Effect of external highfrequency fields on unbounded and bounded plasmas

Abstract

It is widely recognised that the plasmas either in nature or in laboratory are bounded in one way or the other. In many situations, these plasmas are subjected to external oscillating fields such as laser?produced plasma and radio?frequency heating experiments. In the present work the author examines the effect of external hf field on bounded and unbounded plasmas, especially in the frequency regime of the external field that excludes the possibility of parametric coupling. The thesis starts with the presentation of the motivation and summary of the work, in the introductory chapter. In the second chapter, the effect of the external high?frequency (hf) fields on homogeneous infinite plasmas is considered. In addition to elucidating the derivation of dispersion relation, the spectra and damping of the electron and ion Bernstein modes are obtained and compared with the no?external hf field case. The normal modes and their damping of the plasma subjected to an external hf field are enumerated. In the third and fourth chapters, the study of a bounded plasma subjected to an external hf field is taken up. The third chapter is devoted to the presentation of mathematical techniques used in the derivation of the dispersion relation and its connection with those under various limiting situations, such as a pure electron plasma, plasma with no external hf field, etc., is established. The normal modes of the slab and semi? infinite plasmas show that the usual modes are modified by the hf field in that, the hf modes get an additional dispersion due to the hf field and the phase velocity of the low?frequency modes could be entirely determined by the hf field. Under certain conditions, the antisymmetric modes are affected to a larger extent than the symmetric modes in the case of a slab plasma. Another important observation is that the low? frequency sound?like modes which exist only in the presence of the external hf field have a different behaviour, as compared to those in the absence of the external hf field. While the sound modes in the absence of external hf field in the bulk and the surface could not be distinguished, those in the presence of an external hf field have distinguishable character due to their different frequencies. There are no hf Langmuir waves or low?frequency sound waves in the case where the external static magnetic field is normal to the boundary. But the Bernstein modes exist on the surface because of the cyclotron harmonic structure of the particle perturbation density across the magnetic lines of force. The importance of the study of the spatial structure of the surface waves lies in the fact that the wave electric field could be measured outside the plasma. In the fourth chapter, it is found that those surface waves whose existence demands the presence of the external hf field are true surface waves — their field is localised within one wavelength — as against the quasi?surface waves, like the ion sound waves in the absence of hf field. The case of a semi?infinite plasma in which there is a drift of the electrons relative to the ions along the surface is considered in Chapter V. The dispersion relation yields two unstable modes, one having a peak growth rate near the resonance point of the surface plasma oscillations and the other lying close to volume plasma oscillations. The comparison is made with the bulk two?stream instability and the general feature is that both bulk and surface instabilities are stabilised by the external hf field of high intensity, because the oscillation of electrons in the external hf field dominates over the drift motion. In certain regions of the electron stream velocity, the surface is stable, but is flanked by two unstable regions. Finally, in the last chapter, the Langmuir solitons in the presence of an external hf field are studied. The frequency–wave?number dependence of the mode is important to the study of the turbulence. Since the external hf field introduces an additional dispersion, it is interesting to study the case of soliton turbulence. When the thermal dispersion exceeds the dispersion introduced by the hf field, we always get Langmuir solitons. Once this situation reverses, then Langmuir solitons, with vanishing asymptotic amplitude, do not exist. Instead, what are known as "soliton holes" exist. In the situation where the soliton holes exist, the turbulence parameter is determined by the ratio of the Langmuir frequency to the hf field frequency, rather than the electron?to?ion mass ratio. If the depth of modulation of the soliton holes is maximum, then envelope shocks are formed. We conclude therefore that the propagation of non?linear Langmuir waves with and without the presence of the external hf field could be entirely different.