2. Session
TOPIC
Electromagnetic solitary structures in dense electron-positron-ion megnetoplasma
By  Supervised By
ZULIQAR ALI
1JU AM Mr. Muhammad Ayub
Session
Department of Physics
Faculty of Sciences
Mirpur University of Science and Techonology
Mirpur (AJK)
Pakistan

3. ABSTRACT
Our work is the theoretical studies of the linear and nonlinear characteristics obliquely propagating magnetoacoustic waves in dense electron-positron-ion magnetoplasmas by using QMHD model.
The linear dispersion relation and nonlinear KP equation is derived by using the reductive perturbation theory and small amplitude expansion method.
The present investigation may have relevance to
dense astrophysical environments where the quantum effects are expected to dominate.

4. INTRODUCTION TO PLASMA
Matter can appear in four different states mainly solid, liquid, gas and plasma.
Plasmas are the "Fourth State of Matter" because of their unique physical properties, distinct from solids, liquids and gases.
Formed at high temperatures when electrons are stripped from neutral atoms.
In first three states electrons are less or more tightly bound to there atoms but in plasma electrons are independent.
Plasmas are strongly influenced by electric and magnetic fields and form the Van Allen radiation belts.

5. A quasi neutral gas consisting of the charged and neutral particles which exhibits collective behavior is called plasma
“Plasma” is therefore considered as gas showing collective behavior.
plasma interact simultaneously with large number of particles which is termed as collective behavior
Having large number of particles(negative and positive charge) but overall neutral electrically (ne≈ ni =n) which is termed as quasi-neutrality.

6. Criteria for Plasmas
We have given two conditions for an ionized gas to known as plasma must satisfy.
A third condition has to do with collisions. These are given as .
Where ω is the frequency of plasma oscillations and τ is the mean time between collisions with neutral atoms.
Where = Number of particles in Debye Sphere and is Debye length.

7. Plasma Temperature
It is interesting fact that plasma have several temperatures at the same time .i.e. and .
As temperature depends upon kinetic energy and rate of collisions between ions different then electrons collisions ,so the have different temperatures.
Also the single species .i.e. ion may have different temperatures and when component of velocity parallel or perpendicular to B .

8. Occurrence of Plasma in Nature
."99.9 percent of the Universe is made up of plasma," says Dr. Dennis Gallagher .
It would be seen that we live in 1 percent of the universe in which plasma does not exist.
Plasma exists in space and also natural plasma discovered close to the earth’s surface.
The Sun, fire, fluorescent and neon lights contain plasma.
Plasma exists in the solar system and interstellar space and near the earth’s surface

9. Plasma in Space
Solar Wind Which comes from the sun’s outer most layer.
Van Allen Radiation Belts Which are the particles of high energy trapped in earth magnetic field .
Ionosphere Which is the ionized part of the Earth’s upper atmosphere due to UV light.
Stellar Interiors and atmosphere
Interstellar medium behave as plasma and propagate magnetic field and electric currents.
Stellar insides are hot enough to be in the plasma state actually for quite high particle densities.

10. Natural Plasma near the Earth
Solar System
our solar system is round about 99.98% in the form of plasma.
Sun is almost completely in the form of plasma state.
the interplanetary medium and intergalactic medium are 100% in plasma state.
Natural Plasma near the Earth
Two well known examples of common plasma near earth are given underneath.
Auroras Aurora is light which comes from sun’s. radiation, in red, blue, green and fire like colure.
Lightning Lightening is also plasma.

11. Figure 1.1 sun and stars

12. Fig. Solar Wind

13. Fig.Van Allen Belts

14. Fig. Lightening bulb

15. Quantum Plasma
Due to quantum nature of plasma particles ,plasma is also referred as quantum plasma.
The investigation of quantum plasma depends upon the description of quantum particles.
If the quantum plasma is non relativistic then it can be explain by two representations .
Heisenberg’s approach
Schrodinger’s approach

16. Heisenberg’s approach
In this approach time dependence is transferred from function to operator.
Schrodinger’s approach
In this approach the operators are time independent.
But in the latest research Schrödinger’s approach is used in many models which give information about the wave function, density matrix, Wigner’s functions and quantum hydro magneto dynamic equations.

17.  Dusty Plasma
Plasma such as electrons, ions and neutral particles along with dust particles is known as dusty plasma.
Due to these dust particles the plasma becomes very complex so known as complex plasma.
discharges, plasma processing reactors and dirt in fusion devices are examples of dusty plasma .

18. Non linearity in plasma
Plasmas are rich in waves and propagate by means of electric and magnetic fields.
When amplitude of these waves is small then the propagation of waves is linear but for specific high amplitude nonlinearity plays role.
From localization of wave due to nonlinearity we observed vortices, double layers shock waves, solitary waves, and so on.

19. Solitary Structures
Among researchers the solitary waves have great importance due to their applications in the physics.
The solitary structures are explained by using
nonlinear Schrodinger Equation (NLSE)
Korteweg de Vries equation (KdV)
Kadomtsev–Petviashvili equation (KP).

