin flux tubes.
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Invited Review: Effects of surface magnetic field on
Helioseismology
Rekha Jain
Applied Mathematics, University of Sheffield
Abstract
In this talk, the effect of surface magnetic fields on
helioseismology will be discussed. The amplitudes, frequencies
and the travel times of p-modes are altered by the presence of
magnetic fields. Amplitudes are suppressed in the p-band
frequencies. The global frequency shift in p-modes is induced by
solar magnetic activity and the local frequency shifts are induced
by the movement of magnetic region. The travel times of the
acoustic waves are also affected due to the change in the acoustic
cut-off frequencies in the presence of a horizontal field. In this
talk, I will discuss these issues using relevant data analysis and
theoretical work.
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Invited Review: MHD waves in sunspot regions, excited by
solar flares
A. G. Kosovichev
Stanford University
Abstract
Helioseismic response to solar flares ("sunquakes") provides
unique opportunity for direct observations of the interaction of
magnetoacoustic waves with sunspots. These waves are excited by
strong hydrodynamic impact caused by shocks generated by highenergy particles, and are observed as expanding circular-shape
ripples on the surface. The waves propagate through surrounding
sunspots regions, allowing us to observe changes in their
properties, wave speed, amplitude and travel times. I present the
results for several cases, obtained from the MDI instrument on
SOHO, showing new unexpected properties of sunquakes, such as
small distortion of wavefronts in sunspots, large variations of the
decay time, and very strong anisotropy. These results challenge
the current theories of MHD waves in sunspots. Sunquake
observations provide new means for helioseismic diagnostics of
magnetic regions.
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Multi-wavelength detection of 3 minute oscillations in and
around sunspot
D. Banerjee (1), Chia-Hsien Lin(2), E. O’Shea(3), J.G. Doyle(3)
(1) Indian Institute of Astrophysics, Koramangala, bangalore
560034, (2) Astronomy Department, Yale University, 260
Whitney Ave., New Haven, CT06511, (3) Armagh Observatory,
College Hill, Armagh BT61 9DG, N. Ireland
Abstract
We use CDS/NIS time series and images from MDI, CDS,
TRACE and EIT to investigate the chromospheric and transition
region dynamics above the active region AR0554. We examine
the extent and range of 3-min oscillations from a range of features.
Among all the NIS spectral lines analysed, significant oscillations
were found in Si xii 520 °A, Mg x 625 °A, O v 629 °A and He i
522 °A. We found that weak but significant 3-min oscillations are
not confined to the umbra/plume but can be seen in many bright
locations. To find the possible sources of these 3-min oscillations
outside the umbra, we compared the oscillations of single pixels in
different regions. The results of our comparison indicate a possible
connection between the magnetic fields and the oscillations.
Therefore, we suggest that 3-min oscillations may exist in many
magnetic structures. We also detected signatures of a moving
magnetic monopole up to the transition region, suggesting that the
monopole, despite being small, can influence the dynamics in the
upper atmosphere layers.
29
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Session 3: MHD Waves in the Lower Atmosphere
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Invited Review: Dynamics and magnetic coupling in the lower
solar atmosphere
Robert Erdélyi
Solar Physics and Upper-Atmosphere Research Group,
Department of Applied Mathematics, University of Sheffield,
Hicks Building, Hounsfield Road, S3 7RH, England, UK,
email: [email protected]
Abstract
The interaction between solar photospheric coherent motions, e.g.
acoustic or p-modes have important implications for the dynamics
of the solar atmosphere ranging from the low chromosphere even
deeply into corona. Combined high spatial and time resolution
observations (SOHO, TRACE, SVT in La Palma) supplemented
with MHD modelling demonstrated the p-mode leakage into the
chromosphere, transition region and low corona. In my talk I
review the latest results available in the literature on how
photospheric motions interact with the magnetic structures of the
transitional layer between the photosphere and the corona. A
comprehensive study of this transitional layer, also called solar
atmospheric boundary layer, allows us to perform lower
atmospheric magneto-seismology. Theoretical and observational
efforts on the coupling mechanism(s) of coherent and random
motions and fields to the low atmosphere will be discussed. Key
issues will be addressed, including what dynamic impact the
photosphere has on the overlaying magnetic atmosphere; what is
the role of magnetic wave guides in the photosphere chromosphere - transition region dynamics; what are the possible
scenarios and physical details of the boundary layer coupling
mechanism(s); how p/f-modes resonantly interact to lower
atmospheric MHD slow and Alfvén waves; how the coupling
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could be used for diagnostics, lower atmospheric magnetic
seismology and connectivity studies.
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Waveguiding of P-modes Into The Solar Corona
M. S. Marsh
NASA Goddard Space Flight Center, USA
Abstract
Magneto-hydrodynamic (MHD) wave modes propagating from
the photosphere into the corona may be exploited as an
observational tool in an analogous way to the use of acoustic
waves in helio/terrestrial seismology. P-modes are thought to
undergo mode conversion to slow magneto-acoustic waves in
regions of strong magnetic field. Using new spectroscopic
imaging data at transition region temperatures, combined with
coronal imaging, observations are presented of the propagation of
these slow magneto-acoustic p-modes through the transition
region and into the solar corona along active region magnetic eld.
The prospects for new observations with STEREO and Solar-B
are also discussed.
34
MHD waves in magnetically twisted vertical solar flux tubes
Robert Erdélyi (1), Viktor Fedun (2)
(1,2) Solar Physics and upper-Atmosphere Research Group,
Department of Applied Mathematics University of Sheffield,
Hounsfield Road, Hicks Building, Sheffield, S3 7RH, UK
Abstract
Recent high-resolution satellites clearly prove the existence of
wide range of theoretically predicted MHD waves in solar
atmospheric magnetic structures. A detailed analysis of these ways
provides us excellent diagnostic tools of the magnetic waveguide
structure (loops, arcades) they propagate in. In this work we
elaborate on effects due to the presence of magnetic twist in
cylindrical magnetic waveguides. The propagation of surface and
body linear MHD modes in a twisted magnetic flux tube
embedded in a magnetically twisted plasma environment is
considered. Two distinct cases are considered: (i) incompressible
twisted flux tube and magnetised plasma environment, and, (ii)
compressible twisted flux tube with an unmagnetised plasma
environment. The dispersion relation for surface and body modes
are derived assuming constant external twisted field for case (i).
For the compressible case (i.e. more directly relevant for and
applicable to coronal waveguides) the external twisted field is
zero. Analytic approximate solutions to the dispersion equations
are found for the long and short wave limits, respectively.
Solutions of linear the dispersion relations are obtained
numerically for intermediate wavelengths. It was found, that in
case the twisted component of the external magnetic field in the
environmet is constant, the index of Bessel functions in the
corresponding dispersion relation is not integer any more in a
general incompressible plasma. This new feature gives rise to a
35
reach mode-structure of denegerated magneto-acoustic waves in
the flux tubes. In the particular case of 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 also 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. Further detailed analysis is
necessary in order to find the dispersion relation for more realistic
cases, where the magnetic twist diminishes with distance from the
tube. Finally, observational relevances will be discussed in light of
the resolution capabilities of Solar-B and SDO.
