Kinetic Method for Quasi-One-Dimensional Simulation of Magnetic Nozzle Plasmadynamics.

A novel technique was developed modeling two-dimensional magnetic field effects in a one-dimensional electrostatic particle-in-cell code. This quasi-one-dimensional formulation incorporates two-dimensional effects through inclusion of cross-sectional area variation and magnetic field forces. The new method is verified with a newly formulated set of test cases of a two-particle system, magnetic mirrors, and fully two dimensional simulations. Magnetic nozzle physics and ion acceleration in low temperature plasmas were investigated with a test problem using these kinetic simulations. Effects of the density variation due to plasma expansion and the magnetic field forces on ion acceleration were investigated. Density variation only weakly affected ion acceleration. Magnetic field forces acting on the electrons were found to be responsible for the formation of potential structures which accelerate ions. Formation of a high energy ion beam is seen due to ion acceleration. Strongly diverging magnetic fields drive more rapid potential drops and the length of the radio frequency heating region was found to significantly affect the electron temperature profiles. Simulations were performed with both argon and xenon. For the same driving current, argon simulations demonstrated higher ion velocities while xenon simulations showed higher plasma densities. Ion acceleration physics was investigated verifying that ion acceleration occurs due to potential structures established by the magnetic field forces on the electrons. Effects of anisotropic electron pressure tensors were also found to be important for determining an Ohm's law used to solve for the induced electric field which accelerates the ions. Bi-Maxwellian and non-Maxwellian velocity distributions were seen for the electrons along with the anisotropic temperatures, verifying the need for kinetic simulations. Electron thermodynamic relations (isothermal, adiabatic, polytropic, double adiabatic) were evaluated for a number of simulation results. Results from quasi-one-dimensional simulations were used to estimate thruster performance parameters such as specific impulse and thrust. Simulations with parameters similar to the Helicon Double Layer Thruster were performed. Results from these simulations look encouraging for future device studies. Similar electron temperatures and normalized density profiles are seen in the experiments and simulations. Velocity and energy distribution functions for ions and electrons also show similar behavior to that measured in experiments.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133315/1/ebersohn_1.pd

A Two-dimensional Hybrid-Direct Kinetic Model of a Hall Thruster

The goal of this dissertation is to improve the state-of-the art modeling approaches available for simulating the discharge plasma in a Hall effect thruster (HET). A HET is a space propulsion device that utilizes electrical energy to ionize and accelerate propellant, generating thrust. The device features a cross-field configuration, whereby the transverse magnetic field traps electrons, and the axial electric field electrostatically accelerates ions out of the thruster channel. This configuration enables desirable thruster performance characteristics typically characterized by a relatively high specific impulse (1000-3000 s) and a high thrust density (a few Newtons per square meter). High fidelity computational models are useful to investigate the physical processes that govern the HET's performance, efficiency, and lifetime limitations. The non-equilibrium nature of the plasma transport should be resolved so that the flow can be accurately characterized. A grid-based direct kinetic (DK) simulation is capable of modeling the non-equilibrium state of plasma without the numerical noise that is inherent to particle-based methods since the velocity distribution functions (VDFs) are obtained in a deterministic manner. As the primary objective of this work, a two-dimensional, hybrid-DK simulation of the discharge plasma in a HET is developed. As a secondary objective, a plasma sheath, one of the important physical structures that form in the discharge plasma of a HET near the channel walls, is examined via a two-dimensional full DK simulation that highlights slight spatial differences in the sheath as a result of electrically disparate, adjacent wall materials. The memory storage requirements and computational load for the parallelized DK simulation grow with additional species, physical space dimensions, and velocity space dimensions. Some of these numerical limitations are encountered within this work. The hybrid-DK HET model utilizes a quasi-one-dimensional fluid electron algorithm in conjunction with a two-dimensional DK method to simulate the motion of neutral atoms and ions in a HET channel and near-field plume. Upon its development, the hybrid-DK simulation is benchmarked against results obtained from a two-dimensional hybrid-particle-in-cell (PIC) simulation with an identical fluid electron algorithm. To achieve agreement between the simulation results, a boundary condition for the DK model that satisfies particle conservation at the wall boundaries is developed, and electron model boundary conditions that provide solution stability are sought and utilized. For both high-frequency and low-frequency oscillations, the two simulations show good agreement for both time-averaged and dynamic plasma properties. Statistical noise tends to randomize plasma oscillations in the PIC simulation results, whereas the DK results exhibit coherent oscillatory behavior. Furthermore, results indicate that the DK simulation is capable of responding to small changes in electron dynamics, which is promising for future work. The DK plasma sheath simulation models a two-dimensional plasma sheath that highlights slight spatial differences inside the sheath as a result of electrically disparate, adjacent materials. To accomplish this goal, a quasi-one-dimensional sheath model is first built in a two-dimensional framework, boundary conditions are developed, and results are verified against theoretical expectations. Then, the full two-dimensional plasma sheath is modeled. The proof-of-concept model shows that two-dimensional effects are present in the vicinity of the discontinuous plasma potential at the wall, and electron and ion VDFs both clearly exhibit changes due to these effects.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162983/1/astridr_1.pd