20. Electromagnetic solitary structures in dense electron-positron-ion megnetoplasma

21. Formulation and Basic Equations
We here assume that the background magnetic field Bo, making an angle θ with x- axis in the (x, y) plane and wave propagating in the (x, z) plane
our formulism based upon one fluid QMHD where statistical and diffraction terms are included.
ions are considered as classical plasma because these are massive then electrons.
We also neglect the effects of electron spin as theoretically shown by Brodin et al.
Basic set of equation using one fluid QMHD model for e-p-i plasmas is given by

22. And the pressure for electrons and positron is given by following relations
(3.1)
(3.2)
(3.3)
(3.4)
(3.5)

23. Equation of ion continuity and Maxwell’s equations are given by
(3.6)
(3.7)
(3.8)
(3.9)

24. Now by putting from Eq. (3.9) in Eq. (3.2) we get
Using Eqs. (3.1) to (3.7) and the quasi- neutrality,
we obtain the following normalized effective one fluid moment equation
(3.10)
(3.11)

25. From Eqs. (3.1) and (3.8) we get the normalized magnetic field induction equation, given by
Equation of ion continuity is given by
For positron we have
(3.12)
(3.13)
(3.14)

26. Derivation of KP equation
New space and time variable by using method of Washimi and Tanuiti [41] are given by
Also we can write
(3.15)
(3.16)
(3.18)
(3.19)
(3.20)

27. By using expansion, we get following form
Using Eqs. (3.15) and (3.16) in Eqs. (3.18) to (3.20) we get following results
By using expansion, we get following form
And for and
(3.21)
(3.22)
(3.23)
(3.17)

28. , and we get following equations.
By using Eqs. (3.14), to (3.23) in Eqs. (3.10), to (3.13) and then comparing the terms of order
, and we get following equations.
(3.32)
(3.33)
(3.34)
(3.35)
(3.36)

29. , and we get following equations.
By using Eqs. (3.14), to (3.23) in Eqs. (3.10), to (3.13) and then comparing the terms of order
, and we get following equations.
(3.32)
(3.33)
(3.34)
(3.35)
(3.42)
(3.43)

30. (3.44)
(3.45)
(3.46)
(3.47)
(3.48)

31. By eliminating and from eqs. (3. 32,3. 33,3. 34,3. 35 and 3
By eliminating and from eqs.(3.32,3.33,3.34,3.35 and 3.36) we get following quadratic equation. By using quadratic formulae we have following linear dispersion relation
(3.40)
(3.41)

32. By differentiating eq. s (3. 42) to (3. 48) w. r
By differentiating eq.s (3.42) to (3.48) w.r.t and Eliminating and we get
(3.64)
(3.65)
(3.66)
(3.67)

33. Using eq.(3.66 and 3.67) ineq.(3.68) ,we get
(3.69)
(3.70)
(3.73)

34. Using eq.(3.66 and 3.67) in eq(3.69) ,we get Using eq.(3.66 and 3.67) in eq.(3.70) ,we get
(3.74)
(3.75)

35. The standard solution of KP equation may be expressed by
Eliminating second order terms( and ) and first order from eq.s (3.73,3.74 and 3.75) by using eq.s (3.64 &3.65) we get
This is the nonlinear evolution equation known as the KP equation. Where we can define coefficients as and
The standard solution of KP equation may be expressed by
Where and where k is the wave number which is nonlinear and dimensionless.
(3.90)
(3.91)

36. RESULTS AND DISCUSSION
We graphically investigate variation of fast and slow modes according to different factors in dense astrophysical plasmas.
The neutrons, stars and dwarfs are dense astrophysical objects.
They are found in dense astrophysical plasmas their densities are enormous and we cannot neglect the quantum effects.
Parameters for dense astrophysical physical plasma can be given as
cm-3 G.
In the linear dispersion relation (3.41) positive sign indicates the fast quantum magnetoacoustic waves modes and negative sign shows slow modes.

37. Fig 4.1(a) Graph between phase velocity and obliqueness.
(b) Graph between phase velocity and positron concentration.

38. Figure 4.4 Plot between the fast and slow magnetoacoustic potential By1 and positron concentration, p.

39. The results of both fast and slow modes by varying different factors in Eq.s(3.41 & 3.90) underneath,
The plot between phase velocity and obliqueness parameter shows that fast mode increases and slow mode decreases shown in Fig 4.1(a) .
Also the plot between phase velocity and positron concentration increases for fast mode and decreases for slow mode as shown in Fig 4.1(b).
Acoustic character found on the fast mode has while both the acoustic as well Alfvenic character found in slow mode.
All these observations are discussed for low plasmas.

40. The plot between magnetoacoustic potentials and for different positron concentrations, for the fast and slow modes show the rarefractive solitary structure as shown in Fig. (4.4).
The increase in the positron concentrations then the density dip decreases for slow magnetoacoustic solitary waves.
And for fast magnetoacoustic solitary waves there is no effect when we increase the positron concentration.

41. THANK YOU VERY MUCH FOR All RESPECTIBLE GUESTS