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 ...
Nonlinear Plasma DynamicsWhen wave amplitude grows to such high values that linear perturbationtheory cannot be applied to describe the interactions in plasmas. Theninstead of applying Fourier analysis, we transform the original set ofnonlinear equations, that describe the wave dynamics, into lowest ordernonlinear equations (such as KdV equation, Burgers equation and NLSequation) whose properties are well known.For arbitrary amplitude waves, one has to solve the nonlinear differentialequations with full nonlinear glory and difficulties. This method haslimitations and cannot be used in general and applicable to only somespecific problems.Reductive perturbation method is used when one cannot deal theequations with full nonlinearity and weak nonlinearity are assumed in thesystem. The stretched variables in space and time are defined and slowtime variations are induced by the nonlinearity of the system. For example,the KdV equation is obtained for low amplitude nonlinear wave with6appropriate scaling of space and time variables.
2. Brief Introduction of pair-ion Plasmas‣In usual electron-ion plasmas, asymmetry in collective phenomenonoccur due to large difference of mass between electrons and ions.‣However, pair plasmas (e-p) consists of positively and negativelycharged particles of same mass to keep the space, time symmetrybecause the mobility of equal mass particles is same in theelectromagnetic field.‣Pair plasma consists of positrons and electrons have been producedin laboratory experiments. But the identification of collective modes isvery difficult because the annihilation time is short compared with theplasma period.‣Therefore, attention is concentrated on the stable generation of apair-ion plasma in laboratory consisting of positive and negative ionswith an equal mass for collective modes identification.‣It has been found that fullerene (C 60) can be adopted as an ionsource for pair-ion plasma production, based on the fact thatinteraction of electrons with fullerenes lead to the production of bothnegative and positive ions.7
- Page 1 and 2: Nonlinear electrostatic structures
- Page 3 and 4: 1. Soliton‣ Soliton is a nonlinea
- Page 5: Soliton in Plasmas (contd.)Linear w
- 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 and 18: 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
<strong>Non</strong><strong>l<strong>in</strong>ear</strong> Plasma DynamicsWhen wave amplitude grows to such high values that <strong>l<strong>in</strong>ear</strong> perturbat<strong>ion</strong>theory cannot be applied to describe the <strong>in</strong>teract<strong>ion</strong>s <strong>in</strong> <strong>plasmas</strong>. Then<strong>in</strong>stead of apply<strong>in</strong>g Fourier analysis, we transform the orig<strong>in</strong>al set ofnon<strong>l<strong>in</strong>ear</strong> equat<strong>ion</strong>s, that describe the wave dynamics, <strong>in</strong>to lowest ordernon<strong>l<strong>in</strong>ear</strong> equat<strong>ion</strong>s (such as KdV equat<strong>ion</strong>, Burgers equat<strong>ion</strong> and NLSequat<strong>ion</strong>) whose properties are well known.For arbitrary amplitude <strong>waves</strong>, one has to solve the non<strong>l<strong>in</strong>ear</strong> differentialequat<strong>ion</strong>s with full non<strong>l<strong>in</strong>ear</strong> glory and difficulties. This method haslimitat<strong>ion</strong>s and cannot be used <strong>in</strong> general and applicable to only somespecific problems.Reductive perturbat<strong>ion</strong> method is used when one cannot deal theequat<strong>ion</strong>s with full non<strong>l<strong>in</strong>ear</strong>ity and weak non<strong>l<strong>in</strong>ear</strong>ity are assumed <strong>in</strong> thesystem. The stretched variables <strong>in</strong> space and time are def<strong>in</strong>ed and slowtime variat<strong>ion</strong>s are <strong>in</strong>duced by the non<strong>l<strong>in</strong>ear</strong>ity of the system. For example,the KdV equat<strong>ion</strong> is obta<strong>in</strong>ed for low amplitude non<strong>l<strong>in</strong>ear</strong> wave with6appropriate scal<strong>in</strong>g of space and time variables.
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