36
Dynamics of the lower atmosphere in internetwork regions
Sven Wedemeyer-Böhm, Oskar Steiner
Kiepenheuer-Institut für Sonnenphysik, Freiburg, Germany
Abstract
For a long time the chromosphere in internetwork regions of the
quiet Sun was regarded as a static and homogeneous layer. Thanks
to the pioneering work by Carlsson & Stein but also due to
advances on the observational side, the wave nature of these
atmospheric regions received increasing attention during the last
decade. We present results of recent three-dimensional radiation
magnetohydrodynamic simulations with CO5BOLD that show the
chromosphere of internetwork regions as a dynamic and
intermittent phenomenon. It is a direct product of interacting
waves that form a mesh-like pattern of hot shock fronts and cool
post-shock regions. The waves are excited self-consistently in the
lower layers of the model and provide enough acoustic power to
counterbalance radiative losses in the (low) chromosphere. We
also find that the average power spectrum based on synthetic UV
intensity maps can match power spectra derived from the 160 nm
channel of TRACE. However, in the middle chromosphere above
an average height of 1000 km, plasma beta gets larger than one
and magnetic fields become more important. The model
chromosphere exhibits a magnetic field that is much more
homogeneous than in the layers below and evolves much faster.
That includes fast propagating (MHD) waves. We will discuss the
consequences for atmospheric structure of the lower atmosphere,
including the capability of explaining apparently contradicting
diagnostics such as carbon monoxide and UV emission at the
same time. We consider this class of models as a fundament for a
comprehensive, dynamic model of the lower solar atmosphere.
37
Chromospheric oscillations from quiet Sun millimeter
observations
M. A. Loukitcheva (1), (2), S. K. Solanki (2), S. White (3)
(1) Astronomical Institute of St. Petersburg University, Russia
(2) Max-Planck-Institut fuer Sonnensystemforschung, Germany
(3) Astronomy Department, University of Maryland,
United States
Abstract
In this contribution we analyze the millimeter intensity spectrum,
expected from the radiation-hydrodynamic simulations of the solar
non-magnetic atmosphere of Carlsson & Stein, together with the
interferometric observations of the quiet Sun, obtained at a
wavelength of 3.5 mm with the Berkeley-Illinois-Maryland Array.
Model radio emission at millimeter wavelengths is found to be
extremely sensitive to dynamic processes in the chromosphere, if
these are spatially and temporally resolved. The estimated
millimeter brightness temperatures are time-dependent, following
changes in the atmospheric parameters, and clear signatures of
waves with a period of 180 s (corresponding frequency of 5.5
mHz) are seen in the radio intensity as a function of time. With
BIMA data we have constructed two-dimensional maps of the
solar chromosphere with a resolution of 1000, which represents
the highest spatial resolution achieved so far at this wavelength for
non-flare solar observations. Intensity oscillations with RMS
brightness temperature amplitudes of 50-150 K in the frequency
range 1.5-8 mHz are found to be significant in the data. There is a
tendency toward short period oscillations in the quiet Sun
internetwork and longer periods in active regions and the network.
Most of the oscillations are short wave trains lasting for typically
1-3 wave periods. A correspondence between the model
38
predictions based on the RHD simulations of Carlsson and Stein
and the observational data can be established under assumptions
on the horizontal coherence length of the oscillations (of order of
100). We also give estimates of the influence of the limited
available spatial and temporal resolution of observations on the
comparison with the model predictions. We argue that millimeter
continuum observations promise to be an important diagnostic of
the chromospheric dynamics and the appropriate wavelengths to
look for dynamic signatures are in the range 0.8-5.0 mm.
39
40
Session 4: Prominence Oscillations
41
Prominence oscillations (observations)
Ramón Oliver
Departament de Física, Universitat de les Illes Balears,
07122 Palma de Mallorca, Spain
Abstract
The evolution of our observational knowledge of prominence
oscillations is reviewed, from the very first detections of this kind
of phenomenon to the most recent developments, acquired from
ground- and space-based observations. A discussion of future
research trends in this area is given.
42
Evidence for propagating waves in a quiescent filament
Yong Lin(1), Oddbjorn Engvold (1), Luc Rouppe van der Voort (1
; 2), Michiel van Noort (1;3)
(1) Institute of Theoretical Astrophysics, University of Oslo
PO Box 1029, Blindern, N-0315 Oslo, Norway
(2) Center of Mathematics for Applications, University of Oslo
PO Box 1053 Blindern, N-0316 Oslo, Norway
(3) The Institute for Solar Physics of the Royal Swedish Academy
of Sciences
AlbaNova University Center, SE-106 91 Stockholm, Sweden
Abstract
The high resolution Hα filtergrams (0.2 arc sec) used in this study
were recently obtained with the Swedish 1-m Solar Telescope
(SST). These images resolve numerous very thin, thread-like
structures in solar filaments. The threads are thought to represent
sections of thin magnetic flux tubes longer than the observable
threads. Time series of Hα filtergrams and derived Dopplergrams
both revealed counterstreaming with typical speeds of 5-10 km/s
in opposite directions along adjacent threads as previously shown.
We hereby report our new finding of small amplitude (-3 to 3
km/s) waves propagating along a number of the thin threads with
vph ≈ 12 km/s and wavelength ≈ 6 arc sec. Also, the temporal
variation of the Doppler velocities averaged over a small area (3.4
x 10 arc sec) where filament threads are closely packed, shows a
short period (3.6 min) wave pattern. These short period
oscillations could possibly represent so-called string and internal
Love modes in accordance with numerical fibril models derived
by Joarder, Nakariakov and Roberts (1997). In some cases, it is
clear that the propagating waves are moving in the same direction
as the mass flows.We suggest that the flows in filaments may be
43
accelerated by weakly damped waves.
44
Oscillations in a filament with CDS(SOHO): first observation
of long periods in the HeI 584.33 line,
modelling and diagnostic
Guillaume Pouget, Karine Bocchialini, Jacques Solomon
Institut d'Astrophysique Spatiale
Abstract
Three long observations of filaments were carried out, in the
584.33 He1 line, during MEDOC campaigns in 2003 and 2004, by
CDS (Coronal Diagnostic Spectrometer) onboard SOHO. Their
duration is of the order of 15-16 hours. The Fourier analysis of the
Doppler velocities in the filament allows us to detect very slow (57 h) velocity oscillations; faster oscillations are also detected, at a
smaller level. We discuss the possibility of an interpretation of
these velocity oscillations considering the prominence model of
Joarder and Roberts (1993), which treats the prominence as a
whole plasma slab. We use a systematic method to identify,
among the frequencies detected, the six fundamental modes
predicted by the model. If the identification is successful, it
provides a complete diagnostic of the filament, in terms of Alfven
speed, temperature, and angle between the magnetic field and the
main axis of the filament.
