Non-linear electrostatic waves in pair-ion plasmas - National Centre ...

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Nonlinear Electrostatic Waves in Pair-ion Plasmas (contd.)Now collecting the next higher order terms of continuity and momentum equationsof ions (~ε 5/2 ) and Poisson equation (~ ε 2 ) and using relation of parameter λ givenin Eq.(11) after some simplification, we obtain the KdV equation as follows:( 1) ( 1) ( 1) 3 ( 1)∂Φ + AΦ ∂Φ + B∂Φ =τ ξ ξ(12)⎡ 2 232 23( 3λ −1)( λ − μ) −( 3λ − μ) ( λ −1)⎤⎢⎥A =⎣⎦2 2λ( λ − )( λ − μ) ⎡ 22222 1 ( λ − μ) + ( λ −1)⎤⎢⎣⎥⎦2222( λ −1) ( λ − μ)B =λ ⎡ 22222 ( λ − μ) + ( λ −1)⎤⎢⎣⎥⎦Note: The soliton solution will be formed only when T +≠ T -0(coefficient of nonlinear term)(coefficient of dispersive term)holds.18
Nonlinear Electrostatic Waves in Pair-ion Plasmas (contd.)If T +≠T -, then soliton solution of Eq.(12) is given bywhere( 1)2 ⎛ η ⎞Φ = φ msec h ⎜ ⎟⎝ W ⎠φm= 3u0/ A(13)(amplitude of the soliton)W 4B/u=0(width of the soliton)Transformed variableη = ξ − u 0τhas been defined.The velocity of the transformed frame u 0has been normalized with thermalvelocity of positive ion.19
Page 1 and 2: Nonlinear electrostatic structures
Page 3 and 4: 1. Soliton‣ Soliton is a nonlinea
Page 5 and 6: Soliton in Plasmas (contd.)Linear w
Page 7 and 8: 2. Brief Introduction of pair-ion P
Page 9 and 10: Production of pair-ion (fullerene)
Page 11 and 12: Electrostatic Waves in pair-ion Pla
Page 13 and 14: Nonlinear Electrostatic Waves in Pa
Page 15 and 16: Nonlinear Electrostatic Waves in pa
Page 17: Nonlinear Electrostatic Waves in pa
Page 21 and 22: Double Layer in Plasmas5. Double La
Page 23 and 24: Double layer in Pair-ion Plasmas (c
Page 25 and 26: Double layer in Pair-ion Plasmas (c
Page 27 and 28: 6. Dissipative shocks and solitons
Page 29 and 30: Dissipative shocks and solitons in
Page 31 and 32: Dissipative shocks and solitons in
Page 33 and 34: 7. Conclusion• Linear and nonline
Page 35: Thank You35

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