Summary
Study of wave motions on the Sun started in the late 1940s and
theorists realize that waves could carry energy from the convection
zone to the chromosphere and corona. Dissipation of these waves
could explain the observed increase in temperature of the outer
layers of the Sun. In spite of about half a century of study, it is
not fully understood how the million degree temperature of the
corona is maintained against losses due to radiation and energy
outflow into the solar wind. It is believed that propagating waves
are responsible for this heating but are difficult to observe,
because they are transient and are of small spatial scales.
Presence of these waves is inferred from observations of
non-thermal broadening of solar spectral lines. Observations show
that waves and oscillations are ubiquitous in the solar coronal
structures. These propagating wave-like fronts are usually
triggered by flares or CMEs (Coronal Mass Ejections). Examples of
such phenomena can be found in Thompson et al., (1998), Wills-Davey
et al., (1999) Zhukov et al., (2004), and more recently in Long et
al., (2008). The theoretical modelling of such phenomena was first
attempted by Wu et al., (2004) using magnetic field extrapolations
from photospheric magnetograms. Waves in the solar corona are also
present on smaller spatial scales. For example, there is abundant
literature on oscillations reported in solar prominences and
filaments (Oliver, 2009; Ballester, 2010; Arregui et al., 2012).
The magnetically dominated solar coronal plasma is an elastic and
compressible medium which supports a variety of magnetohydrodynamic
(MHD) waves. MHD waves in the corona have been intensively
investigated for more than two decades, primarily in the context of
the enigmatic problems of coronal heating and acceleration of the
fast solar wind. It is also believed that the MHD waves play an
important role in solar-terrestrial connections. Coronal loops and
prominences are magnetic structures that also show oscillatory
phenomena. Standing acoustic oscillations have been reported in hot
coronal loops (e.g., Wang et al., 2003a; Wang et al., 2003b; Wang,
2011). Propagating longitudinal waves involving compressions have
also been found in coronal plumes (see, Deforest and Gurman, 1998;
Ofman et al., 1999; Ofman et al., 2000).
MHD waves have been broken into two subcategories namely Alfvn
waves and magneto-acoustic waves. Alfvn waves are transverse and
incompressible propagating along the magnetic field.
Magneto-acoustic waves (slow and fast modes) cause compression and
rarefaction of the coronal plasma as they propagate into the corona
from the lower atmosphere. Fast waves are intrinsically compressive
and therefore subject to dissipation by viscosity, heat conduction
and radiation, or by Landau and transit-time damping in the high
frequency limit where Coloumb collisions are ineffective. In
contrast, slow-mode waves carry a small amount of energy flux due
to their low group velocity and are likely to be strongly damped in
the lower corona.
The objective of the thesis is to answer certain fundamental
questions concerning with the propagation and dissipation of MHD
waves in certain coronal magnetic structures. The present thesis is
roughly divided into two parts. Part 1 (Chapters 2-4) treats the
problem of MHD wave generation and dissipation in coronal loops
whereas Part 2 (Chapter 5-6) deals with the study of MHD waves in
solar prominences.The first chapter Introduction explores the Suns
interior, to its surface and high into the corona, detailing core
energy production, energy transfer through the solar body and some
of the instrumentation used to observe the solar environment. In
this chapter we begin in the solar core where fusion generates the
necessary energy and briefly explain how this energy is transmitted
through the radiative zone and into the convection zone where
plasma is convected and energy transferred to the photosphere. The
atmosphere of the Sun from photosphere to extended corona has also
been detailed in this chapter. In Chapter 2, we outline the basic
equation and theory behind the structure and evolution of plasma in
the solar atmosphere. The set of equations which govern the
magnetized plasma on the Sun are known as magnetohydrodynamics
(MHD) and the foundation of MHD theory is outlined. The equations
of magnetohydrodynamics, base of coronal physics are useful in
order to understand the different theoretical issues investigated
in this Thesis. We also briefly show the general properties of
three MHD wave modes in a simple equilibrium configuration. In
order to derive these equations we have combined Maxwells equations
with the equations of gas dynamics and equations In Chapter 3, we
have investigated the individual effects of compressive viscosity,
thermal conduction and heat radiation on the spatial damping of
slow magneto-acoustic waves in coronal loops observed by SUMER and
TRACE. We have considered homogeneous, isothermal, and unbounded
coronal plasma permeated by a uniform magnetic field, with physical
properties akin to those of coronal loops. Taking into account an
energy equation with optically thin radiative losses, thermal
conduction, and heating we obtained a fourth-order polynomial in
the wave number k, which represents the dispersion relation for
slow and thermal MHD waves. The fourth order dispersion relation
has been solved numerically to study the damping length of slow
waves in a medium having physical properties akin to those of solar
coronal loops. It is found that damping length of slow-mode waves
exhibits varying behavior depending upon the physical parameters of
the loop. We found that for solar coronal loops, the dominant wave
damping mechanism is compressive viscosity and thermal conduction
with less significant contribution by radiation. For any considered
period, slow waves have much shorter damping length in hot coronal
loops than that in cool loops. It is also found that slow waves
damped very quickly in hot and long coronal loops. Our results
indicate that in cool coronal loops (T 2106 K) irrespective of
viscous parameter short period waves (P < 0.5) damp very quickly
whereas long period waves (P > 0.5) travel undamped along the
length of loop. However, in the case of hot coronal loop (T 4106 K)
, damping length of slow waves shows a appreciable decrease as we
go from long to short period waves.Chapter 4 of the thesis explores
the effect of steady plasma flow on the dissipation of slow
magneto-acoustic waves in the solar coronal loops permeated by
uniform magnetic field. In the solar corona waves and oscillatory
activities are observed with modern imaging and spectral
instruments. These oscillations are interpreted as slow
magneto-acoustic waves excited impulsively in coronal loops. The
inclusion of equilibrium steady flow not only produces a shift in
oscillatory frequency but also breaks the symmetry between parallel
and anti-parallel wave propagation. We have investigated the
damping of slow waves in the coronal plasma taking into account
viscosity and thermal conductivity as dissipative processes. On
solving the dispersion relation it is found that the presence of
plasma flow influences the characteristics of wave propagation and
dissipation. We have shown that the time damping of slow waves
exhibits varying behavior depending upon the physical parameters of
the loop. We have found that in the presence of steady flow slow
waves are strongly damped in coronal loops irrespective of
temperature and loop length. The wave periods are in agreement with
the observed period of loop oscillations. The wave energy flux
associated with slow magneto-acoustic waves turns out to be of the
order of 106 erg cm2 s1 which is high enough to replace the energy
lost through optically thin coronal emission and the thermal
conduction below to the transition region.
