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

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