Planar and Nonplanar Solitary and Shock Waves in Electron-positron-ion Plasma

Abstract

In a number of astrophysical as well as laboratory environments, positrons, the antiparticles of electrons, coexist with electrons and ions to form three-component electron-positron-ion (e-p-i) plasma. The wave dynamics in this three-component plasma system is very di¤erent from that in the two component electron-ion (e-i) or electron-positron (e-p) plasmas. In the presence of ions, the low-frequency electrostatic and electromagnetic waves can exist in such a plasma but the presence of positrons in addition to the electrons, drastically changes the properties of these waves from those of conventional electron-ion plasma. In this thesis we have explored low-frequency electrostatic and electromagnetic solitary and shock waves in electron-positron-ion plasma. The linear and nonlinear dynamics of both planar and nonplanar cylindrically and spherically symmetric imploding waves are examined. Using reductive perturbative method, we have derived modi...ed Korteweg–de Vries Burgers equation for the ion-acoustic and magnetosonic nonlinear waves. Under appropriate limits, this equation describes the dynamics of planar as well as nonplanar small amplitude ion-acoustic and magnetosonic solitary and shock waves in three component e-p-i plasma. For the ion-acoustic waves (IAWs), the dynamics of the adiabatically hot ion ‡uid is governed by the continuity and momentum conservation equations and isothermal electrons and positrons are assumed to follow Maxwell- Boltzmann distribution. Whereas for the magnetosonic waves (MSWs), all the three species are assumed to be adiabatically hot and follow the ‡uid continuity and momentum balance equations. The major source of dissipation in both cases is the viscosity of the plasma. Maxwell’s equations govern the dynamics of electromagnetic ...elds generated due to the charge separation and current densities of the three species within the perturbed plasma. The e¤ect of changes in various plasma parameters (such as density and temperature ratios, plasma beta, kinematic viscosity etc.) as well as that of the nonplanar geometry, on the dynamics and properties of solitary and shock structures are investigated. It is found that both the amplitude as well as the width of ion-acoustic solitary waves decrease with the increase of positron-to-electron density as well as ion-to-electron temperature ratios. Whereas the amplitude of magnetosonic solitary waves decreases but width increases if the positron-to-electron density ratio increases. With respect to increase in plasma beta, the similar behavior is observed, provided positron-to-electron density ratio and plasma beta are larger than certain critical values. Below these critical values there exists a small range for plasma beta, where width of magnetosonic solitary structures decreases when the plasma beta is increased. The e¤ects of variation of various plasma parameters on the analytical as well as numerical shock wave solutions of the modi...ed Korteweg–de Vries Burgers equation are also explored. The numerical and analytical investigation of nonplanar solitary and shock waves show that, in contrast to the planar case, the speed and amplitude of imploding cylindrical and spherical solitary and shock structures continuously increase. A residue behind the main symmetric part of the solitary pulse also develops for the nonplanar waves as well as for the planar waves propagating through the viscous plasma. Viscous dissipation also results into the reduction of the amplitude and speed of the solitary waves, however broader solitary waves are less a¤ected by the viscous dissipation than the narrower ones. Further, using pseudopotential method, we have investigated the stationary pro...les of the ar- bitrary amplitude electrostatic (coupled ion-acoustic and ion–cyclotron) solitary waves in a mag- netized dense e-p-i plasma with dynamic classical ions and Thomas-Fermi distributed degenerate electron and positron species. We derive an energy integral type equation which is then numerically iiintegrated to obtain the solitary wave pro...le. In contrast to the solitary waves in tenuous non- degenerate classical e-p-i plasma with Boltzmannian electrons and positrons, the Thomas-Fermi distribution of positrons and electrons places additional limits on the amplitude and Mach number of the waves. The e¤ects of variation of concentration ratio of the various species and the angle of propagation with the external magnetic ...eld are examined and found to substantially a¤ect the solitary wave pro...les. Our model predicts only subsonic (with respect to the IAWs speed in unmag- netized dense e-i and e-p-i plasma) and hump-like positive-polarity (in wave potential) electrostatic solitary waves in the dense e-p-i magnetoplasma. Finally, using Krylov–Bogoliubov–Mitropolsky perturbation method, we have derived nonlinear Schrödinger (NLS) equation for the electrostatic ion (ion-acoustic and ion cyclotron) waves prop- agating obliquely and electromagnetic (magnetosonic) waves propagating perpendicular to the di- rection of magnetic ...eld through magnetized e-p-i classical plasma. We explored the criteria for the modulation instability and characteristic of envelope solitary structures formed by these nonlinear waves. We found that the ion-acoustic mode, which propagates below the ion-cyclotron frequency, is stable if the strength of the external magnetic ...eld is small. However, as the strength of the magnetic ...eld increases, this mode becomes modulationally unstable for a range of wave numbers and angles of propagation. For the ion-cyclotron mode, which propagates above the ion-cyclotron frequency, a number of stability/instability regions appear in the ( ; k) plane even for a very small value of the magnetic ...eld, where k is the wave number and is the angle of propagation with the direction of external magnetic ...eld. It is found that, for both modes, critical wave number separat- ing the stability and instability regions, shifts towards higher values as the density of the positron increases. Further, if rest of the parameters are ...xed, the width of both bright and dark envelope solitons decreases as the positron-to-electron density ratio increases. Perpendicular propagating MSWs in e-p-i plasma split into two modes. The modulation instability criterion for the MSWs in cold e-p-i plasma, reveals that the low frequency mode is always stable, whereas the high frequency mode becomes modulationally unstable for certain ranges of wave number and positron-to-electron density ratio. Furthermore, the positron-to-electron density ratio as well as the strength of ambient magnetic ...eld have been found to have signi...cant e¤ect on the growth rate of modulation instability as well as on the characteristics of solitary wave solutions of the nonlinear Schrödinger equation, namely, dark and bright envelope solitons. The nonstationary explode-decay type solitary wave so- lutions and their dependence on various plasma parameters through the dispersion and nonlinearity coe¢ cients of the NLS equation have also been brie‡y described.