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All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Numerical Investigation of Plasma Flows in Magnetic Nozzles

Magnetic nozzles are used in many laboratory experiments in which plasma flows are to be confined, cooled. accelerated, or directed. At present, however, there is no generally accepted theoretical description that explains the phenomena of plasma detachment from an externally-imposed magnetic field. This is an important problem in the field of plasma propulsion, where the ionized gas must detach from the applied, solenoidal magnetic field to realize thrust production. In this paper we simulate a plasma flowing in the presence of an applied magnetic field using a multidimensional numerical simulation tool that includes theoretical models of the various dispersive and dissipative processes present in the plasma. This is an extension of the simulation tool employed in previous work by Sankaran et al. The new tool employs the same formulation of the governing equation set. but retains the axial and radial components of magnetic field and the azimuthal component of velocity that were neglected in other works. We aim to compare the computational results with the various proposed magnetic nozzle detachment theories to develop an understanding of the physical mechanisms that cause detachment. An applied magnetic field topology is obtained using a magnetostatic field solver and this field is superimposed on the time-dependent magnetic field induced in the plasma to provide a self-consistent field description. The applied magnetic field and model geometry match those found in experiments by Kurtki and Okada. We model this geometry because there ts a substantial amount of experimental data that can be compared to our computations, allowing for validation of the model. In addition, comparison of the simulation results with the experimentally obtained plasma parameters will provide insight into the mechanisms that lead to plasma detachment, revealing how the 3 scale with different input parameters.

Polzin, K. A.↗
NASA NTRS2009

Numerical Investigation of Plasma Flows in Magnetic Nozzles

Magnetic nozzles are used in many laboratory experiments in which plasma flows are to be confined, cooled, accelerated, or directed. At present, however, there is no generally accepted theoretical description that explains the phenomena of plasma expansion in and detachment from an externally-imposed magnetic field. The latter is an especially important problem in the field of plasma propulsion, where the ionized gas must detach from the applied, solenoidal magnetic field to realize thrust production. In this paper we simulate a plasma flowing in the presence of an applied magnetic field using a multidimensional numerical simulation tool that includes theoretical models of the various dispersive and dissipative processes present in the plasma. This is an extension of the simulation tool employed in previous work by Sankaran et al. The new tool employs the same formulation of the governing equation set, but retains the axial and radial components of magnetic field and the azimuthal component of velocity that were neglected. We aim to compare the computational results with the various proposed magnetic nozzle detachment theories to develop an understanding of the physical mechanisms that cause detachment. An applied magnetic field topology is obtained using a magnetostatic field solver, and this field is superimposed on the time-dependent magnetic field induced in the plasma to provide a self-consistent field description. The applied magnetic field and model geometry match those found in experiments by Kuriki and Okada. 4 A schematic showing the setup used in those experiments is shown. We model this geometry because there is a substantial amount of experimental data that can be compared to our computations, allowing for validation of the model. In addition, comparison of the simulation results with the experimentally obtained plasma parameters will provide insight into the mechanisms that lead to plasma detachment, revealing how they scale with different input parameters.

Sankaran, Kamesh↗
NASA NTRS2004

Magnetic-Nozzle Studies for Fusion Propulsion Applications: Gigawatt Plasma Source Operation and Magnetic Nozzle Analysis

This project has been a multiyear effort to assess the feasibility of a key process inherent to virtually all fusion propulsion concepts: the expansion of a fusion-grade plasma through a diverging magnetic field. Current fusion energy research touches on this process only indirectly through studies of plasma divertors designed to remove the fusion products from a reactor. This project was aimed at directly addressing propulsion system issues, without the expense of constructing a fusion reactor. Instead, the program designed, constructed, and operated a facility suitable for simulating fusion reactor grade edge plasmas, and to examine their expansion in an expanding magnetic nozzle. The approach was to create and accelerate a dense (up to l0(exp 20)/m) plasma, stagnate it in a converging magnetic field to convert kinetic energy to thermal energy, and examine the subsequent expansion of the hot (100's eV) plasma in a subsequent magnetic nozzle. Throughout the project, there has been a parallel effort between theoretical and numerical design and modelling of the experiment and the experiment itself. In particular, the MACH2 code was used to design and predict the performance of the magnetoplasmadynamic (MPD) plasma accelerator, and to design and predict the design and expected behavior for the magnetic field coils that could be added later. Progress to date includes the theoretical accelerator design and construction, development of the power and vacuum systems to accommodate the powers and mass flow rates of interest to out research, operation of the accelerator and comparison to theoretical predictions, and computational analysis of future magnetic field coils and the expected performance of an integrated source-nozzle experiment.