45
Theory of small-amplitude prominence oscillations: Historical
review
J. L. Ballester
Dept. Física. Univ. Illes Balears.
E-07122 Palma de Mallorca (Spain)
Abstract
Nowadays, an extense observational background about smallamplitude oscillations in solar prominences has been gathered.
From the beginning of nineties, simple theoretical models to
explain these oscillations have been developed, but they are still
far from the complexity needed to reproduce the reality. Here, I
plan to review, in a historical way, theoretical developments about
small-amplitude prominence oscillations.
46
Filling factor on prominence oscillations
A. J. Díaz & B. Roberts
Mathematical Institute, University of St Andrews,
St Andrews, KY16 9SS, Scotland (UK)
Abstract
During recent years a number of observations of prominence
oscillations have been reported. These data is used for prominence
seismology with the help of theoretical oscillatory models of
prominences as homogeneous slabs. However, it is well known
that there is a fine structure, whose effect in the global oscillations
has been neglected. Here we discuss the role of this fine structure
and show that the homogeneous model should take into account at
least the filling factor, since it may lead to important shifts in the
measured periods of certain modes.
47
48
Session 5: Waves in the Corona. MHD Coronal Seismology
49
Invited Review: Current trends in MHD Coronal Seismology
V.M. Nakariakov
Centre for Fusion, Space & Astrophysics,
University of Warwick, Coventry CV4 7AL, United Kingdom
Abstract
The review presents the current trends in the observational and
theoretical aspects of remote diagnostics of the solar coronal
plasma by magnetohydrodynamic waves and oscillations. Physical
mechanisms responsible for the observed periodicities and wave
signatures are discussed. Coronal seismological methods for the
estimation of the magnetic field in active regions, for probing the
transverse sub-resolution structure of coronal loops and for the
study of the coronal heating function are presented.
50
Slow magnetoacoustic waves in curved hot coronal loops
Zaqarashvili, T.V., Oliver, R., Ballester, J. L., Terradas, J.
Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
Abstract
Recent observations by SUMER spectrometer on SOHO show the
rapidly damped standing slow magnetoacoustic waves in hot
coronal loops. Several different mechanisms can be responsible
for the damping of the oscillations but, so far, only straight
magnetic tube has been used for modelling the oscillations.
However the loop curvature can be of importance in the dynamics
of lower order harmonics. Here we study the infuence of curvature
on the standing slow magnetoacoustic waves in hot coronal loops
embedded in the cool environment. It is shown that the first
harmonic of the slow magnetoacoustic standing waves is rapidly
damped due to the energy leakage by fast waves from the loop
outer boundary. The damping time is shorter for wider loops.
Theoretically estimated damping rate seems to be in perfect
agreement to the observations (Wang et al. 2003).
51
Transverse oscillations in coronal loops: the effects of
curvature and transverse structuring
E. Verwichte (1), C. Foullon (2), V. M. Nakariakov (1),
C. S. Brady (3) & T. D. Arber (1)
(1) Department of Physics, University of Warwick,
Coventry CV4 7AL, UK
(2) Mullard Space Science Laboratory, University College
London, Holmbury St. Mary, Dorking, Surrey RH5 6NT, UK
(3) School of Mathematics and Statistics, University of St
Andrews, St Andrews, Fife KY16 9SS, UK
Abstract
Transverse loop oscillations have first been reported in 1999 using
EUV image sequences and are interpreted as fast magnetoacoustic
kink modes, impulsively excited by a nearby flare or eruption.
Such modes offer a unique seismological tool for determining the
strength of the local coronal magnetic field. Moreover, the
observed rapid decay of these modes has received much interest as
it cannot be explained by straightforward dissipation. Stock is
taken of the achievements and current developments. In particular,
the effects of curvature and transverse structuring on the
behaviour of transverse loop oscillations are modelled. It is shown
that for a range of realistic loop structures, wave energy naturally
leaks out of the loop through the mechanism of wave tunneling.
The efficiency of this damping mechanism is discussed.
Furthermore, the potential of this model for coronal seismology is
explored and a few examples of comparisons with observations
are given.
52
Invited Review: Global coronal seismology
Istvan Ballai
SPARG, Dept. of Applied Mathematics, University of Sheffield,
Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
Abstract
Large scale eruption events in the solar atmosphere can generate
global waves, i.e. waves which 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. Since EIT
waves carry information about their environment, they can be used
for diagnostics of, e.g. the local and global magnetic field. This
contribution presents theoretical models for finding values of
magnetic field in the quiet Sun and coronal loops based on the
interaction of global waves and coronal loops. We will also
explore the physical connection between local and global solar
coronal events (e.g. flares, EIT waves and coronal loop
oscillations).
53
Coronal loop oscillations: Collective behaviour and damping
in a system of two coronal slabs
I. Arregui, J. Terradas, R. Oliver, & J. L. Ballester
Departament de Física, Universitat de les Illes Balears
E-07122 Palma de Mallorca, Spain
Abstract
The magnetohydrodynamic normal modes of oscillation of a sys
tem of two coronal slabs including longitudinal propagation is
studied. The period and damping rate of the collective resonantly
damped mode is computed for different values of the longitudinal
propagation and of several equilibrium parameters such as the
width of the inhomogeneous layers, the distance between the slabs
and their density contrasts. The obtained results are then compared
with the oscillatory properties of single-loop equilibrium models.
54
Random heating excitation of waves in solar coronal loops
César A. Mendoza-Briceño (1), Robert Erdélyi (2)
(1) Centro de Física Fundamental, CFF, Facultad de Ciencias,
Universidad de Los Andes, Apartado Postal 26, La Hechicera,
Mérida 5251, Venezuela, [email protected]
(2) Solar Physics & Upper-Atmosphere Research Group,
Department of Applied Mathematics, University of Sheffield,
Hicks Building, Hounsfield Road, S3 7RH, England, UK,
[email protected]
Abstract
In a recent work by Mendoza-Briceño et al. (2005) ApJ, 625, 1080
the dynamic response and heating efficiency of coronal plasma to
a series of random impulsive heating was studied in coronal loops.
In the present work we focus on the nature of oscillatory patterns
that appear during the evolution of coronal loops undergoing
impulsive heating through the release of localized energy pulses
near the loop's footpoints. We investigate these oscillatory patterns
by using wavelet analysis technique. We found periodic features,
like wave packets, with periods of 150-220, 500-600 and 8001000 s. These periods are also found to scale (increase) with the
loop length and decrease with the length of the loop segments
along which the pulses are injected. Implications of our results
upon the latest coronal observations are also briefly discussed.