Fully kinetic numerical modeling of a plasma thruster

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2001.Includes bibliographical references (p. 372-375).A Hall effect plasma thruster with conductive acceleration channel walls was numerically modeled using 2D3V Particle-in-Cell (PIC) and Monte-Carlo Collision (MCC) methodolo- gies. Electron, ion, and neutral dynamics were treated kinetically on the electron time scale to study transport, instabilities, and the electron energy distribution function. Axisymmet- ric R-Z coordinates were used with a non-orthogonal variable mesh to account for important small-scale plasma structures and a complex physical geometry. Electric field and sheath structures were treated self-consistently. Conductive channel walls were allowed to float electrically. The simulation included, via MCC, elastic and inelastic electron-neutral colli- sions, ion-neutral scattering and charge exchange collisions, and Coulomb collisions. The latter were also treated through a Langevin (stochastic) differential equation for the particle trajectories in velocity space. Ion-electron recombination was modeled at the boundaries, and neutrals were recycled into the flow. The cathode was modeled indirectly by inject- ing electrons at a rate which preserved quasineutrality. Anomalous diffusion was included through an equivalent scattering frequency. Free space permittivity was increased to allow a coarser grid and longer time-step. A method for changing the ion to electron mass ratio and retrieving physical results was developed and used throughout. Results were compared with theory, experiments. Gradients and anisotropy in electron temperature were observed. Non-Maxwellian electron energy distribution functions were observed. The thruster was numerically redesigned; substantial performance benefits were predicted.by James Joseph Szabo, Jr.Ph.D

The high latitude ionosphere-magnetosphere transition region: Simulation and data comparison

A brief description of the major activities pursued during the last year (March 1994 - February 1995) of this grant are: (1) the development of a 200 km to 1 Re, O(+) H(+) Model; (2) the extension of the E x B convection heating study to include centrifugal effects; (3) the study of electron precipitation effects; (4) the study of wave heating of O(+); and (5) the polar wind acceleration study. A list of both papers published and papers submitted, along with a proposal for next year's study and a copy of the published paper is included

Flows and instabilities in low-temperature plasmas with ionization and charge-exchange processes

Plasma is rich with waves and instabilities, on scales ranging from the fastest electron plasma waves down to the slow fluctuations due to ion and atom inertial effects. The common theme of this study is flows, nonlinear waves and instabilities in low-temperature plasmas with atomic processes such as ionization and instabilities. Several nonlinear plasma problems related to applications in electric propulsion and open-mirror linear fusion devices are studied in this thesis. Hall thrusters, the devices for electric propulsion, are prone to many waves and instability phenomena, and the low-frequency ionization oscillations (propagating along its channel) stand as most commonly observed (so-called breathing mode). Though the ionization nature of the breathing mode is generally accepted, with the mode frequency scaling as the fly-by time of the slow neutral atoms, exact mechanisms remain poorly understood. In this study, we formulate a full fluid model for three species: atoms, ions, and electrons, and perform a comprehensive benchmark study between the fluid model and hybrid model (heavy kinetic species and fluid electrons). A novel result of this study is the identification of two different regimes of breathing modes. In one regime, the breathing mode co-exists with the higher frequency resistive mode, and the second - is clear breathing mode. The main features and characteristics of these regimes are identified and confirmed in both models. Generally, the benchmark study shows a good agreement between the fluid and kinetic models. A simple reduced fluid model is proposed for the solo regime. In this regime, the ion backflow region (the near-anode region with negative ion velocity) is identified as a driving mechanism for the breathing mode. The related theme of this work is the role of atomic physics effects (ionization and charge exchange) on plasma flow in the divertors of linear fusion devices. In open magnetic field configurations, the magnetic mirrors are placed at the ends both to confine the plasma in the core and to distribute output energy over a larger area, thus reducing the wall load. Direct interaction of plasma flow with the material wall results in the re-emission of neutrals into the plasma (recycling) due to particles' reflection, desorption, and other processes. This re-emitted neutral component can dramatically impact the whole system. It is found that the low-energy neutral component has the largest influence, generating ion sources (via ionization and charge exchange) in the region near the wall and resulting in strong modification of plasma potential and flow. To study these effects, we have developed a time-dependent hybrid drift-kinetic code with a detailed model of atom transport near the wall, including collision processes. This tool can be used for studying global quasineutral plasma flow dynamics and its interaction with atom components, such as in divertors of linear fusion devices. To illustrate its capabilities, we confirm previous findings (based on qualitative and steady-state analysis) that the ion temperature in the source generally reduces the transport of neutral atoms. Additionally, we show that an increase in the density of slow atoms above some critical value results in dramatic destabilization of plasma flow via ion streaming instabilities

1997 international Sherwood fusion theory conference

Papers presented during the conference are indexed separately