{"id":{"repo_id":"gmu","oai_identifier":"oai:MARS:1920/14506"},"canonical_url":"https://search.dev.ndltd.org/etd/gmu/oai:MARS:1920/14506","repository":{"repo_id":"gmu","name":"George Mason University","base_url":"https://mars.gmu.edu/server/oai/request"},"display":{"title":"Plasma Impedance Tomography","abstract":"This dissertation derives the plasma complete electrode model (PCEM), a numerical method for predicting the self- and -mutual impedances of dipoles in a plasma. The PCEM is then used as a forward operator in plasma impedance tomography (PIT), a new method developed in this dissertation, to form cross-sectional images of electron density in plasma. The PCEM extends the analytic work of Balmain from the 1960s on the impedance of dipoles in cold, fluid, magnetized plasma. Balmain’s result was limited to simple dipole geometry such as cylinders and to homogenous plasma. The PCEM assumes the same plasma permittivity derived by Balmain, but uses the finite element method to solve Poisson’s equation numerically. Consequently, the PCEM can be applied to arbitrarily shaped antennas and inhomogeneous plasma. The PCEM has good agreement with both Balmain’s analytic model and experimental data collected in the U.S. Naval Research Laboratory Space Physics Simulation Chamber with a cylindrical dipole impedance probe. During comparisons with experimental data, the PCEM also revealed connections between some features in the impedance spectrum and the plasma sheath around the dipole. To compute tomographic images of plasma density, this dissertation derives the Jacobian of the PCEM. This Jacobian solves a linearized version of the inverse problem associated with the PCEM, predicting plasma density from impedance probe measurements. In the cases studied in this dissertation, the Jacobian is a rank-deficient wide matrix and regularized using truncated singular value decomposition (TSVD). TSVD gives useful insight into the pixel point-spread-functions in the reconstructed image as well as estimates of signal-to-noise ratio based on the magnitudes of the non-zero singular values. This work derives a computationally efficiently method to compute the Jacobian for unmagnetized plasma. A more computationally expensive perturbation method estimates the Jacobian under arbitrary plasma conditions. This dissertation applies PIT to numerical studies of 8- and 12- dipole arrays. Three metrics, signal-to-noise ratio, resolution, and distortion, quantify the performance improvements of the 12-dipole array over the 8-dipole array as well as the impact to performance of rotating the dipoles so they are orthogonal to the imaging plane. Finally, these tools are used to investigate the frequency dependence of PIT, where it is shown that, for a given array and noise floor, and an assumption of an unmagnetized, homogenous background plasma, the array performs better below the plasma frequency.","abstract_html":"This dissertation derives the plasma complete electrode model (PCEM), a numerical method for predicting the self- and -mutual impedances of dipoles in a plasma. The PCEM is then used as a forward operator in plasma impedance tomography (PIT), a new method developed in this dissertation, to form cross-sectional images of electron density in plasma. The PCEM extends the analytic work of Balmain from the 1960s on the impedance of dipoles in cold, fluid, magnetized plasma. Balmain’s result was limited to simple dipole geometry such as cylinders and to homogenous plasma. The PCEM assumes the same plasma permittivity derived by Balmain, but uses the finite element method to solve Poisson’s equation numerically. Consequently, the PCEM can be applied to arbitrarily shaped antennas and inhomogeneous plasma. The PCEM has good agreement with both Balmain’s analytic model and experimental data collected in the U.S. Naval Research Laboratory Space Physics Simulation Chamber with a cylindrical dipole impedance probe. During comparisons with experimental data, the PCEM also revealed connections between some features in the impedance spectrum and the plasma sheath around the dipole. To compute tomographic images of plasma density, this dissertation derives the Jacobian of the PCEM. This Jacobian solves a linearized version of the inverse problem associated with the PCEM, predicting plasma density from impedance probe measurements. In the cases studied in this dissertation, the Jacobian is a rank-deficient wide matrix and regularized using truncated singular value decomposition (TSVD). TSVD gives useful insight into the pixel point-spread-functions in the reconstructed image as well as estimates of signal-to-noise ratio based on the magnitudes of the non-zero singular values. This work derives a computationally efficiently method to compute the Jacobian for unmagnetized plasma. A more computationally expensive perturbation method estimates the Jacobian under arbitrary plasma conditions. This dissertation applies PIT to numerical studies of 8- and 12- dipole arrays. Three metrics, signal-to-noise ratio, resolution, and distortion, quantify the performance improvements of the 12-dipole array over the 8-dipole array as well as the impact to performance of rotating the dipoles so they are orthogonal to the imaging plane. Finally, these tools are used to investigate the frequency dependence of PIT, where it is shown that, for a given array and noise floor, and an assumption of an unmagnetized, homogenous background plasma, the array performs better below the plasma frequency.","abstract_has_math":false,"creators":["Gatling, George"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024","date_published":"2024","updated_at":"2026-07-27T19:51:44Z","subjects":["electrical","impedance","plasma","tomography"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:1920/14506"],"render_values":[{"text":"hdl:1920/14506","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2024"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["electrical","impedance","plasma","tomography"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:1920/14506"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["This