55
Possible methods to determine if a magnetic field is constant
or varying along a coronal loop by direct observation of fast
kink standing mode oscillations
G.Verth and R. Erdélyi
Department of Applied Mathematics
University of Sheffield,
Sheffield, S3 7RH, UK
Abstract
One of the mysteries of coronal loops is that they do not appear to
vary in width with increasing height in the corona. A flux tube of
constant width suggests that the magnetic field strength is constant
along a loop. This is in contradiction with potential extrapolation
models based on magnetogram data that always produce B fields
decreasing in strength with distance from photospheric magnetic
sources. Our recently developed MHD theory may be used to
determine if a magnetic field is constant or varying along a
coronal loop by direct observation of standing fast kink mode
oscillations.
56
Invited Review: Numerical simulations of impulsively
generated waves in solar coronal loops
K. Murawski
Group of Astrophysics and Gravity Theory,
Institute of Physics, UMCS, 20-031 Lublin, Poland
Abstract
We present numerical results of a temporal evolution of impul
sively triggered magnetosonic waves in solar coronal loops that
are approximated by mass density enhancement regions. We
discuss both monolithic and multi-stranded slabs and loops. In
particular, in a case of a monolithic slab we show a simultaneous
presence of standing slow and fast magnetosonic waves. We show
that standing slow waves in an arcade loop can be excited by a
pulse launched at a foot-point. Such pulse is able to trigger a
distortion mode, leading to asymmetric oscillations which are
distinct from the vertical or horizontal kink oscillations. We show
that these oscillations are affected by a constant gravity which
alters their excitation and attenuation times. As examples of multistranded structures we discuss propagating waves in two parallel
identical slabs and standing fast magnetosonic kink waves in a
two-stranded arcade loop. The results of the numerical simulations
reveal wave signatures which are reminiscent of recent TRACE
observations.
57
Detection of slow magnetoacoustic waves in open field regions
E. O'Shea, D. Banerjee, J. G. Doyle
Armagh Observatory
Northern Ireland
Abstract
Using time series data obtained from the CDS instrument on
SOHO, we will present results of a statistical study of phase
delays measured between oscillations in intensity (flux) and
between oscillations in line-of-sight velocity. These measurements
allow for the identification of compressional MHD waves present
in the open field regions being studied, that is, in off-limb polar
regions and in on-disk coronal holes, which may be responsible
for the (fast) solar wind acceleration. From a calculation of
propagation speeds, we show that it is slow magnetoacoustic
waves that produce the observed time delays between the
oscillations of the transition region and coronal spectral lines. The
evidence for a change in the propagation speeds of the observed
waves in open field locations off-limb at the poles as opposed to
similar open field regions in equatorial and polar coronal holes on
the disk of the Sun will be discussed as will the evidence for a
resonant cavity effect to be present at coronal temperatures.
58
Global Sausage Modes of Coronal Loops
D. J. Pascoe (1), V. M. Nakariakov (1), T. D. Arber (1)
(1) University of Warwick, Coventry, CV4 7AL, UK
Abstract
Symmetric fast magnetoacoustic perturbations of solar coronal
loops (sausage, or m = 0 modes) are modelled using the Lare2d
code. Analytical theory predicts the existence of trapped global
modes of this kind in sufficiently thick and dense loops only, with
the periods estimated as the ratio of double the loop length and the
Alfvén speed outside the loop. Our numerical modelling
generalises this study to the case of long loops with sufficiently
small density contrast. It was found that these loops can support
global sausage leaky modes of detectable quality and with the
wave numbers smaller than the theoretical cut-off for trapped
modes. The periods of the leaky modes are found to be
approximately determined by the loop length and the external
Alfvén speed. When the loop length can be estimated from
imaging observations, the observed period of this mode provides
us with the seismological information about the Alfv´en speed
outside the loop. For typical flaring loops, the estimated periods of
the global sausage modes are about 10-60 s.
59
On The Period Ratio P1/2P2 in the Oscillations of Coronal
Loops
M. P. McEwan, G. R. Donnelly, A. J. Diaz and B. Roberts
Mathematical Institute, University of St
Andrews, St. Andrews (Scotland)
Abstract
With strong evidence of fast and slow magnetoacoustic modes
arising in the solar atmosphere there is scope for improved
determinations of coronal parameters through coronal seismology.
Of particular interest is the ratio P1/2P2 between the period P1 of
the fundamental mode and the period P2 of its first harmonic. In
an homogeneous medium this ratio is one, but in more complex
configurations P1/2P2 is shifted from unity. We consider
analytically the effects on various MHD modes of structuring and
stratification, pointing out that transverse or longitudinal
structuring or gravitational stratification modifies the ratio P1/2P2.
The departure of P1/2P2 from unity can be used as a seismological
tool in the corona. We illustrate our method by reference to
observations by Verwichte et al. (2004).
60
Seismology of Dynamically Heated Quiescent Coronal Loops
Y. Taroyan (1), R. Erdélyi (1)
(1) Solar Physics and upper-Atmosphere Research Group,
Department of Applied Mathematics University of Sheffield,
Sheffield, S3 7RH, UK
Abstract
The determination of the physical parameters of coronal loops
remains both an observational and a theoretical challenge. A new
diagnostic technique for quiescent dynamically heated coronal
loops, based on the analysis of the power spectra of the Doppler
shift time series, is proposed. It is assumed that a given loop is
heated randomly both in space and time by small-scale discrete
impulsive events of unspecified nature. The results show that
depending on the heliographic position of the loop and the
orientation of the observing instrument various harmonics can be
identified in the power spectra of the line shift time series. The
highest power peak corresponds to the fundamental mode. The
peaks become smaller as the frequency of harmonics increases.
The frequency peaks are sensitive to changes in the average loop
temperature and thus could be used as temperature diagnostic tool.
The analysis of the power spectra also allows to distinguish
uniformly heated loops from loops heated near their footpoints.
The proposed method could, in principle, be used to study the
multi-thermal structure of the loops.
61
Oscillations of solar coronal magnetic loops in microwaves
M. L. Khodachenko 1, A.G. Kislyakov 2, H.O. Rucker 1, V.V.
Zaitsev 3, S. Urpo 4
1
Space Research Institute, Austrian Academy of Sciences,
Schmiedlstr. 6, A-8042 Graz, Austria
([email protected]; [email protected])
2
Lobachevsky State University, Nizhny Novgorod,
Gagarin av., 23, 603950, Nizhny Novgorod, Russia
([email protected])
3
Institute of Applied Physics, Russian Academy of Sciences,
Ulyanov str. 46, 603950, Nizhny Novgorod, Russia
([email protected];)
4
Metsaehovi Radio Observatory,
Metsaehovintie 114, 02540, Kylmaelae, Finland
([email protected])
Abstract
Analysis of the Low-Frequency fluctuations of solar microwave
radiation (37 GHz and 11.7 GHz) appears as a relatively new
direction of investigations in the traditional branch of the
microwave radio astronomy. For this purpose a "sliding window"
Fourier transform combined with the Wigner-Ville technique is
applied. It has been shown that slow variations of the electric
current and associated magnetic field in a source of solar
microwave emission, as well as a large-scale motion of the source,
can modulate the intensity of the received signal. Special attention
in the present study is paid to the analysis of modulations of
62
microwave emission recorded at the same time when TRACE
EUV telescope observed large scale oscillations of coronal loops.