Gilland, James H.↗
NASA NTRS2013

Computational Studies of Magnetic Nozzle Performance

An extensive literature review of magnetic nozzle research has been performed, examining previous work, as well as a review of fundamental principles. This has allow us to catalog all basic physical mechanisms which we believe underlie the thrust generation process. Energy conversion mechanisms include the approximate conservation of the magnetic moment adiabatic invariant, generalized hall and thermoelectric acceleration, swirl acceleration, thermal energy transformation into directed kinetic energy, and Joule heating. Momentum transfer results from the interaction of the applied magnetic field with currents induced in the plasma plume., while plasma detachment mechanisms include resistive diffusion, recombination and charge exchange collisions, magnetic reconnection, loss of adiabaticity, inertial forces, current closure, and self-field detachment. We have performed a preliminary study of Hall effects on magnetic nozzle jets with weak guiding magnetic fields and weak expansions (p(sub jet) approx. = P(sub background)). The conclusion from this study is that the Hall effect creates an azimuthal rotation of the plasma jet and, more generally, creates helical structures in the induced current, velocity field, and magnetic fields. We have studied plasma jet expansion to near vacuum without a guiding magnetic field, and are presently including a guiding magnetic field using a resistive MHD solver. This research is progressing toward the implementation of a full generalized Ohm's law solver. In our paper, we will summarize the basic principle, as well as the literature survey and briefly review our previous results. Our most recent results at the time of submittal will also be included. Efforts are currently underway to construct an experiment at the University of Michigan Plasmadynamics and Electric Propulsion Laboratory (PEPL) to study magnetic nozzle physics for a RF-thruster. Our computational study will work directly with this experiment to validate the numerical model, in order to study magnetic nozzle physics and optimize magnetic nozzle design. Preliminary results from the PEPL experiment will also be presented.

Ebersohn, Frans H.↗
NASA NTRS1992

Qualitative spectroscopic study of magnetic nozzle flow

The physics of the magnetic nozzle flow for a 100-kW-level quasi-steady MPD thruster was studied by photographic spectroscopy focusing on the plasma model in the flow and the acceleration mechanism. Spectroscopic visualization for the flow-species analysis indicates that the plasma-exhaust flow dominated by NII species were confined by the magnetic nozzle effect to collimate the flow for the better thruster performance. Inside the nozzle, the plasma flow was found to be in nonhomogeneous collisional-radiative condition. There appears to be a substantial flow acceleration from the magnetic nozzle inlet to the outlet with slight expansion. This suggests that the flow resembles that of constant area supersonic duct flow with cooling.

Umeki, T.↗
NASA NTRS2013

MHD Simulations of the Plasma Flow in the Magnetic Nozzle

The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the magnetic field in both the near- and far-field regions. However, in that work the downstream domain was constrained to a channel of constant cross-sectional area. In the present work we seek to address this issue by modeling the downstream region with a domain that permits free expansion of the plasma, permitting a better evaluation of the downstream effects the applied field has on the plasma. The inlet boundary conditions and applied magnetic field values will also be varied to determine the effect the initial plasma energy content and applied magnetic field energy density have on the near- and far-field plasma properties on the MHD code. This will determine the effect of inlet boundary conditions on the results downstream and address issues related to the restrictive numerical domain previously used.

Smith, T. E. R.↗
NASA NTRSDate not supplied

Continued Development of the Pulsed Magnetic Nozzle for the Pulsed Fission Fusion (PuFF) Vehicle

High thrust, high specific impulse propulsion systems, such as PuFF (Pulsed Fission-Fusion)offer a new paradigm of speed and safety when exploring the solar system. To realize thesepossibilites, PuFF needs a mature magnetic nozzle design. PuFF’s magnetic nozzle is uniquein that it must provide power in addition to thrust. In the authors’ opinion, the power systemdesign is fairly mature, but nozzle thrust coil design is less so. Previous work has suggested thatthe PuFF magnetic nozzle will behave similarly to a ‘magnetic reflection chamber,’ relying onprinciples of magnetic flux compression to re-direct nozzle flow. However, recent work, usingthe 3D modeling software SPFMax, suggests that plasma motion in the nozzle will be drivenby the Lorentz force. This recent work is limited in that the plasma did not completely leavethe nozzle before the simulation ended. In this work, we aim to extend the SPFMax modelfrom previous work, with a bolstered electromagnetic field solver, so the model can run untilthe plasma is fully evacuated. We hope to confirm previous results regarding the ideal PuFFnozzle design, but we could be surprised. Through improving the PuFF nozzle model, weaim to reduce technical risk with building the nozzle, realize paradigm-shifting performancenumbers, and allow rapid, reliable, and safe exploration of the solar system.