dissertation derives the plasma complete electrode model (PCEM), a numerical method for predicting the self- and -mutual impedances of dipoles in a plasma. The PCEM is then used as a forward operator in plasma impedance tomography (PIT), a new method developed in this dissertation, to form cross-sectional images of electron density in plasma. The PCEM extends the analytic work of Balmain from the 1960s on the impedance of dipoles in cold, fluid, magnetized plasma. Balmain’s result was limited to simple dipole geometry such as cylinders and to homogenous plasma. The PCEM assumes the same plasma permittivity derived by Balmain, but uses the finite element method to solve Poisson’s equation numerically. Consequently, the PCEM can be applied to arbitrarily shaped antennas and inhomogeneous plasma. The PCEM has good agreement with both Balmain’s analytic model and experimental data collected in the U.S. Naval Research Laboratory Space Physics Simulation Chamber with a cylindrical dipole impedance probe. During comparisons with experimental data, the PCEM also revealed connections between some features in the impedance spectrum and the plasma sheath around the dipole. To compute tomographic images of plasma density, this dissertation derives the Jacobian of the PCEM. This Jacobian solves a linearized version of the inverse problem associated with the PCEM, predicting plasma density from impedance probe measurements. In the cases studied in this dissertation, the Jacobian is a rank-deficient wide matrix and regularized using truncated singular value decomposition (TSVD). TSVD gives useful insight into the pixel point-spread-functions in the reconstructed image as well as estimates of signal-to-noise ratio based on the magnitudes of the non-zero singular values. This work derives a computationally efficiently method to compute the Jacobian for unmagnetized plasma. A more computationally expensive perturbation method estimates the Jacobian under arbitrary plasma conditions. This dissertation applies PIT to numerical studies of 8- and 12- dipole arrays. Three metrics, signal-to-noise ratio, resolution, and distortion, quantify the performance improvements of the 12-dipole array over the 8-dipole array as well as the impact to performance of rotating the dipoles so they are orthogonal to the imaging plane. Finally, these tools are used to investigate the frequency dependence of PIT, where it is shown that, for a given array and noise floor, and an assumption of an unmagnetized, homogenous background plasma, the array performs better below the plasma frequency."]},{"key":"dc:title","label":"Title","values":["Plasma Impedance Tomography"]}]}],"canonical_facts":{"dc:date.issued":["2024"],"dc:description.other":["This dissertation derives the plasma complete electrode model (PCEM), a numerical method for predicting the self- and -mutual impedances of dipoles in a plasma. The PCEM is then used as a forward operator in plasma impedance tomography (PIT), a new method developed in this dissertation, to form cross-sectional images of electron density in plasma. The PCEM extends the analytic work of Balmain from the 1960s on the impedance of dipoles in cold, fluid, magnetized plasma. Balmain’s result was limited to simple dipole geometry such as cylinders and to homogenous plasma. The PCEM assumes the same plasma permittivity derived by Balmain, but uses the finite element method to solve Poisson’s equation numerically. Consequently, the PCEM can be applied to arbitrarily shaped antennas and inhomogeneous plasma. The PCEM has good agreement with both Balmain’s analytic model and experimental data collected in the U.S. Naval Research Laboratory Space Physics Simulation Chamber with a cylindrical dipole impedance probe. During comparisons with experimental data, the PCEM also revealed connections between some features in the impedance spectrum and the plasma sheath around the dipole. To compute tomographic images of plasma density, this dissertation derives the Jacobian of the PCEM. This Jacobian solves a linearized version of the inverse problem associated with the PCEM, predicting plasma density from impedance probe measurements. In the cases studied in this dissertation, the Jacobian is a rank-deficient wide matrix and regularized using truncated singular value decomposition (TSVD). TSVD gives useful insight into the pixel point-spread-functions in the reconstructed image as well as estimates of signal-to-noise ratio based on the magnitudes of the non-zero singular values. This work derives a computationally efficiently method to compute the Jacobian for unmagnetized plasma. A more computationally expensive perturbation method estimates the Jacobian under arbitrary plasma conditions. This dissertation applies PIT to numerical studies of 8- and 12- dipole arrays. Three metrics, signal-to-noise ratio, resolution, and distortion, quantify the performance improvements of the 12-dipole array over the 8-dipole array as well as the impact to performance of rotating the dipoles so they are orthogonal to the imaging plane. Finally, these tools are used to investigate the frequency dependence of PIT, where it is shown that, for a given array and noise floor, and an assumption of an unmagnetized, homogenous background plasma, the array performs better below the plasma frequency."],"dc:identifier":["hdl:1920/14506"],"dc:subject":["electrical","impedance","plasma","tomography"],"dc:title":["Plasma Impedance Tomography"],"dc:type":["Dissertation"]},"updated_at":"2026-07-27T19:51:44Z"}