Éric Choinière

Self-Consistent 2-D Kinetic Simulations of High-Voltage Plasma Sheaths Surrounding Ion-Attracting Conductive Cylinders in Flowing Plasmas

Using the self-consistent steady-state 2-D Kinetic Plasma Solver (KIPS-2D), thorough characterizations are performed of high-voltage cylindrical sheaths surrounding ion-attracting conductive cylinders immersed in stationary as well as flowing collisionless plasmas. Analytical fits are obtained that allow for the accurate prediction of stationary sheath sizes for round-cylinder radii anywhere from one thousandth of a Debye length to five Debye lengths and for any bias potential beyond a small lower bound. Plasma flow is shown to progressively compress the sheath on its ram and lateral sides, down to a limit that closely matches the stationary frozen-ion sheath radius. Conversely, plasma flow is shown to cause a significant wake-side elongation of the sheath. The quasi-elliptical sheath-edge contours observed under flowing conditions can be characterized by their along-flow and across-flow dimensions. By normalizing these dimensions against stationary-sheath diameters, contour plots of the corresponding flow-effect correction factors can be obtained that account for plasma-flow velocity effects in a wide range of speed regimes and bias potentials. In this paper, Mach numbers up to ten and bias potentials from -10Te to -500Te (where Te is the electron temperature in units of volts) are simulated and corresponding correction factors are computed, although KiPS is capable of simulating even higher speeds and bias potentials. These correction factors appear to stabilize at high voltages, suggesting that their values at the highest simulated potential bias possibly can be used with reasonable accuracy to predict performance at even higher (but nonrelativistic) bias-potential values using analytical equations derived from stationary simulations. For example, at a Mach number of 1.1, the along-flow and across-flow sheath dimensions at high voltages are expected to be around 115% and 85% of the stationary-sheath diameter, respectively. Flow-effect correction factors for current collection are also obtained for the ram-side, wake-side, and total collected current. For the same plasma-velocity example, at high voltages, total current collection is minimized to about half of the stationary value, which would translate into a 50% reduction in power to collect the current. This example is of significance for Earth-radiation-belt remediation-system concepts using high-voltage tethers

Analysis of chamber simulations of long collecting probes in high-speed dense plasmas

Chamber tests of simulated electrodynamic tethers (EDTs) of different geometries operating in a dense high-speed plasma are described. The geometries tested and described here are cylindrical and flat-ribbon tape. By moving the probe samples relative to the plasma source it was possible to vary the density and therefore the effective width over a range of approximately 1 to 2 Debye lengths (/spl lambda//sub D/) for the cylinder sample and 6 to 19 /spl lambda//sub D/ for the tape samples. Several important conclusions can be drawn from the tests. 1) The current-voltage characteristics of the cylinder behave as predicted by orbital-motion-limited (OML) current collection theory in the saturation region. 2) The tape tether had comparable current levels to a theoretical equal area OML cylinder up to an effective width of at least /spl sim/11/spl lambda//sub D/ and possibly wider. 3) Orienting the tape samples parallel or perpendicular to the plasma flow yielded different current responses (perpendicular is larger) above a bias potential that is near the estimated energy of the incoming beam ions. The observed difference was generally more pronounced at larger effective widths (higher densities). 4) It was also necessary to be above this bias potential to have a V/sup 0.5/ current-voltage character appropriate for an ideal cylinder in the OML regime. It is concluded that wide ribbon-like tape tethers can be effective current collectors but that velocity effects will be a factor to consider, especially as relative width of the tape tether (with respect to /spl lambda//sub D/) grows.

Experimental investigation of electron collection to solid and slotted tape probes in a high-speed flowing plasma

This paper presents the analysis and comparison of measurements of electron current collection to round cylinder, solid tape, and slotted tape electrodynamic-tether samples in a mesosonic flowing plasma. A Hall thruster was used to simulate a flowing unmagnetized space plasma in a large 6-m /spl times/ 9-m vacuum chamber. Guarded tether samples were employed to mitigate end effects. Plasma parameters were determined based on the ion saturation and electron retardation regimes of a cylindrical Langmuir probes current characteristics. Solid tape samples with widths spanning from 4.9 to 41.9 Debye lengths, and slotted tapes with center-to-center line spacings spanning from 1.4 to 13.2 Debye lengths were tested. Several conclusions can be drawn from the analysis of the results: 1) the plasma flow leads to significant current enhancements over that predicted by the orbital-motion-limited theory; 2) the electron current collected per unit area on solid tapes decreases as the width of the tape is increased; 3) beyond a threshold bias close to the beam energy, solid and slotted tapes both collect more current when oriented transverse to the flow; 4) slotted tapes are more efficient electron collectors per unit area than solid tapes; and 5) our data suggests that the electron current collected on slotted tapes decreases with increasing line spacing until a possible minimum is attained, beyond which it is expected to start increasing again. The minimum was attained in the case of the samples oriented transverse to the flow, but not in the case of the samples aligned with the flow, for which the critical spacing is likely higher (due to an increased sheath interaction radius of each line caused by flow-induced sheath elongation).