Nathan M Schilling↗
NASA NTRS2015

Quasi-One-Dimensional Particle-in-Cell Simulation of Magnetic Nozzles

A method for the quasi-one-dimensional simulation of magnetic nozzles is presented and simulations of a magnetic nozzle are performed. The effects of the density variation due to plasma expansion and the magnetic field forces on ion acceleration are investigated. Magnetic field forces acting on the electrons are found to be responsible for the formation of potential structures which accelerate ions. The effects of the plasma density variation alone are found to only weakly affect ion acceleration. Strongly diverging magnetic fields drive more rapid potential drops.

Ebersohn, Frans H.↗
NASA NTRS2009

Integrity of the Plasma Magnetic Nozzle

This report examines the physics governing certain aspects of plasma propellant flow through a magnetic nozzle, specifically the integrity of the interface between the plasma and the nozzle s magnetic field. The injection of 100s of eV plasma into a magnetic flux nozzle that converts thermal energy into directed thrust is fundamental to enabling 10 000s of seconds specific impulse and 10s of kW/kg specific power piloted interplanetary propulsion. An expression for the initial thickness of the interface is derived and found to be approx.10(exp -2) m. An algorithm is reviewed and applied to compare classical resistivity to gradient-driven microturbulent (anomalous) resistivity, in terms of the spatial rate and time integral of resistive interface broadening, which can then be related to the geometry of the nozzle. An algorithm characterizing plasma temperature, density, and velocity dependencies is derived and found to be comparable to classical resistivity at local plasma temperatures of approx. 200 eV. Macroscopic flute-mode instabilities in regions of "adverse magnetic curvature" are discussed; a growth rate formula is derived and found to be one to two e-foldings of the most unstable Rayleigh-Taylor (RT) mode. After establishing the necessity of incorporating the Hall effect into Ohm s law (allowing full Hall current to flow and concomitant plasma rotation), a critical nozzle length expression is derived in which the interface thickness is limited to about 1 ion gyroradius.

Gerwin, Richard A.↗
NASA NTRS2008

Numerical Investigation of Plasma Detachment in Magnetic Nozzle Experiments

At present there exists no generally accepted theoretical model that provides a consistent physical explanation of plasma detachment from an externally-imposed magnetic nozzle. To make progress towards that end, simulation of plasma flow in the magnetic nozzle of an arcjet experiment is performed using a multidimensional numerical simulation tool that includes theoretical models of the various dispersive and dissipative processes present in the plasma. This is an extension of the simulation tool employed in previous work by Sankaran et al. The aim is to compare the computational results with various proposed magnetic nozzle detachment theories to develop an understanding of the physical mechanisms that cause detachment. An applied magnetic field topology is obtained using a magnetostatic field solver (see Fig. I), and this field is superimposed on the time-dependent magnetic field induced in the plasma to provide a self-consistent field description. The applied magnetic field and model geometry match those found in experiments by Kuriki and Okada. This geometry is modeled because there is a substantial amount of experimental data that can be compared to the computational results, allowing for validation of the model. In addition, comparison of the simulation results with the experimentally obtained plasma parameters will provide insight into the mechanisms that lead to plasma detachment, revealing how they scale with different input parameters. Further studies will focus on modeling literature experiments both for the purpose of additional code validation and to extract physical insight regarding the mechanisms driving detachment.

Sankaran, Kamesh↗
NASA NTRS2009

Numerical Investigation of Near-Field Plasma Flows in Magnetic Nozzles

The development and application of a multidimensional numerical simulation code for investigating near-field plasma processes in magnetic nozzles are presented. The code calculates the time-dependent evolution of all three spatial components of both the magnetic field and velocity in a plasma flow, and includes physical models of relevant transport phenomena. It has been applied to an investigation of the behavior of plasma flows found in high-power thrusters, employing a realistic magnetic nozzle configuration. Simulation of a channel-flow case where the flow was super-Alfvenic has demonstrated that such a flow produces adequate back-emf to significantly alter the shape of the total magnetic field, preventing the flow from curving back to the magnetic field coil in the near-field region. Results from this simulation can be insightful in predicting far-field behavior and can be used as a set of self-consistent boundary conditions for far-field simulations. Future investigations will focus on cases where the inlet flow is sub-Alfvenic and where the flow is allowed to freely expand in the radial direction once it is downstream of the coil.

