Non-linear electrostatic waves in pair-ion plasmas - National Centre ...
Non-linear electrostatic waves in pair-ion plasmas - National Centre ...
Non-linear electrostatic waves in pair-ion plasmas - National Centre ...
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<strong>Non</strong><strong>l<strong>in</strong>ear</strong> Electrostatic Waves <strong>in</strong> Pair-<strong>ion</strong> Plasmas (contd.)Momentum equat<strong>ion</strong>s for positively and negatively charged <strong>ion</strong>s are describedas,(where φ is <strong>electrostatic</strong> potential) i.e.,2∂ φPoisson equat<strong>ion</strong> gives, = 4π e n− −2 +∂xEquilibrium is def<strong>in</strong>ed as,∂ v+ ∂v+e ∂φT+1 ∂n++ v+= − −∂t∂xm ∂xm n ∂x∂v∂t∂v+∂φ−∂x− − e− 1+ v−=∂xm−m−n−( n )( )n = n = n say0+ 0−0T++∂n−∂x∂φE = −∂x(3)(4)(5)(6)Dispers<strong>ion</strong> relat<strong>ion</strong>⎡⎢⎢⎣1 1⎤1+ ⎥ − =− + ⎦2 2 2 2 2 2 2( ω −VTk ) ( ω −VTk ) ⎥ ωp0(7)whereVTα⎛Tα⎞= ⎜ ⎟⎝m⎠12andωp12 2⎛4πne ⎞0= ⎜ ⎟⎝ m ⎠m +=m -(=m say)13
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