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> <strong>pair</strong>-<strong>ion</strong> Plasmas (contd.)L<strong>in</strong>ear analysis of the modes <strong>in</strong> <strong>pair</strong>-<strong>ion</strong> <strong>plasmas</strong>Case (i)If T +=T -(=T say), then Eq.(7) givesω= 2ω+ V k2 2 2 2p Twhich is the usual Langmuir <strong>waves</strong> <strong>in</strong> <strong>pair</strong>-<strong>ion</strong> unmagnetized <strong>plasmas</strong>.(8)Case (ii) If T +≠T -, then Eq.(7) gives quartic equat<strong>ion</strong> as followswhere( ) ( )ω − V k + V k + 2ω ω + ω V + V k + k V V = 04 2 2 2 2 2 2 2 2 2 2 4 2 2T T p p T T T Tω+ − + − + −1= ( V k T+ VT k + 2ωp)± Δ+ −2{ }2 2 2 2 2 22( 2ω) 4 ω ( ){ }Δ= V k + V k + − V + V k + k V V2 2 2 2 2 2 2 2 2 4 2 2T T p p T T T T+ − + − + −(9)(10)here (+ve) and (-ve) sign gives higher and lower frequency Langmuir <strong>waves</strong><strong>in</strong> <strong>pair</strong>-<strong>ion</strong> <strong>plasmas</strong>.14
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