Sankaran, Kamesh↗
NASA NTRS2020

Hall2De Simulations of a Magnetic Nozzle

The two-dimensional, fluid-based Hall thruster code Hall2De is adapted to simulate a low temperature propulsive magnetic nozzle. Electron cyclotron resonance (ECR) thrusters developed at the Office National d’Etudes et de Recherches Aérospatiales (ONERA) in France and the University of Michigan are investigated. For each device, the simulated domain is defined from the nozzle throat to a location 10 thruster radii downstream. A numerical mesh is defined based on the measured magnetic field, and the governing fluid equations for singlycharge ions, electrons, and neutrals are solved. The boundary conditions for the throat of the magnetic nozzle are based on measured values of electron temperature and ion velocity. Multiple boundary conditions for the electron temperature in the downstream regions of the domain are considered. The simulated ion velocity and potential agrees well with experiment, while the simulated divergence efficiencies and thrusts are 25% lower and 45-55% higher than experiment. When a Neumann boundary condition for electron temperature is applied to the far-plume boundaries, the nozzle was seen to be purely isothermal. This suggests that the thermal conductivity along field lines in real devices is much lower than classical simulations predict, and anomalous resistivity may be needed to reproduce the temperature distribution observed in experiment. The larger beam divergence observed in our simulation may also be related to the lack of anomalous resistivity.

Jorns, Benjamin A.↗
NASA NTRS2007

Development of Numerical Tools for the Investigation of Plasma Detachment from Magnetic Nozzles

A multidimensional numerical simulation framework aimed at investigating the process of plasma detachment from a magnetic nozzle is introduced. An existing numerical code based on a magnetohydrodynamic formulation of the plasma flow equations that accounts for various dispersive and dissipative processes in plasmas was significantly enhanced to allow for the modeling of axisymmetric domains containing three.dimensiunai momentum and magnetic flux vectors. A separate magnetostatic solver was used to simulate the applied magnetic field topologies found in various nozzle experiments. Numerical results from a magnetic diffusion test problem in which all three components of the magnetic field were present exhibit excellent quantitative agreement with the analytical solution, and the lack of numerical instabilities due to fluctuations in the value of del(raised dot)B indicate that the conservative MHD framework with dissipative effects is well-suited for multi-dimensional analysis of magnetic nozzles. Further studies will focus on modeling literature experiments both for the purpose of code validation and to extract physical insight regarding the mechanisms driving detachment.

Sankaran, Kamesh↗
NASA NTRS1990

Simple model of plasma acceleration in a magnetic nozzle

A collisionless, steady-state, cold-plasma model is used to calculate the three-dimensional trajectory of a plasma as it is accelerated through a diverging magnetic field. The magnetic field is assumed to be axisymmetric with nonzero radial and axial components and zero azimuthal component. Although random thermal motion of plasma species is neglected in the cold plasma approximation, an important effect of plasma thermal energy is accounted for in the model as the kinetic energy of electrons in their Larmor motion about magnetic field lines. Calculations based on this model confirm previous studies which suggested that plasma separation from the field of a magnetic nozzle can take place even in the absence of collisional diffusion. It is shown that plasma divergence in a magnetic nozzle can be controlled by tailoring the field geometry.

Sercel, Joel C.↗
NASA NTRS1993

Plasma separation from magnetic field lines in a magnetic nozzle

This paper discusses conditions for separation of a plasma from the magnetic field of a magnetic nozzle. The analysis assumes a collisionless, quasineutral plasma, and therefore the results represent a lower bound on the amount of detachment possible for a given set of plasma conditions. We show that collisionless separation can occur because finite electron mass inhibits the flow of azimuthal currents in the nozzle. Separation conditions are governed by a parameter G which depends on plasma and nozzle conditions. Several methods of improving plasma detachment are presented, including moving the plasma generation zone downstream from the region of strongest magnetic field and using dual magnets to focus the plasma beam. Plasma detachment can be enhanced by manipulation of the nozzle configuration.

Kaufman, D. A.↗
NASA NTRS2001

Flux Compression Magnetic Nozzle

In pulsed fusion propulsion schemes in which the fusion energy creates a radially expanding plasma, a magnetic nozzle is required to redirect the radially diverging flow of the expanding fusion plasma into a rearward axial flow, thereby producing a forward axial impulse to the vehicle. In a highly electrically conducting plasma, the presence of a magnetic field B in the plasma creates a pressure B(exp 2)/2(mu) in the plasma, the magnetic pressure. A gradient in the magnetic pressure can be used to decelerate the plasma traveling in the direction of increasing magnetic field, or to accelerate a plasma from rest in the direction of decreasing magnetic pressure. In principle, ignoring dissipative processes, it is possible to design magnetic configurations to produce an 'elastic' deflection of a plasma beam. In particular, it is conceivable that, by an appropriate arrangement of a set of coils, a good approximation to a parabolic 'magnetic mirror' may be formed, such that a beam of charged particles emanating from the focal point of the parabolic mirror would be reflected by the mirror to travel axially away from the mirror. The degree to which this may be accomplished depends on the degree of control one has over the flux surface of the magnetic field, which changes as a result of its interaction with a moving plasma.

Thio, Y. C. Francis↗