Study Of Exact Solutions For Electrostatic Waves In Electron-Positron Plasma

A pure electron-positron (EP) plasma consists of electrons and positions with equal mass but opposite charge. But most EP plasmas also contain ions with different charges, so that such plasmas can be considered as complex plasmas.EP plasmas are ubiquitous in the very early Universe (according to the Big Bang theory). They are also relevant in other astrophysical phenomena such as neutron stars, pulsars, cosmic solar flares, black holes, jets of galactic nuclei, etc. since gamma ray scattering off atoms can also produce electrons and positrons. More recently, EP plasmas have been produced in the laboratory by ultraintense laser light interaction with matter and have been widely investigated.Since there is no difference in the electron and positron masses, in a pure EP plasma there is basically only one characteristic time scale. This implies that all the cooperative phenomena, such as the ion acoustic waves, the lower hybrid waves, and the other low-frequency phenomena on the ion time scale familiar in plasma physics will not appear. Since the electrons and positrons have opposite charges, the contributions from the two species can completely cancel each other, which lead to unique properties of the EP plasma. On the other hand, an EP plasma fully satisfies the definition of plasma, and has many of familiar properties of a classical plasma.In this thesis, we consider the non-perturbative solutions of EP waves in EP plasmas.In most existing investigations of nonlinear waves, finite but small-amplitude perturbations of a given equilibrium or steady state are made. That is, one considers weakly-nonlinear or quasilinear wave-wave or wave-particle interactions based on the linear normal modes.But in many physical systems, such as the early Universe or some high energy-density systems, a truly equilibrium or steady state does not readily exist even at very long time scales. That is, the system does not attain a truly stationary state, but it can still be in a dynamic equilibrium state that behaves periodically or quasi-periodically. Such states can be described by solving the governing equations in a frame moving with the wave or structure under appropriate boundary conditions. The mathematically exact solutions are nonperturbative and thus inherently stable within the description of the governing equations. They are until recently not much investigated. The background of the present work is discussed. We first introduce the basics of a plasma and the EP plasma, their properties of the waves in them, especially the nonlinear waves. Existing research work in this area are surveyed and summarized.We consider exact quasistationary wave solutions of the one-dimensional adiabatic warm-fluid equations for pure electron-positron plasmas. The results show that both smooth and spiky waves can exist. It is found that slow waves are only of small amplitude, and large-amplitude waves can have very high speeds. The results here imply that the energy in a newly produced EP plasma can be rapidly transported away by the large-amplitude EP waves, whereas in the linear or weakly nonlinear limit the wave group velocity and energy transport would depend mainly on the wavelength. There are no solitary solutions for the Sagdeev potentials are symmetric.We consider electron-positron plasmas with a stationary ion background. The plasma is adiabatic and the ions form a uniform background. The equations are integrated to a quadrature nonperturbatively. It is found that the quadrature for the electron density involves a singularity. It is shown that the plasma system can have a variety of dynamic quasistationary states in the form of waves, including that with spiky electron and/or positron density structures. Moreover, small-amplitude waves necessarily have small phase velocities, but large-amplitude waves can have high as well as low speeds. Although the Sagdeev potentials are not symmetric, from their profiles we can conclude that there are no solitary solutions.We consider the relativistic adiabatic motion of electrons and positrons in a plasma. It is found that exact plasma waves with very large density variations can exist. Depending on the physical parameters, these waves can be smooth or peaked. Very long wavelength sharply peaked periodic density structures are also found. There are no soliton solutions since the Sagdeev potential for the electrostatic potential is always symmetric. As such wave structures can allow for very high quasistatic electrostatic fields, they can be relevant in the interpretation of energetic astrophysical phenomena, as well as useful in the design of schemes for laser production and acceleration of electrons and positrons. Because the system Hamiltonians are similar, the results here are also directly applicable to electron-hole semiconductor systems in which the particle momentum-energy relation is nonparabolic in the presence of strong fields.The one-dimensional solutions investigated here may be useful as a guide in more detailed analytical or numerical investigations of large-amplitude waves in plasmas.In the conclusion, a brief summary of the thesis is given and topics for possible future work are discussed.