For some events the spatial resolution of the radio telescope at 37
GHz allows also to localize an active region containing the
oscillating loops. The applied data analysis technique, besides of
the modulations probably connected with loop oscillations
detected by TRACE, makes possible to detect additional
modulations, which may be associated with oscillations of smaller
(invisible for TRACE) loops. These modulations can be connected
as well with specific wave modes (sausage mode) excited in solar
coronal structures. Comparative analysis of phases of oscillations
of TRACE loops and the microwave emission modulation allows
deeper insight into the global dynamics and structure of solar
active regions. This makes the analysis of LF modulations of
microwave radiation intensity to be an important and useful tool
for diagnostics of the solar corona.
63
64
Session 6: MHD Waves in Astrophysical Magnetic Structures
65
Invited Review: Magnetoseismology of accretion disks
Rony Keppens (1,2,3), Jan-Willem Blokland (2), Hans
Goedbloed(2,3)
(1) Centre for Plasma-Astrophysics, K.U.Leuven
(2) FOM-Institute for Plasma Physics Rijnhuizen
(3) Astronomical Institute, Utrecht University
Abstract
We review recent insights on magnetohydrodynamic waves and
instabilities in accretion disk models. We apply MHD
spectroscopy, i.e. the ability to compute all waves and instabilities
for a given equilibrium configuration, and use the knowledge that
the continuous parts (Alfvén and slow) in the spectrum form the
basic organizing structure for categorizing the various wave types.
The application of MHD spectroscopy to magnetized accretion
disks is challenging due to the presence of a stationary (i.e.
flowing), gravitationally stratified equilibrium state. In particular,
we point out how:
• the transition from static to stationary equilibria introduces
forward and backward Doppler shifted continua and how the
familiar MHD Alfvén and slow continua reduce to the flow
continuum of a stationary hydrodynamic equilibrium;
• the application of the Frieman-Rotenberg formalism to radially
stratified accretion disks has provided new insights into the nature
and relative importance of the magneto-rotational instability in
accretion flows;
• a fully self-consistent computation of axisymmetric accretion
disk tori and their MHD spectra demonstrated the existence of a
novel class of violently unstable Alfvén continuum modes when
crosssectional poloidal flows exceed the slow magnetosonic
speed. These ‘trans-slow’ Alfvén continuum modes are
66
intrinsically localized to individual flux surfaces, and thus form
ideal candidates to explain the observationally inferred highly
turbulent nature of accretion disks.
67
The periodic variations of stellar flares
M. Mathioudakis (1), S. Bloomfield (1,2), D.B.Jess (1)
(1) Physics and Astronomy, Queens University Belfast, Northern
Ireland
(2) currently at : Max Planck Institute, Katlenburg-Lindau,
Germany
Abstract
The white-light flares observed in cool stars can be as much as
104 times more energetic than their solar counterparts. Multiwavelength observations of stellar flares have revealed the
existence of periodic signatures on the flare light-curves. I will
review some recent observations on the subject and discuss the
application of solar atmospheric seismology techniques to stellar
studies.
68
Damping of hydromagnetic waves by bulk viscosity
Miguel H. Ibáñez S.
Centro de Física Fundamental, Universidad de los Andes,
Apartado 26, Ipostel, La Hechicera, Mérida, Venezuela
Abstract
As it was shown in a previous paper (2004) for certain kind of
plasmas the coefficient of second (bulk) viscosity can be orders of
magnitude larger than the coefficient of the dynamical viscosity
and the thermometric conductivity. At the present paper the
damping effects of the second viscosity on the hydromagnetic
waves propagating in optically thin plasmas is analyzed. In
particular, mhd waves propagating in a photoionized gas of
arbitrary metallicity Z and mean photon energy of the ionizing
photons E where an initial steady magnetic field H is present.
69
Slow nonlinear and shock waves in flux tubes
Y.D.Zhugzhda
IZMIRAN, Troitsk, Moscow Region, 142190 Russia
Abstract
The theory of weakly nonlinear waves in flux tubes is described. It
is pointed out that it is not possible to make a choice between
different model equations obtained in the long-wavelength
approximation. The only way to obtain an adequate description of
slow waves is to use the model equation based on the dispersion
law which has correct limits for short and long waves. Such kind
of model equations for slow surface and body waves are
presented. The model equation for slow shock waves in flux tubes
is presented. This model equation is the extension of KdV-Burgers
equation. It is revealed that along with shock waves the slow body
bore wave occurs in flux tubes. The bore waves are well-known in
hydrodynamics.
70
Session 7: Modern Data Analysis Methods for Wave and
Oscillation Phenomena
71
Invited Review: Modern Data Analysis Methods for
Wave and Oscillation Phenomena
Bernhard Fleck (1), Jack Ireland (2)
(1) European Space Agency, c/o NASA/GSFC
(2) L3Com/GSI, c/o NASA/GSFC
Abstract
Waves and oscillations in the Sun’s atmosphere have been studied
in great detail since the discovery of the 5-min oscillations in the
early sixties. The recent discoveries of oscillations in coronal
structures by SOHO and TRACE have opened new prospects for
”coronal seismology”. In many cases the characterization of the
waves and oscillations is difficult because of a number of
compounding factors. The waves usually have low amplitudes and
thus low signal to noise in the observations, and their nonstationary behaviour in the dynamic, ever-changing atmosphere of
the Sun adds to the complexity. Various methods have been
developed to characterize and analyze waves and oscillations
observed in the Sun’s atmosphere. Most prominent among them
are Fourier methods (power, phase, coherence spectra) and
Wavelet techniques, which have become en vogue in recent years
after their implementation in IDL by Torrence & Compo. Other
techniques have been somewhat overlooked. In this talk we will
review a number of analysis techniques and highlight both their
strengths as well as shortcomings.
72
Application of statistical techniques to the analysis of solar
coronal oscillations
J. Terradas, R. Oliver, J. L. Ballester
Departament de Física, Universitat de les Illes Balears,
07122 Palma de Mallorca, Spain
Abstract
In this work, the application of two different techniques to the
analysis of coronal time series is investigated. The first technique,
called Empirical Mode Decomposition (EMD) can be used to
decompose a signal in its characteristic time scales, allowing,
among other applications, to filter the signal efficiently. The
second technique, called Complex Empirical Orthogonal Function
(CEOF) analysis, is an extension of the well-known Principal
Component analysis. The CEOF analysis allows to identify the
dominant spatial and temporal structures in a multivariate data set
and is thus ideally suited for the study of propagating and standing
features that can be associated with waves or oscillations. The
application of both methods to time series obtained from a coronal
loop are presented here. Detailed two-dimensional information of
a propagating and a standing wave with periods around 5 and 10
min, respectively, is obtained.
