PULSE PROPAGATION ALONG CONDUCTORS IN LOW – DENSITY , COLD PLASMAS AS APPLIED TO ELECTRODYNAMIC TETHERS by

Abstract

[Taken from section Contributions of Work and Scope of Study]The primary contributions of this work are two. The first is the developmentof a voltage-{dependent sheath model valid in the frequency regime between theelectron and ion plasma frequencies and for negative high voltages. This model isdeveloped analytically and veried via plasma-chamber experiments and particle-in-{cell computer simulations.The second contribution is a circuit model for electrodynamic-{tether transmissionlines that incorporates the high{voltage sheath dynamics. The transmission-linecircuit model, which can be applied to insulated and uninsulated plasma-immersedcylinders, is implemented with the standard SPICE circuit-simulation program. TheSPICE implementation allows complete tether systems to be modeled by includingcircuit{models of the endpoints (which produce perturbations on the tether) withthe tether model itself. A range of excitation methods can be analyzed. Implementationin SPICE also requires closed{form (i.e., non{transcendental and non{iterative)solutions for the parameters. This is in contrast with the complicated dispersionrelations often derived for waves on plasma{immersed conductors.There are two other contributions of this work that are included in the appendices.The rst is an analysis of the far{eld plasma environment of the hollow{cathodeassembly (HCA). This experimental characterization shows that the HCA can beused to provide a plasma environment which closely resembles that found in theionosphere. The remaining contribution is a transient circuit model of the TetheredSatellite System that was developed. This model was used to analyze TSS{1 missiondata and used a rigid coaxial model of the TSS tether which is valid under thelow{voltage conditions of the TSS{1 mission.Throughout this work we assume a tether transmission line with TSS geometry.The models can be extended to other tether geometries, in addition to other plasma{(insulator){conductor geometries for which the conductor diameter is on the orderof or smaller than the Debye length or, alternately, much smaller than the sheathdistance.In developing the transmission{line model, we rst developed a model of thesheath response for a section of the transmission line. Then, certain assumptionswere made to allow the model to become distributed along the length of the line.Direct distributed results were not possible for three reasons. First, no Earth{boundexperimental system was large enough to contain even a few tens of meters of tethertransmission line. This is certainly the case for the low{density plasmas and highvoltages needed to simulate propagation along the tethered system in the ionospheresince the dynamic sheath can be large and magnetic elds can penetrate a longdistance from the line.2 Second, particle{in{cell simulations of such a system arenot possible due to the computational costs of simulating even a few tens of meters.In addition, since the scope of this work was not PIC{code development, we reliedon an available code which does not simulate propagation delay along a conductor.3Third, the TSS system might have been able to provide some info on propagationvelocities, but the unfortunate break before achieving full deployment made mootthe scheduled experiments.The six chapters of this dissertation are structured as follows:Chapter I gives an introduction to the research, the contributions made by it, thescope of the study, and an outline of the dissertation.Chapter II provides background information relevant to this work as well as aliterature survey on previous work in the eld.Chapter III develops a voltage{dependent sheath model valid in the frequencyregime between the electron and ion plasma frequencies. This model is developedanalytically and veried via plasma{chamber experiments and particle{in{cell simulations.Chapter IV develops a circuit model of the tether transmission line with parametersbased on the dynamic, voltage{dependent sheath.Chapter V implements the tether{transmission{line circuit model in SPICE andemploys the model to examine several dierent excitations along the tether.Chapter VI presents the conclusions of this dissertation and provides suggestionsfor future research.In addition, this dissertation contains six appendices which are structured asfollows:Appendix A summarizes the ionospheric plasma parameters used in this work.Appendix B presents the results of a study on the far{eld plasma environment ofa hollow{cathode assembly and its application to ionospheric plasma research.Appendix C presents Langmuir{probe measurement theory for plasma measurementsin the orbital{motion{limited regime.Appendix D includes the description of a transient circuit model of the TetheredSatellite System which was developed and analyses of TSS mission data performedwith the model.Appendix E contains listings of the simulation input les for the numerical simulationsperformed in the dissertation.Appendix F presents a table of the nomenclature used in the dissertation.