Thesis Presentation

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WELCOME TO MY THESIS PRESENTATION

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SOLITARY WAVES AND DOUBLE LAYERS IN ULTRA- RELATIVISTIC ULTRA-COLD DEGENERATE ELECTRON-POSITRON-ION PLASMA Submitted by : NIPA ROY Roll No: 090453 Reg. No : 21535 Session : 2008-09 Supervised by : Dr. A. A. MAMUN Professor Dept. of Physics Jahangirnagar University

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OUTLINE INTRODUCTION LINEAR DIA WAVES DIA SOLITARY WAVES DIA DOUBLE LAYERS APPLICATIONS

INTRODUCTION: 

INTRODUCTION PLASMA ELECTRON-POSITRON-ION PLASMA DUSTY ELECTRON-POSITRON-ION PLASMA DEGENERACY ULTRA-RELATIVISTIC LIMIT

INTRODUCTION : 

INTRODUCTION PLASMA On earth we live upon an island of "ordinary" matter. Sir William Crookes, an English physicist, identified a fourth state of matter, now called plasma, in 1879 . In an ancient era people recognized holy elements: Earth, Water, Air, and Fire. Ancient time Soil Water Air Fire Now S olid Liquid Gas ??

INTRODUCTION : 

INTRODUCTION PLASMA A macroscopically neutral substance containing many interacting charged particles (electrons and ions) and neutrals, which exhibit collective behaviour due to the long-range Coulomb forces is known as plasma or electron-ion plasma . Plasma temperatures and densities range from to very hot and dense (10 2 -10 14 K).

INTRODUCTION : 

INTRODUCTION ELECTRON-POSITRON-ION PLASMA Consists of two fermions, electrons and positrons: Masses: equal Charges: equal Polarity: opposite Example: Astrophysical objects Laboratory plasma PLASMA e + ION e -

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INTRODUCTION DUSTY ELECTRON-POSITRON-ION PLASMA A dusty e-p- i plasma is roughly defined as a normal electron-positron-ion plasma with an additional charged component of dust particle. PLASMA ION DUST e + DUST Mass: not constant (10-10 6 times heavier than ion) Size: not constant (10 -3 -10 -6 m) Charge polarity: not constant Plasma: “Complex Plasma” e -

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INTRODUCTION DEGENERACY Degenerate plasma is cooled and compressed plasma with e xtraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. Heisenberg uncertainty principle : ΔpΔx ≥ ħ/2 leads to uncertainty in momentum fast particles All matter experiences normal thermal pressure Fermion degeneracy pressure

INTRODUCTION : 

INTRODUCTION ULTRA-RELATIVISTIC LIMIT Given by: Subrahmanyan Chandrasekhar (1910-1995, N.Prize 1983)

LINEAR DIA WAVES: 

LINEAR DIA WAVES MODEL LINEAR DISPERSION RELATION RESULTS FINDING

LINEAR DIA WAVES : 

LINEAR DIA WAVES MODEL Degenerate electron Degenerate positron Positively charged ion Negatively charged static dust

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LINEAR DIA WAVES LINEAR DISPERSION RELATION

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LINEAR DIA WAVES RESULTS Figure: The dispersion properties of the electrostatic waves Figure: Showing the variation of physical parameter in dispersion relation

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LINEAR DIA WAVES FINDINGS All the parameters changes linearly with the change of frequency and wave number as well as wavelength Degenerate positron gives the sharp increase in wave frequency

DIA SOLITARY WAVES: 

DIA SOLITARY WAVES MODEL RESULTS OF K- dV METHOD RESULTS OF PSEUDO-POTENTIAL APPROACH FINDING

DIA SOLITARY WAVES : 

DIA SOLITARY WAVES MODEL Degenerate electron Degenerate positron Positively charged ion Negatively charged static dust

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DIA SOLITARY WAVES RESULTS OF K- dV METHOD Figure: The effect of physical parameter in wave potential. Figure: The effect of physical parameter in wave potential.

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DIA SOLITARY WAVES RESULTS OF K- dV METHOD Figure: The effect of physical parameter in wave potential. Figure: The effect of physical parameter in wave potential.

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DIA SOLITARY WAVES RESULTS OF PSEUDO-POTENTIAL APPROACH Figure: The variation of Mach number with physical parameter. Figure: The variation of Mach number with physical parameter.

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DIA SOLITARY WAVES RESULTS OF PSEUDO-POTENTIAL APPROACH Figure: The variation of Mach number with physical parameter. Figure: Showing the existence of both positive and negative solitary waves.

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DIA SOLITARY WAVES RESULTS OF PSEUDO-POTENTIAL APPROACH Figure: Solitary waves with negative potential . Figure: Showing the existence of both positive and negative solitary waves.

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DIA SOLITARY WAVES FINDINGS The K- dV method supports positive solitary profiles Pseudo-potential method supports both positive and negative solitary profiles

DIA DOUBLE LAYERS: 

DIA DOUBLE LAYERS MODEL RESULTS OF SMALL AMPLITUDE PSEUDO-POTENTIAL APPROACH RESULTS OF ARBITRARY AMPLITUDE PSEUDO-POTENTIAL APPROACH FINDING

DIA DOUBLE LAYERS : 

DIA DOUBLE LAYERS MODEL Degenerate electron Degenerate positron Positively charged ion Negatively charged static dust

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DIA SOLITARY WAVES RESULTS OF SMALL AMPLITUDE PSEUDO-POTENTIAL APPROACH Figure: Showing the variation of Mach number with physical parameter. Figure: Showing the existence of negative double layer.

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DIA SOLITARY WAVES RESULTS OF SMALL AMPLITUDE PSEUDO-POTENTIAL APPROACH Figure: Showing the variation of Mach number with physical parameter. Figure: Showing the existence of negative double layer.

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DIA SOLITARY WAVES RESULTS OF ARBITRARY AMPLITUDE PSEUDO-POTENTIAL APPROACH Figure: The limit of Mach number. Figure: Numerical solution of conditions in critical Mach number.

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DIA SOLITARY WAVES RESULTS OF ARBITRARY AMPLITUDE PSEUDO-POTENTIAL APPROACH Figure: Numerical solution of conditions in Mach number more than the critical value. Figure: Numerical solution of last condition in Mach number more than the critical value.

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DIA SOLITARY WAVES RESULTS OF ARBITRARY AMPLITUDE PSEUDO-POTENTIAL APPROACH Figure: Existence of negative double layer. Figure: Existence of negative double layer .

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DIA DOUBLE LAYERS FINDINGS Both amplitude limits of the pseudo-potential method supports negative double layers Small amplitude limit supports the negative double layer violating the basic assumption, arbitrary amplitude case overcomes that shorcoming

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APPLICATIONS ASTROPHYSICAL COMPACT OBJECTS WHITE DWARF NEUTRON STAR

APPLICATIONS : 

APPLICATIONS ASTROPHYSICAL COMPACT OBJECTS White Dwarf Supported by the balance between Inward pulling Degenerate pressure Formed for Burning up all its hydrogen fuel Forced to fuse helium into carbon and oxygen Mass limit: within Density limit: 10 30 -10 36 cm 3

APPLICATIONS : 

APPLICATIONS ASTROPHYSICAL COMPACT OBJECTS NEUTRON STAR Formed for The gravitational collapse of a massive star during a supernova explosion Mass limit: to

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