Modeling Long Probes in Flowing Plasmas using KiPS-2D, a Novel Steady-State Vlasov Solver

A Consistent steady-state kinetic 2D plasma model and the corresponding computational solver were developed and used for the modeling of long conductive electron-collecting probes in o wing mesosonic plasmas. Sheath asymmetries, not accounted for in previous treatments of ion-collecting probes in o wing plasmas, are modeled here and shown to consititute an important mechanism for the departure from OML theory for electron current collection in the mesosonic regime. The eects of collisions are addressed by dividing the space surrounding the probe into a collisionless computational space and a collisional background plasma. The implementation of the solver consists of successive linearizations of the nonlinear Poisson-Vlasov operator, within a Tikhonov-regularized Newton iterative process. The Finite Element Method is used for the Poisson solver, while the inside-out trajectory tracking procedure is used for the Vlasov solver. The parallel solver allows for the arbitrary velocity distributions of both species within the computational domain, provides an adaptive, unstructured meshing strategy, and allows simulation of very large computational domains. Results show indication of a small enhancement, with respect to OML theory, of the collected current to an electron-attracting probe in a o wing plasma. This enhancement is attributed to the elongation of the pre-sheath into the collisional zone of the plasma, which causes an enhanced density of incoming electrons upstream from the probe, and is seen to dominate the opposing decrease in electron collection due to additional potential barriers created by a wake-side depression of the electric potential. The primary issue is the accumulation of noise in the solution that subsides in spite of the employed Tikhonov regularization, limiting the progress of the iterative scheme. Improvements in the Vlasov solver to reduce the amount of quadrature noise it generates are planned to improve the consistency of solutions.

Current Collection to Electrodynamic-Tether Systems in Space

Three important electrodynamic-tether system configurations have been investigated: an insulated tether with an end body collector, bare tether, and bare tether with end body collector. This paper discusses the current collection capabilities of these configurations and their respective advantages and disadvantages. University of Michigan’s TEMPEST computer model was used to conduct the analyses of the three configurations. Analysis has determined that all three configurations allow orbit raising from 400 km to 700 km in around 18.5 days under similar ionospheric and system conditions. In addition, the best tether geometry to use for any of these configurations would be a slotted tether oriented perpendicular to the plasma flow with the individual wires as far apart as possible and as narrow as possible. This would minimize atmospheric drag, increase collision survivability, and keep the electron collection level close to the orbital-motion limit, while increasing the redundancy of the tether in case of micrometer collision..

Measurement of cross-section geometry effects on electron collection to long probes in mesosonic flowing plasmas

This paper presents the analysis and comparison of measured electron current collection to cylindrical, solid tape, and slotted tape electrodynamic-tether samples in a mesosonic o wing plasma. A Hall thruster was used to simulate a o wing unmagnetized space plasma in a large 6m 9m vacuum chamber. Guarded tether samples were designed to mitigate end eects. Plasma parameters were determined based on the ion saturation and electron retardation regimes of a Langmuir probe’s current characteristics. Solid tape samples with eectiv e widths spanning from 4.9 to 41.9 Debye lengths, and slotted tapes with line spacings spanning from 1.4 to 13.2 Debye lengths were tested. Several conclusions can be drawn from the analysis of the results: 1) The plasma o w leads to current enhancements over that predicted by the orbital-motion-limited theory; 2) the electron collection eciency of solid tapes (on a per area basis) decreases as the width of the tape is increased; 3) beyond a threshold bias close to the beam energy, solid and slotted tapes both collect more current when oriented transverse to the o w; 4) equivalent width slotted tapes are more ecien t electron collectors than solid tapes on a per area basis; 5) our data suggests the electron collection eciency of slotted tapes decreases with increasing line spacing until a possible minimum eciency is attained, beyond which it is expected to start increasing again. The minimum was attained in the case of the samples oriented transverse to the o w, but not in the case of the samples aligned with the o w, for which the critical spacing is likely higher due to an increased sheath interaction radius of each line caused by the elongation of the sheath associated with plasma o w.