73
High frequency oscillations in active regions and sunspots
K. Muglach
Naval Research Laboratory
Washington, (USA)
Abstract
High frequency waves are supposed to play an important role in
the heating of the solar chromosphere according to various
models. Recent oscillation simulations studied the propagation of
waves in a magnetized solar atmosphere. This contribution
presents the results of an observational study of the presence of
high frequency oscillations (υ > 15mHz) in active regions and
sunspots. In addition to standard Fourier techniques we will also
use wavelet transforms to identify the high frequency waves and
test the presence of significant oscillation power statistically.
74
Application of the POD in the study of the solar atmospheric
dynamics
A. Vecchio, G. Cauzzi, K. Janssen
INAF-Osservatorio Astro sico di Arcetri
Largo Enrico Fermi 5, 50125
Firenze, Italy
Abstract
The POD has been traditionally employed to study coherent structures in laboratory turbulent flow and was recently successfully
applied to analyze oscillations (Vecchio et al. (2005)) and
magnetic fields (Cadavid et al.(2005)) in the solar atmosphere We
present here some applications of the POD for the analysis of
periodic signals in the lower solar atmosphere, using both intensity
and velocity data obtained with the imaging interferometer IBIS
(mounted at the DST of NSO). In particular we show how the
technique can isolate the contribution of spatially coherent
phenomena (e.g. magnetic network) maintaining the resolution a
orded by the full eld of view.
Cadavid, A. C.; Lawrence, J. K.; McDonald, D. P.; Ruzmaikin, A.,
Solar Physics, Volume 226, Issue 2, pp.359
Vecchio A. et al., Physical Review Letters, vol. 95, Issue 6, id.
061102
75
Closing Summary: B. Roberts
76
Posters
77
Wave-like magnetic disturbances within solar flux ropes
E. Romashets and S. Poedts
Centre for Plasma Astrophysics, KU Leuven
Abstract
To treat local disturbances in a solar flux rope we consider the
magnetic field in its interior as a superposition of two linear
(alpha=const.) force-free distributions: first a global one, which is
locally similar to a part of a cylinder, and next local toroidal
distribution. The axes of the toroid and the cylinder coincide. The
large and small radii of the toroid are set equal to the cylinder’s
radius. Depending on the field magnitude and the handedness
there is a local decrease or increase of the flux tube diameter. The
different physical nature of processes caused by this
inhomogeneity can lead to motions along the tube or to
oscillations at a given point in the tube. We are going to use this
approach for the interpretation of limb observations. The newly
derived solution for a toroid with an aspect ratio close to unity is
applied, in terms of full elliptical integrals. Force-free toroidal
distributions that are available in the literature (for example Miller
and Turner, 1981) can be applied only to the case of small inverse
aspect ratios.
78
Coronal seismology using periods and damping rates of
oscillating loops
I. Arregui (1), J. Andries (2), T. Van Doorsselaere (2),
M. Goossens (2), & S. Poedts (2)
(1) Departament de Física, Universitat de les Illes Balears
E-07122 Palma de Mallorca, Spain
(2) Centrum voor Plasma Astrofysica, KULeuven,
Celestijnenlaan 200B, B-3001 Heverlee, Belgium
Abstract
We report on how the combination of observational values of the
period and the damping rate of transverse loop oscillations and
theoretical and numerical results for resonantly damped quasimode kink oscillations in non-uniform flux tubes can be used to
extract information on physical parameters in oscillating coronal
loops. Observationally estimated periods and damping rates of
coronal loops are used together with parametric studies of the
period and damping of quasi-mode kink oscillations to calculate
equilibrium models that have the same period and damping rate as
observed through the assumed damping mechanism. The use of
both the observed periods and damping rates allows us to obtain
the valid equilibrium models in the form of a one-dimensional
curve in the three-dimensional parameter space (density contrast;
Alfvén speed; inhomogeneity length-scale). The possible values
for the internal Alfvén speed are found to be restricted to a rather
narrow range, showing also an upper limit. The present method
not only allows the estimation of unknown physical parameters of
coronal loops, but is also a test of the assumed physical damping
mechanism.
79
Fast magnetohydrodynamic oscillations in two cylindrical
coronal loops: Collective behaviour
M. Luna, J. Terradas, R. Oliver, J.L. Ballester
Departament de Física, Universitat de les Illes Balears,
07122 Palma de Mallorca, Spain
Abstract
We study fast magnetohydrodynamic waves in a system of two
coronal loops modeled as smoothed, dense plasma cylindrical flux
tubes in a uniform magnetic field. The time-dependent problem of
the excitation of loop oscillations is analysed by numerically
solving the initial value problem. We investigate the behaviour of
the system for several shapes of planar pulses. This allows us to
study in a simple configuration the collective behaviour of the
structure due to the interaction between the two cylinders. We nd
that for any initial disturbance the loops oscillate with the normal
modes of the coupled system, which are different from the modes
of the individual loops. In addition, we show that for some initial
conditions there is a continuous exchange of energy between the
individual
magnetic
flux
tubes.
80
Time dependent simulations of sideways driven coronal loop
oscillations
Tom Van Doorsselaere (1), Stefaan Poedts (1),
Inigo Arregui (2), Jesse Andries (1)
(1) Centrum voor Plasma-Astrofysica, KULeuven,
Celestijnenlaan 200B, B-3001 Leuven, Belgium
(2) Departament de Física, Universitat de les Illes Balears,
E-07122 Palma de Mallorca, Spain
Abstract
We use the computer code PET to study the time evolution of a
two dimensional cylindrical coronal loop. The coronal loop is
driven monoperiodically from the side in the framework of linear
MHD. When the driver period matches the kink quasi-mode
frequency closely, a resonant layer is formed and damping occurs.
As a result of the resonance, three phases in the time evolution can
be distinguished. Initially, we have a build-up phase when the
resonant layer is set up. In this phase the amplitude of the global
oscillation increases linearly. Secondly, a steady state is obtained.
In this state, the driver energy is exactly dissipated in the resonant
layer. Consequently, the amplitude of the oscillations is constant.
As a last phase, we distinguish the time interval when the driver is
stopped. As expected, in this phase, the global kink oscillation
damps out exponentially. The measured damping times
correspond very closely to the values obtained in the eigenvalue
problem (Arregui et al. 2005). When considering a radially highly
inhomogeneous coronal loop and a large density contrast between
the interior of the loop and the surroundings, the oscillations are
heavily damped. As a result, the build-up phase is very short (only
a few periods) and the amplitude in the steady state is small.
Consequently, after a few cycles, much more driver energy than
81
the energy in the global oscillation is dissipated. The classical
argument that not enough oscillatory energy is observed in the
solar corona to sustain the heating, is therefore invalid. The fact
that little oscillations are observed, does not mean that no
oscillation energy is dissipated. The amount of observed
oscillatory energy is not related to the total energy dissipated by
waves.
82
Time damping of non-adiabatic MHD waves in a multilayer
slab model
R. Soler, R. Oliver, and J. L. Ballester
Departament de Física. Universitat de les Illes Balears,
E-07122 Palma de Mallorca, Spain.