In Chapter 5, we have studied the spatial damping of linear
non-adiabatic magneto-acoustic waves in a homogeneous, isothermal,
and unbounded medium permeated by a uniform magnetic field, with
physical properties akin to those of solar prominences. The linear
non-adiabatic waves can provide interesting physical effects such
as time and spatial damping of disturbances (Field, 1965). The
simplest approach for non-adiabatic waves is to take into
consideration a radiative loss term in the energy equation based on
Newtons law of cooling with a constant radiative relaxation time.
In the case of a magnetized medium, this approach was used by Webb
and Roberts (1980), who analyzed MHD waves in an unbounded
atmosphere in the presence of a uniform vertical magnetic field,
while in the case of slab prominence models, the above approach
used by Terradas et al. (2001) to study the radiative damping of
oscillations. We have removed the adiabaticity assumption by means
of an energy equation which includes optically thin radiative
losses, thermal conduction and heating to study the spatial damping
of linear non-adiabatic MHD waves. We have linearized the MHD
equations to obtain a sixth-order polynomial in the wave number k,
which represents the dispersion relation for slow, fast, and
thermal MHD waves. As we are interested in the spatial damping, we
have taken as real and have numerically solved the dispersion
relation to obtain complex solutions for the wave number k
corresponding to fast, slow, and thermal waves. The general
dispersion relation has been solved numerically for linear
non-adiabatic MHD waves in magnetized prominence plasma to study
the behavior of the wavelength, damping length and damping per
wavelength for the different considered solar prominence regimes
and heating mechanisms. Within this study, we found that the
wavelength, damping length, and damping length per wavelength for
slow-, fast- and thermal-mode waves do not change significantly in
any of the three prominence regimes when different heating
mechanisms are taken into account. It is found that linear
magneto-acoustic waves are spatially damped by thermal effects, and
the strongest damping is obtained for slow waves. At periods
greater than 1 s the spatial damping of magneto-acoustic waves is
dominated by radiation, while at shorter periods the spatial
damping is dominated by thermal conduction. Radiative effects on
linear magneto-acoustic slow waves can be a viable mechanism for
the spatial damping of short period prominence oscillations, while
thermal conduction does not play any role. Finally, Chapter 6 deals
with the study of the effect of background plasma flow on the
damping of slow and thermal waves in solar prominence.
Field-aligned flows are ubiquitous in magnetic structures in the
solar atmosphere (Winebarger et al., 2002; Okamoto et al., 2007;
Ofman and Wang, 2008). Material flows are typical features of
prominences and are routinely observed in Ha, UV and EUV lines
((Zirker et al., 1998; Lin et al., 2003, 2005). The non-adiabatic
MHD equations are linearized to obtain the dispersion relation for
different wave modes considering an equilibrium made of an
unbounded prominence plasma embedded in corona. By considering only
field-aligned propagation, we focus our study in the behaviour of
thermal and slow waves. On solving the dispersion relation for a
fixed wave number, a complex oscillatory frequency is obtained, and
the period and the damping time are computed. When a flow is
present, two slow waves with different periods appear while the
damping time remains unchanged. On the other hand, in this case
thermal wave becomes a propagating wave with finite period while
its damping time remains also unmodified. As a consequence of the
changes in the periods produced by the flow the damping per period
of the different waves is modified. In the case of slow waves for a
fixed flow speed, the damping per period of the high-period slow
wave is increased while the opposite happens for the low-period
slow wave. The strongest finite damping per period for the
high-period slow wave is obtained for flow speeds close to the
non-adiabatic sound speed. In the case of the thermal wave, a
finite value for the damping per period is obtained for any
non-zero flow speed. In this case the strongest finite damping per
period is obtained for values of the flow speed close to zero.
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