Derivation of Macroscopic Equations for a Warm Two-Fluid Turbulent Plasma and Applications of the Results.

A system of equations for the description of a turbulent plasma is obtained in a fully ionized, collisionless, warm two-fluid plasma model. The time-averaged macroscopic motion of the plasma is shown to be modified by ponderomotive forces arising from the interactions of fluctuating fields. A new expression for the ponderomotive force found in this thesis work is compared in detail with the results obtained by Washimi & Karpman and Klima & Petrizilka. These authors used the cold plasma approximation. It is shown that our expression reduces to the results of the aforementioned authors under the same conditions assumed by them. But, for a more general condition--a finite temperature, an inhomogeneous and a nonstationary plasma--the results we derive contain additional terms. The importance of these new terms in low frequency fields is discussed. Until now, studies of the effects of the ponderomotive force have been limited to high frequency fields or long wavelength fields, primarily because previous derivations of the ponderomotive forces were based on cold plasma approximation. The use of the more general expression derived in this thesis is expected to broaden the area of application of the ponderomotive force effects in collisionless plasma physics. As a specific application of our results, a plasma consisting of hot electrons and cold ions in low frequency electrostatic waves is studied. It is shown that the effects of the ponderomotive force caused by ion waves can dominate the effects of the thermal pressure of the plasma. It is suggested that the ponderomotive force of low frequency waves can support a D.C. electric field in plasma and many account for the magnetic-field-aligned large scale electric field observed in space. We also derive a generalized non-linear Schrodinger equation for the envelope of electrostatic waves. We have examined this non-linear equation and have found that the ion acoustic waves can have either a growing solution (modulation type instability) or a soliton-like solution, depending on the flow and thermal energies of the plasma as well as on the wave energy. These results are discussed in connection to space observations.