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[Taken from section Contributions of Work and Scope of Study]
The primary contributions of this work are two. The first is the development
of a voltage-{dependent sheath model valid in the frequency regime between the
electron and ion plasma frequencies and for negative high voltages. This model is
developed analytically and veried via plasma-chamber experiments and particle-
in-{cell computer simulations.
The second contribution is a circuit model for electrodynamic-{tether transmission
lines that incorporates the high{voltage sheath dynamics. The transmission-line
circuit model, which can be applied to insulated and uninsulated plasma-immersed
cylinders, is implemented with the standard SPICE circuit-simulation program. The
SPICE implementation allows complete tether systems to be modeled by including
circuit{models of the endpoints (which produce perturbations on the tether) with
the tether model itself. A range of excitation methods can be analyzed. Implementation
in SPICE also requires closed{form (i.e., non{transcendental and non{iterative)
solutions for the parameters. This is in contrast with the complicated dispersion
relations 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{cathode
assembly (HCA). This experimental characterization shows that the HCA can be
used to provide a plasma environment which closely resembles that found in the
ionosphere. The remaining contribution is a transient circuit model of the Tethered
Satellite System that was developed. This model was used to analyze TSS{1 mission
data and used a rigid coaxial model of the TSS tether which is valid under the
low{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 order
of or smaller than the Debye length or, alternately, much smaller than the sheath
In developing the transmission{line model, we rst developed a model of the
sheath response for a section of the transmission line. Then, certain assumptions
were 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{bound
experimental system was large enough to contain even a few tens of meters of tether
transmission line. This is certainly the case for the low{density plasmas and high
voltages needed to simulate propagation along the tethered system in the ionosphere
since the dynamic sheath can be large and magnetic elds can penetrate a long
distance from the line.2 Second, particle{in{cell simulations of such a system are
not 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 relied
on an available code which does not simulate propagation delay along a conductor.3
Third, the TSS system might have been able to provide some info on propagation
velocities, but the unfortunate break before achieving full deployment made moot
the 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, the
scope of the study, and an outline of the dissertation.
Chapter II provides background information relevant to this work as well as a
literature survey on previous work in the eld.
Chapter III develops a voltage{dependent sheath model valid in the frequency
regime between the electron and ion plasma frequencies. This model is developed
analytically and veried via plasma{chamber experiments and particle{
in{cell simulations.
Chapter IV develops a circuit model of the tether transmission line with parameters
based on the dynamic, voltage{dependent sheath.
Chapter V implements the tether{transmission{line circuit model in SPICE and
employs the model to examine several dierent excitations along the tether.
Chapter VI presents the conclusions of this dissertation and provides suggestions
for future research.
In addition, this dissertation contains six appendices which are structured as
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 of
a hollow{cathode assembly and its application to ionospheric plasma research.
Appendix C presents Langmuir{probe measurement theory for plasma measurements
in the orbital{motion{limited regime.
Appendix D includes the description of a transient circuit model of the Tethered
Satellite System which was developed and analyses of TSS mission data performed
with the model.
Appendix E contains listings of the simulation input les for the numerical simulations
performed in the dissertation.
Appendix F presents a table of the nomenclature used in the dissertation.

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  • Sven Gunnar Bil

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