Linear and nonlinear electron-acoustic waves in plasmas with two electron components.
Mace, Richard Lester.
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Measurements of broadband electrostatic wave emIssons in conjunction with particle distributions in the earth's magnetosphere, have provided motivation for a number of studies of waves in plasmas with two electron components. One such wave-the electron-acoustic wave-arises when the two electron components have widely disparate temperatures (Watanabe & Taniuti 1977), and has a characteristic frequency that lies between the ion and electron plasma frequencies. Because of this broadband nature and because it is predominantly electrostatic, it provides a likely candidate for the explanation of the electrostatic component of "cusp auroral hiss" observed in the dayside polar cusp at between 2 and 4 earth radii as well as the broadband electrostatic noise (BEN) observed in the dayside polar regions and in the geomagnetic tail. The electron-acoustic wave and its properties provide the subjects for much of the investigation undertaken in this thesis. The thesis is divided into two parts. Part I is concerned with certain aspects of the linear theory of the electron-acoustic wave and is based on a kinetic description of the plasma. The dispersion relation for plane electrostatic waves obtained via linearisation of the Vlasov-Poisson system is studied in detail using analytical and numerical/geometrical techniques, and conditions under which the electron-acoustic wave arises are expounded. This work represents an extension of earlier works on Langmuir waves (Dell, Gledhill & Hellberg 1987) and the electron-acoustic wave (Gary & Tokar 1985). The effects of electron drifts and magnetization are investigated. These result, respectively, in a destabilization of the electron-acoustic wave and a modification of the dispersive properties. In this plasma configuration the model more closely replicates the conditions to be found in the terrestrial polar regions. We extend the parameter regimes considered in earlier works (Tokar &Gary 1984) and in addition, identify another electron sound branch related to the electron-cyclotron wave/instability. Effects of ion-beam destabilization of the electron-acoustic wave are also investigated briefly with a view to explaining BEN in the geomagnetic tail and also to provide a comparison with the electron-driven instability. In part II the nonlinear electron-acoustic wave is studied by employing a warm hydrodynamic model of the plasma components. We first consider weak nonlinearity and employ the asymptotic reductive perturbation technique of Washimi &Taniuti (1966) to render the hydrodynamical equations in the form of simpler evolutionary equations describing weakly-nonlinear electron-acoustic waves. These equations admit solitary-wave or soliton solutions which are studied in detail. Wherever possible we have justified our small amplitude results with full numerical integration of the original hydrodynamical equations. In so doing we extended the range of validity of our results to arbitrary wave amplitudes and also find some interesting features not directly predicted by the small amplitude wave equations. In this respect we were able to determine the important role played by the cool- to-hot electron temperature ratio for soliton existence. This important effect is in accordance with linear theory where the electron temperature ratio is found to be critical for electron-acoustic wave existence. The effects of magnetization on electron-acoustic soliton propagation is examined. We found that the magnetized electron-acoustic solitons are governed by a Korteweg-de Vries-Zakharov-Kusnetsov equation. In addition, it is shown that in very strong magnetic fields ion magnetization can become important yielding significant changes in the soliton characteristics. Multi-dimensional electron-acoustic solitons, which have greater stability than their plane counterparts, are also briefly discussed. Employing a weakly-relativistic hydrodynamic model of the plasma, the effect of a cool, relativistic electron beam on such soliton parameters as width, amplitude and speed is studied in detail. Both small- and large amplitude solitons are considered. The arbitrary-amplitude theory of Baboolal et al. (1988) is generalised to include relativistic streaming as well as relativistic thermal effects. The importance of the cool electron (beam)to- hot electron temperature in conjunction with the beam speed is pointed out. Finally, we derive a modified Korteweg-de Vries (mKdV) equation in an attempt to establish whether electron-acoustic double layers are admitted by our fluid model. Although double layers formally appear as stationary solutions to the mKdV equation, the parameter values required are prohibitive. This is borne out by the full fluid theory where no double layer solutions are found.