Annual Progress Report

Researcher:

Bhupendra Singh

(J. R. F.)

F. No. 08/043 (0009)/2009-EMR-1

Department of Physics

Hindu College

Moradabad-244001

Duration: One Year (01.05.2009 – 30.04.2010)Introduction: Sun is a self-luminous ball of hot plasma held together by its own

gravity and powered by thermonuclear fusion in its core. It is a fascinating star which

shows some extra ordinary phenomena such as solar flare, solar wind, coronal loops,

coronal holes, coronal mass ejections etc. occurring in its atmosphere and Sun quakes,

solar dynamo etc. in its interior.

The solar atmosphere is highly non-uniform plasma and consists of three regions, the

photosphere, the chromosphere and the corona, with different physical properties. The

corona which extends from the top of a narrow transition region to Earth and beyond is

seen as highly filamentary inhomogeneous medium consisting of a complex myriad of a

magnetic loop-like structure.

The photosphere is a thin, opaque layer of plasma, around 0.5 Mm (1 Mm = 1000 km)

in thickness lies between the optically opaque interior and transparent solar

atmosphere. The temperature at the top of the photosphere drops to around 4300 K

and the density decreases to around 8.0 × 10-5 kg m-3. Above the photosphere lies a

narrow layer, around 2.5 Mm thick, called the chromosphere. The temperature of the

chromosphere begins to rise steadily, to around 50000 K. The transition region lies

between the chromosphere and the outer atmosphere of the Sun, the corona. In the

corona, the temperature increasing dramatically to several million degrees Kelvin and

the density drops to around 10-10 kg m-3. The images obtained with instruments

onboard spacecrafts show different magnetic structures on a wide range of spatial

scales from bright points, with sizes of a few thousand km, to large coronal streamers,

which extend to several solar radii. Two different types of regions with different

physical properties can be seen.

Open-field regions, in which the magnetic field is unipolar, appear relatively dark

and are called coronal holes. They are dark because of the low plasma density. Coronal

holes are observed to rotate fairly rigidly and can maintain their shape through

several 27-day solar rotations. These regions exist usually in the poles although they

can sometimes extend towards the equator. Here the plasma is flowing outwards to

give the solar wind and therefore connect the solar surface with the interplanetary

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medium. Related to these structures one can also find polar plumes, which are cool,

dense, magnetically open structures that arise from predominantly magnetic

footpoints inside polar coronal holes.

Closed-field regions consist of myriads of hot and dense coronal loops. The term

coronal loop is commonly used to describe bright coronal structures that are

significantly longer than they are wide. These loops are made of X-ray emitting plasma

and are believed to outline the closed coronal magnetic field, primarily because heat

conduction and mass transport across the field is strongly suppressed in a strong

magnetic field. These loops are in a continuous state of change they can rise from

inside the Sun, sink back down into it, or expand into space. They often come together,

sometimes merging with each other and sometimes destroying each other. The

magnetic loops store magnetic energy. When they interact, the magnetic loops release

their stored energy into the corona, providing the energy that keeps the corona so hot.

Sometimes one can find coronal loops placed one after another to form a tunnel-like

structure, or coronal arcade. Other amazing structures in the corona are solar

prominences, which are clouds of relatively cool (≤104 K) and dense gas (1017 m-3).

All coronal structures are dominated by the magnetic field and its interaction with the

coronal plasma. Magnetohydrodynamics (MHD) studies such interaction between

plasma and a magnetic field, providing an important tool for understanding many

solar phenomena (Cowling 1957; Priest, 1982; Boyd and Sanderson, 2003). Magneto-

hydrodynamics (MHD) is a fluid theory, expressed in terms of macroscopic

parameters, such as density, pressure, temperature, and flow speed of the plasma.

MHD waves have been broken into two subcategories namely Alfvén waves and

magneto-acoustic waves. Alfvén 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.

There are clear observational evidences for the existence of waves and oscillations in

the solar coronal structures. These observations have confirmed the prediction that

various structures of the solar corona can support MHD waves. The study of waves and

oscillations in these structures is of utmost important in the community of solar

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physicists all over the world. Presently, I am working on some specific problems in the

field of solar MHD.

The brief outline of the problem carried out is as follows:

Effect of equilibrium plasma flow on slow magneto-acoustic waves in

coronal loops:

In this problem we study the role of plasma flow on the damping of slow MHD waves in

solar coronal loops. 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. This study 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. 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. The wave energy flux

associated with slow magneto–acoustic waves turns out to be of the order of 106 erg

cm−2 s−1 which is high enough to replace the energy lost through optically thin coronal

emission and the thermal conduction below to the transition region.

This paper has been communicated to the ‘International Journal of Physics’. A copy of

the communicated manuscript (paper) has been enclosed herewith.

RESEARCH WORK IN PROGRESS:

In Particular, the brief outline of the problem which is in progress is as follows:

Dissipation of magneto-acoustic waves in coronal loop:- The problem dealing

with the damping of MHD waves in an inhomogeneous plasma by taking into account

the effect of viscosity and thermal conduction is in progress. In this problem we

considered a coronal loop as a static, axisymmetric, straight, and low- slab with lengthβ

L and thickness a. In our Cartesian coordinate system the x-coordinate corresponds to

the radial direction, the y-coordinate to the azimuthal direction, and the z-coordinate to

the direction along the field lines. The plasma is permeated by a uniform straight

magnetic field (B = B0êz), while the inhomogeneity is denoted by4

(x) = ρ ρ0(1+ cos( x/a)) where,ξ π ρ0 is the loop density at the base of the corona and isξ

the inhomogeneous index determines the ratio between maximum and minimum

densities.

This models the higher density inside the loop. In this problem we shall derive a

general dispersion relation for damped magnetoacoustic waves in the presence of

viscosity and thermal conductivity. It is conjectured that our results might be useful to

understand various physical processes in coronal flux tubes.

I have presented a research paper in the “24th National Symposium on Plasma Science

and Technology, PLASMA-2209 held at NIT, Hamirpur (HP). For the aforesaid research

work I have visited IIT Delhi, IIT Roorkee, ARIES, Nainital and Delhi University to

consults libraries and to have discussions with eminent scientist regarding my

problems.

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