Assessment of Plasma-Flow Effect on Langmuir Triple-Probe Operation via Kinetic Simulation

A self-consistent steady-state 2-D kinetic plasma solver has been applied to the problem of Langmuir triple-probe plasma diagnostic measurements in a flowing collisionless plasma. The triple-probe response is simulated for ion Mach numbers M = 0 - 5 and probe radii rp = 1 - 90 lambdaD (Debye length). Results indicate that a high probe radius and high ion Mach numbers more closely approximate the ideal thin-sheath triple-probe response. Small probe radii on the order of the Debye length can result in temperature errors of the ideal model greater than 70% for a probe bias of 20 V. An analytical approximation is described, approximating triple-probe measurement offsets given arbitrary probe bias and probe radius and ion Mach numbers 0 < M < 5. The fitting error from this analytical approximation is estimated at 2%-6%.

Investigation of Ionospheric Plasma Flow Effects on Current Collection to Parallel Wires Using Self-Consistent Steady-State Kinetic Simulations

Multi-wire structures are needed for practical implementations of bare electrodynamic tether systems in space propulsion and radiation belt remediation applications. Using KiPS-2D, a self-consistent, steady-state kinetic solver developed at the University of Michigan, we study the sheath structure and ion current collection properties of a set of two ion-attracting cylinders immersed in a flowing plasma. The effect of plasma flow, center-tocenter spacing and orientation of the set of wires with respect to plasma flow is analyzed. Results indicate that a strong coupling exists between the cylinders’ sheath structures even when their sheaths are separated spatially, whether in a stationary or flowing plasma and for both the parallel-to-flow and perpendicular-to-flow orientations. This coupling reflects strongly in the ion current collection levels observed, through unpopulated bounded ion trajectories connecting both cylinders (reducing current collection) and ion beam focusing of one cylinder onto the other (enhancing current collection). Results at wide spacings show that, when oriented parallel to plasma flow, the set of cylinders collects significantly less (by about 20%) ion current than in a stationary plasma. Conversely, at wide spacings a set of cylinders oriented perpendicular to plasma flow collects significantly more (about 30% more) current than in a stationary plasma. The latter enhancement is primarily attributed to the focusing of ions by each cylinder onto the other cylinder’s wake-side surface.

Poisson-Vlasov Modeling of Parallel Cylinders in Ionospheric Plasmas

Bare electrodynamic tethers have been proposed for two important space applications: in-orbit propellantless propulsion [1,2] and remediation of Earth-bound radiation belts through the scattering of high-energy electrons leading to their accelerated precipitation [3–5]. The latter application is oftentimes referred to as space remediation. In both applications, the use of multiple parallel conducting wires is being considered. Such a multistrand structure would provide improved survivability to collisions with micrometeroid. Additionally, since sheath size is roughly a function of the total amount of linear surface charge held on the tether system [6], a multi-wire structure might allow for the formation of the large plasma sheath required for effective scattering in the space remediation application, at a reduced cost in terms of expended power due to the increased capacitance provided by the relative proximity of parallel wires. In an effort to get a basic understanding of the physics of plasma-immersed multi-wire conductive structures, we consider in this paper a structure consisting of two parallel, identical round cylinders with equal potential bias. Both cylinders have a radius r0 and their centers are spaced apart by a distance ∆x. Section II presents an overview of the theory used in our plasma solvers. Section III presents our simulation results.

High-Voltage Plasma Sheaths Around Long Conductive Structures in Flowing Plasmas: Simulations and Experiments

Summary form only given. Long conductive structures immersed in flowing space plasmas have several potential science and engineering applications. Among them are propellantless in-orbit spacecraft tether propulsion and high-energy charge precipitation from the Earths radiation belts, also known as remediation of radiation belts. In addition, the use of Langmuir probes as in-space plasma diagnostic tool is well known. However, existing models commonly used as design tools for these applications are limited in terms of cross-sectional geometry and the range of voltage bias or plasma flow speed. To address this need, a steady-state kinetic computational model called kinetic plasma solver (KiPS-1D and KiPS-2D) was developed allowing for self-consistent simulations of collisionless, unmagnetized flowing plasmas in a vast region surrounding any two-dimensional conductive object. Using the KiPS simulations it was possible to assess interference effects between two parallel cylinders. It was also possible to predict for negatively biased probes substantial sheath asymmetries causing compression on the ram side and long tails on the wake side and to predict this behavior as a function of plasma flow characteristics and high bias potentials. We were able to test basic predictions over certain ranges of plasma flow and bias using Michigans Large Vacuum Tank Facility (LVTF) and an expanding plasma source. From these experiments we were able to establish good agreement with simulation predictions. Finally, we were able to validate the basic prediction that much larger overall sheath structures could be generated by multi-wire structures (arranged to make a larger, but porous cylinder) but requiring less power than would otherwise be needed for the same number of isolated wires