Abstract
We study the time damping of non-adiabatic MHD waves in a
multilayer slab model made of a prominence region, a
prominence-corona transition region and a coronal region.
83
X-ray quasi-periodic pulsations in solar flares driven by
magnetohydrodynamic oscillations in a nearby loop
C. Foullon (1,2), V. M. Nakariakov (1), E. Verwichte (1),
L. Fletcher (3) & N. P. Young (1)
(1) Centre for Fusion, Space and Astrophysics, Department of
Physics, University of Warwick, Coventry CV4 7AL, UK
(2) Mullard Space Science Laboratory, University College London
Holmbury St. Mary, Dorking, Surrey RH5 6NT, UK
(3) Department of Physics and Astronomy, University of Glasgow
Glasgow G12 8QQ, UK
Abstract
In Foullon et al. (2005), we analysed long-period (8-12 min)
quasiperiodic pulsations (QPP) of X-ray radiation during solar
flares, made possible with the Reuven Ramaty High Energy Solar
Spectroscopic Imager (RHESSI), supported by complementary
data at other wavelengths from space-based and ground-based
telescopes. Evidence for the presence of a transequatorial loop
possibly responsible for the detected periodicity connected with its
kink mode was found. Our findings suggested that QPP can be
interpreted as a periodic pumping of electrons in a compact flaring
loop, modulated by oscillations in a magnetically linked and larger
loop acting as a long-period magnetohydrodynamic resonator. Our
new model for quasi-periodic modulation of solar and stellar
flaring emission (Nakariakov et al., 2006) can explain the
coupling of oscillations in nearby loops with QPP of flaring
energy release. The interaction between fast magnetoacoustic
oscillations of a non-flaring loop and a nearby flaring active
region occurs when part of the oscillation situated outside the loop
reaches the regions of steep gradients in magnetic field within an
active region and produce periodic variations of electric current
84
density. The modulation depth of these variations is a few orders
of magnitude greater than the amplitude of the driving oscillation.
The variations of the current can induce current-driven plasma
micro-instabilities and thus anomalous resistivity. This can
periodically trigger magnetic reconnection, and hence acceleration
of charged particles, producing quasiperiodic pulsations of X-ray,
optical and radio emission at the arcade footpoints.
85
Fast and Slow MHD Waves in a Gravitationally Stratified
Corona
A. M. D. McDougall, A. W. Hood and I. De Moortel
School of Mathematics and Statistics.
St Andrews University, St Andrews,
Fife KY16 9SS (Scotland)
Abstract
We wish to investigate the coupling between fast and slow wave
modes in a gravitationally stratified magnetic field. The
investigation has taken the form of a numerical study backed up
by analytical work using, for example, the WKB method. Having
verified the code results, a number of simulations have been run in
order to examine the behaviour and interaction of the different
wave modes across the region where the sound and Alfven speeds
are of comparible size.
86
Resonantly damped oscillations of longitudinally stratified
coronal loops
Maria V. Dymova, Michael S. Ruderman
Department of Applied Mathematics, University of She eld, Hicks
Building, Hounsfield Road, She eld S3 7RH, UK
e-mail: [email protected]
Abstract
Soon after coronal loop oscillations were observed by TRACE
spacecraft for the first time in 1999, various theoretical models
have been put forward to explain the rapid damping of the
oscillations of these intriguing objects. Coronal loop oscillations
are often interpreted as fast kink modes of a straight cylindrical
magnetic flux tube with immovable edges modelling dense
photospheric plasma at the ends of the loop. Taking this model as
a basis we use cold plasma approximation and consider the tube to
be thin to simplify the problem and be able to deal with it
analytically. In its equilibrium state the tube is permeated by a
homogeneous magnetic field directed along the tube axis. We
include the effect of stratification in our model supposing that
plasma density varies along the tube. There is also density
inhomogeneity in the radial direction confined in a layer with
thickness much smaller than the radius of the tube. Considering
the system of linearized MHD equations we study the dependence
of the spectrum of tube oscillations and its damping due to
resonant absorption on the parameters of the unperturbed state.
The implication of the obtained result on coronal seismology is
discussed.
87
Anomalous dissipation of torsional flux-tube waves
T.Siversky, Y.Voitenko, M.Goossens
Centre for Plasma Astrophysics, K.U.Leuven,
Celestijnenlaan 200B, B-3001 Heverlee, Belgium
e-mail: [email protected]
Abstract
Torsional waves and perturbations in magnetic flux-tubes are
efficient agents for transporting energy in the solar corona. We
study a mechanism for the damping of these waves and its
possible role in coronal heating. There is a field-aligned electric
current inside the magnetic flux-tube when the torsional wave
propagates along it. This current is a subject to anomalous
dissipation due to current-driven instability of kinetic Alfvén
waves. We use the kinetic electro-magnetic approach to study this
micro-instability. We found that the cross-field gradient of the
electron current reduces the threshold current velocity for the
instability well bellow the Alfvén velocity.
88
Spatial damping of MHD waves in a prominence medium
M. Carbonell (1), J. Terradas(2), R. Oliver(2) & J. L.
Ballester (2)
(1) Dept. Matemàtiques. Univ. Illes Balears. E-07122 Palma de
Mallorca, (Spain)
(2) Dept. Física. Univ. Illes Balears. E-07122. Palma de Mallorca,
(Spain)
Abstract
Using an energy equation with optically thin radiative losses,
thermal conduction and heating, we have studied the spatial
damping of MHD waves in a prominence medium. The results
point out that at long and intermediate periods, the spatial
damping of magnetoacoustic waves is dominated by radiation,
while at short periods thermal conduction dominates. Then, for
the interval of periods detected in prominence oscillations,
radiation is responsible for the spatial damping of
magnetoacoustic waves and, while the fast wave displays a very
long damping length, the slow wave shows that for typical periods
of prominence oscillations between 5 and 15 minutes, the damping
length is order 104 – 105 km. On the other hand, the thermal wave,
which in this case of spatial damping is a propagating wave,
displays, when compared with the magnetoacoustic waves, the
shortest damping length and damping length per wavelength.
89
The damping of prominence oscillations by ion-neutral
collisions
P. Forteza (1), R. Oliver (1), J. L. Ballester (1),
M. L. Khodachenko (2)
(1) Departament de Física, Universitat de les Illes Balears, E07122 Palma de Mallorca, Spain
(2) Space Research Institute, Austrian Academy of Sciences,
A-8042 Graz, Austria
Abstract
Small-amplitude oscillations in quiescent prominences have been
known for long time. Often, these oscillations have been
interpreted in terms of MHD waves and the observations show
that one of the typical features of those oscillations is that they are
damped with time. Since solar prominences are partially ionised
plasmas, one can consider the ion-neutral collisions as one of the
potential mechanisms to explain this damping. Here, we report the
results obtained about the time damping of fast and slow waves
by means of ion-neutral collisions.
