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

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Nonlinear Electrostatic Waves in Pair-ion Plasmas (contd.)Nonlinear set of equations in normalized form are written as follows:∂n∂t+∂+ ( nv+ + ) =∂x0∂n∂t−∂+ ( nv− −)=∂x0∂v⎛ ∂ ⎞ ∂Φ 1 ∂n+ ⎜v+ ⎟v+= − −∂t ⎝ ∂x ⎠ ∂x n ∂x+ +∂v−⎛ ∂ ⎞ ∂Φ μ ∂n+ ⎜v−⎟v−= −∂t ⎝ ∂x ⎠ ∂x n ∂x2∂Φ( n− n2 = −+ )∂x⎛eφ⎞T−where Φ=⎜ ⎟⎝Tand μ = have been defined.+ ⎠TNormalization of time, space and velocityhas been done byVT++−⎛T+⎞= ⎜ ⎟⎝m⎠+12λD−+⎛ T ⎞+= ⎜ 2 ⎟⎝4πne0 ⎠12ωp12 2⎛4πne ⎞0= ⎜ ⎟⎝ m ⎠16
Nonlinear Electrostatic Waves in pair-ion Plasmas (contd.)Using reductive perturbation method, the perturbed quantities can beexpanded in the power series of ε as follows:( 1) 2 ( 2)n = 1 + εn + ε n + .....j j j( 1) 2 ( 2)v = εv + ε v + .....j j j( 1) 2 ( 2)Φ= εΦ + ε Φ + .....The stretching of independent variables are introduced in the following fashion:1ξ = ε 2( x −λt),τ = ε3 2twhere 0
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: Nonlinear Electrostatic Waves in pa
Page 19 and 20: 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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