Echoes and Scattering from Plasma in a Magnetic Field

Creators: Blum, F. A.

Abstract

A study of the high frequency properties of a low temperature plasma column in a longitudinal magnetic field is described. The experimental observations give a relatively complete picture of the microwave (extraordinary mode) properties of the plasmas studied, encompassing continuous wave scattering and noise emission measurements, as well as the demonstration of the occurrence of related echo processes. Theoretical developments deal largely with a physical model consisting of a one-dimensional slab of cold (zero temperature) plasma which is nonuniform in the steady state and immersed in a uniform magnetic field. Data on the continuous wave reflection and noise emission from some afterglow rare gas discharges are given. The electron temperature in these plasmas is low, approaching room temperature. The reflection and emission are measured as a function of magnetic field in the vicinity of electron cyclotron resonance with electron density as a parameter. The electron densities are such that (ω_(p)/ω) ≤ 1 , where ω_p is the electron plasma frequency and ω is the signal frequency. Both types of experiment show the presence of collective effects which yield a normal mode spectrum strongly dependent on the electron density. A broad peak is observed in the region (ω_(c)/ω) ≤ 1 where ω_c is the electron cyclotron frequency. This peak shifts to lower values of (ω_(c)/ω) and broadens as the electron density increases. For all values of electron density, a sharp peak is found very close to (ω_(c)/ω) = 1, the cyclotron resonance condition. The experimental and theoretical results suggest that the phenomena observed involve resonance effects at the upper hybrid frequencies (ω_(h)^(2 = ω_(c)^(2) + ω_(p)^(2)) of the plasma. Data are also given on a new two-pulse echo process which occurs in these after-glow plasmas. The results establish the intimate relation between the echoes and the upper hybrid normal modes studied in the CW experiments, demonstrating the dominant role played by collective effects in the formation of this echo. A weakly nonlinear cold plasma theory yields upper hybrid echoes which are strongest in a narrow band of frequencies near the maximum upper hybrid frequency of the nonuniform plasma, in agreement with experiment. Furthermore, large signal computations of the dependence of the echo amplitude on excitation pulse separation and amplitude show a complex behavior in qualitative agreement with experiment. As a supplementary topic, the properties of echoes from a general collection of anharmonic oscillators are discussed. The oscillators in this discussion are a general mathematical analog of the upper hybrid normal modes of a cold nonuniform plasma. Through emphasis of effects due to the finite width of the excitation pulses, the calculations show explicitly the role of the various characteristics of the oscillators in echo processes, further delineating the general features thought requisite of classical multiple-pulse echo systems.

Additional Information

The writing of this thesis marks the culmination of many years of work toward a long standing goal. My achievements during these years are due in part to the advice, encouragement, and training of many people. In a real sense, all of these people contributed to this thesis. To each of them I extend my sincere thanks. However, two people stand out conspicuously: Professor R. N. Little of the University of Texas and Professor L. Davis of Caltech. The open office doors, obvious concern and generous spirit of these men gave invaluable impetus to my career as a student and physicist. There are several people who have contributed in a more direct sense to the accomplishment embodied in this thesis. I am thoroughly grateful and indebted to Professor R. W. Gould for his profound influence on my professional advancement and achievement in recent years. His direct contributions to the work, willingness to collaborate, and patience are exceptional. In addition, I wish to thank my colleague L. 0. Bauer for his cooperation and invaluable contributions to the material in this paper. My thanks go also to others of the Plasma Laboratory and Caltech who have played a useful role at one time or another during the course of this work. Particularly, I thank Professor R. S. Harp for his enlightened comments and advice, and R. Stenzel for collaboration and the use of his radiometer. I am indebted to Hughes Aircraft Company and the National Science Foundation for financial support during the course of my graduate studies. My sincere thanks go to Mrs. Ruth Stratton for the patience, loving care and efficiency she exercised in typing this manuscript. Finally, I am deeply grateful to my wife, Joy; her love and devotion as a wife and mother have made the task at hand palatable and worth while.

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