90
Sunspot oscillations: theory and
comparison with observations
Y.D.Zhugzhda
IZMIRAN, Troitsk, Moscow Region, 142190 Russia
Abstract
The exploration of sunspot oscillations lasts for long time but
there is no generally accepted theory of the phenomenon. An
adequacy of different mathematical approaches to the problem and
real physical problem is discussed. Wealth of observational
evidence and analysis of sunspot models testify against
eigenoscillations of sunspots. In contrast with p-modes, the
eigenvalue approach is not suitable for sunspot oscillations since
oscillations are not captured by sunspots. The exploration of
filtering properties of sunspot atmosphere is the correct way to
develop the theory. The filtering through temperature minimum
and chromosphere is considered. The possibility of the seismology
of sunspot atmosphere is considered. The theory is compared with
observations. The effects of inhomogeneity of the atmosphere is
discussed. The nonlinear 3-min oscillations are discussed.
91
Analytical signal as a new tool for helioseismology
Y. D. Zhugzhda
IZMIRAN, Troitsk, Moscow Region, 142190 Russia
Abstract
A new method of treatment for narrow band oscillatory processes
is described. The method is based on the concept of analytical
signal. It makes possible to obtain instant frequency, amplitude
and phase of oscillations. The resolution of rather closed lines in
spectrum is possible. It makes possible to separate the effects of
amplitude and frequency fluctuations on line broadening. The
method is applied to the treatment of brightness oscillations of the
Sun observed by the multichannel photometer on the board of
CORONAS satellite. It is revealed that the line width of p-modes
appears mostly due to amplitude fluctuations while frequency
fluctuations are very low. The exploration of phase relations
between different channels of the photometer discovers that pmodes from deep and upper layers of photosphere are running to
the middle layers. This effect is possible only for nonadiabatic
evanescent p-modes.
92
List of Participants
J. Andries
Centre for Plasma Astrophysics
K. U. Leuven (Belgium)
I. Arregui
Departament de Física, Universitat
de les Illes Balears, Palma de Mallorca (Spain)
I. Ballai
Space and Atmosphere Research Centre
Department of Applied Mathematics
University of Sheffield (UK)
J. L. Ballester
Departament de Física, Universitat
de les Illes Balears, Palma de Mallorca (Spain)
D. Banerjee
Indian Institute of Astrophysics
Koramangala, Bangalore (India)
A. Birch
NWRA/CoRA, Boulder, CO, (USA)
M. Carbonell
Departament de Matemátiques i Informática, Universitat
de les Illes Balears, Palma de Mallorca (Spain)
93
A. Díaz
School of Mathematics and Statistics
St Andrews University (Scotland)
G. Doyle
Armagh Observatory,
Armagh (Northern Ireland)
M. Dymova
Dept. of Applied Mathematics,
University of Sheffield (UK)
R. Erdélyi
Space & Atmosphere Research Center,
Dept. of Applied Mathematics,
University of Sheffield (UK)
V. Fedun
Space & Atmosphere Research Center,
Dept. of Applied Mathematics,
University of Sheffield (UK)
B. Fleck
European Space Agency
NASA/GSFC 20771 (USA)
P. Forteza
Departament de Física, Universitat
de les Illes Balears, Palma de Mallorca (Spain)
94
M. Goossens
Centre for Plasma Astrophysics
K. U. Leuven (Belgium)
A. W. Hood
School of Mathematics and Statistics.
St Andrews University (Scotland)
M. H. Ibañez
Centro de Física Fundamental
Universidad de los Andes
Merida (Venezuela)
R. Jain
Space & Atmosphere Research Center,
Dept. of Applied Mathematics,
University of Sheffield (UK)
R. Keppens
Centre for Plasma Astrophysics
K. U. Leuven (Belgium)
M. L. Khodachenko
Space Research Institute
Austrian Academy of Sciences,
(Austria)
A. Kosovichev
HEPL A204, Stanford University
Stanford (USA)
95
Y. Lin
Institute of Theoretical Astrophysics
University of Oslo
(Norway)
M. A. Loukitcheva
Astronomical Institute, St Petersburg
(Russia)
M. Luna
Departament de Física, Universitat
de les Illes Balears, Palma de Mallorca (Spain)
M. S. Marsh
NASA/GSFC
(USA)
M. Mathioudakis
Physics and Astronomy
Queens University
Belfast (Northern Ireland)
A. M. D. McDougall
School of Mathematics and Statistics.
St Andrews University, St Andrews,
(Scotland)
M. P. McEwan
Mathematical Institute, University of St
Andrews, St. Andrews (Scotland)
96
C. A. Mendoza-Briceño
Centro de Astrofisica Teorica, CAT
Universidad de los Andes
Merida (Venezuela)
K. Muglach
Naval Research Laboratory
Washington (USA)
K. Murawski
Institute of Physics
UMCS, Lublin (Poland)
V. Nakariakov
Centre for Fusion, Space & Astrophysics
University of Warwick (UK)
R. Oliver
Departament de Física, Universitat
de les Illes Balears, Palma de Mallorca (Spain)
E. O’Shea
Armagh Observatory,
Armagh (Northern Ireland)
D. J. Pascoe
University of Warwick (UK)
B. Pinter
Space & Atmosphere Research Center,
Dept. of Applied Mathematics,
University of Sheffield (UK)
97
G. Pouget
Institute d’Astrophysique Spatiale
(France)
A. Roberts
Mathematical Institute
University of St Andrews (Scotland)
M. Ruderman
Space & Atmosphere Research Center,
Dept. of Applied Mathematics,
University of Sheffield (UK)
R. J. Rutten
Sterrenkundig Instituut, Universiteit Utrecht,
Utrecht (The Netherlands)
M. Ryutova
LLNL, California (USA)
B. Shegerlasvili
Centre for Plasma Astrophysics
K. U. Leuven (Belgium)
R. Soler
Departament de Física, Universitat
de les Illes Balears, Palma de Mallorca (Spain)
Y. Taroyan
Space & Atmosphere Research Center,
Dept. of Applied Mathematics,
University of Sheffield (UK)
98
J. Terradas
Departament de Física, Universitat
de les Illes Balears, Palma de Mallorca (Spain)
D. Tsiklauri
Institute for Materials Research, University of Salford,
Greater Manchester (UK)
T. Van Doorsselaere
Centre for Plasma Astrophysics
Katholieke Universiteit Leuven
(Belgium)
A. Vecchio
Osservatorio Astrofisico Arcetri
Firenze (Italy)
G. Verth
Space & Atmosphere Research Center,
Dept. of Applied Mathematics,
University of Sheffield (UK)
E. Verwichte
Departament of Physics
University of Warwick (UK)
S. Wedemeyer-Böhm
Kiepenheuer-Institut für Sonnenphysik
Freiburg (Germany)
99
N. P. Young
Physics Department,
University of Warwick
Coventry (UK)
T. Zaqarashvili
Abastumani Astrophysical Observatory
(Georgia)
Y. D. Zhugzhda
IZMIRAN, Troitsk
Moscow region (Russia)
100