Investigation Of Exact Nonlinear Electron Plasma Wake Waves In Isothermal And Adiabatic Plasmas

Electron plasma waves (EPWs) can be considered as ubiquitous in any plasma and have been investigated extensively since the beginning of plasma physics research. Most studies on nonlinear EPWs are based on perturbation analyses, so that the maximum possible wave amplitude is usually limited. On the other hand, there exists a few exact wave solutions of the fluid equations describing cold and warm electron plasmas. In this thesis, the problem of exact quasistationary wave solutions of the electron fluid equations are reconsidered in more detail. Also investigated are exact EPWs driven by moving charged object(s), relativistic EPWs, as well as adiabatic EPWs.Quasistationary electron plasma waves of arbitrary amplitude and speed that are exact solutions of the isothermal electron fluid equations are shown to exist. Besides the existing solutions, very-large-amplitude non-neutral EPWs propagating at suprathermal speeds are shown to exist. Within the limitations of the non-relativistic warm-fluid theory, smooth as well as spiky quasistationary EPWs and solitary structures of nearly any phase speed can appear. In rarefied plasmas, such wave structures can involve positively charged (due to the immobile ions) phase regions that are almost completely void of electrons.Fully nonlinear quasistationary wake plasma waves excited by and comoving with charged objects and pulse(s) are investigated next. The characteristics of the excited plasma wave depend on a (nonlinear) resonance between the wave and the pulse. Under certain conditions there can be almost no wake wave excitation as well as excitation of highly localized plasma wave packets with only a few oscillations. We also consider plasma wave excitation by two consecutive pulses. With two comoving charged Gaussian driver pulses, localized wake structures with only very weak plasma oscillations and no long tails can be produced. Such localized wake structures appear if the separation distance between the two driving pulses satisfies a scaling law. In this case the pulse pair is well shielded despite their suprathermal motion.Nonlinear electron plasma waves driven by a charged particle pulse or rigid object moving at relativistic speeds are also investigated. It is found that relativistic effects can be important in determining the characteristics of the wake plasma waves even for relatively slow-moving objects since the amplitude, and therefore the speeds of the oscillating electrons, of the resonantly excited waves can be large. Quasistationary smooth and spiky wake waves comoving with the object are found. Localized soliton-like solutions are also shown to exist. However, relativistic effects tend to hinder their formation because of the electron mass increase. Application of the very-large-amplitude wake density waves as a source for ultrahigh-energy cosmic-ray events is discussed.Large amplitude EPWs in adiabatic electron plasmas are also considered. In this case, the characteristic of EPWs is similar to that in isothermal electron plasmas.