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Collisional tearing in a field-reversed sheet pinch assuming nonparallel propagation

Linear tearing in a collisional reversed-field sheet pinch is examined assuming that the wave vector k is not parallel to the equilibrium magnetic field. Equilibrium and magnetic geometry are defined, and a set of perturbed moment equations is derived assuming quasi-parallel propagation. It is shown that the usual expression for collisional growth is recovered, assuming that k sub y = 0. It is shown that the y component of momentum balance requires the generation of nonzero dJ sub x well away from the null, and an interial coupling when z not equal to 0. The effects of k sub y not equal to 0 on the growth rate are discussed.

Quest, K. B.↗

Collisionless tearing in a field-reversed sheet pinch assuming nonparallel propagation

The problem of collisionless linear tearing is examined assuming a wave vector with a component normal to the equilibrium field. The geometry is defined and the general form of the linear dispersion equation is calculated. The linear theory results when k is parallel to B are reviewed, and Ampere's law is calculated for the external adiabatic region when k times B does not equal zero, using two-fluid theory. A solution is obtained for the approximate form of the perturbed currents and vector potential assuming quasi-parallel k. The resonant current contributions within the singular layer are calculated, obtaining an estimate of the dispersion equation. The form of the adiabatic currents within the singular layer is calculated, showing that an x-z current system persists even in the limit k perpendicular to B goes to zero. Finally, the perturbed vector potential solutions across the singular layer are matched to obtain the shape of the complete eigenfunction.

Quest, K. B.↗

Rigid-drift magnetohydrodynamic equilibria for cylindrical screw pinches

The rigid-drift equations of MHD equilibria in cylindrical geometry are solved analytically in terms of an infinite series of hypergeometric functions for the case where the pressure is proportional to the square of number density and the current density is arbitrarily pitched. Solutions are obtained for a pure Z pinch, a pure theta pinch, and a general screw pinch. It is found that the shapes of the pressure and magnetic-field profiles are completely determined by the model once two parameters are specified: the local plasma beta on the axis and a quantity related to the pitch of the current density. A set of profiles that resemble those observed experimentally in reversed-field pinches is presented. The results also indicate that hollow pressure profiles and reversed Bz profiles can occur either simultaneously or independently and that the pressure always falls to zero at a finite value of the radius.

Turner, L.↗

Driven, steady-state RFP computations

The pseudospectral three-dimensional MHD code of Dahlburg et al. (1986 and 1987) is used to compute the dynamical behavior of a channel of magnetofluid carrying an axial current and magnetic flux. This situation contains the essential MHD behavior of the reversed-field pinch (RFP). An externally imposed electric field is applied to an initially current-free magnetofluid and drives currents that rise and eventually fluctuate about values corresponding to pinch ratios Theta of about 1.3, 2.2, and 4.5. A period of violent turbulence leads to an approximately force-free core, surrounded by an active MHD boundary layer that is not force-free. A steady state is reached that can apparently be sustained indefinitely (for several hundred Alfven transit times or longer). The turbulence level and time variability in the steady state increase with increasing Theta. The average toroidal magnetic field at the wall reverses for Theta = 2.2 and 4.5, but not for Theta = 1.3. Negative toroidal current filaments are observed. The Lundquist numbers are of the order of a few hundred.

Dahlburg, J. P.↗

Hyper-resistivity produced by tearing mode turbulence

Tearing mode turbulence produces a hyperresistivity or effective anomalous electron viscosity. The hyperresistivity is calculated for the mean magnetic field quasi-linearly, and for long-wavelength modes using the direct interaction approximation. The hyperresistivity accounts for current relaxation in reversed-field pinch experiments, and gives a magnetic fluctuation scaling of S to the -1/3. It causes enhanced tearing mode growth rates in the turbulent phase of tokamak disruptions. In astrophysics, it limits magnetic energy growth because of the dynamo effect, and may explain rapid reconnection phenomena such as solar flares.

Strauss, H. R.↗

Magnetic field diffusion and dissipation in reversed-field plasmas

A diffusion equation is derived which describes the evolution of a magnetic field in a plasma of arbitrary beta and resistivity. The equation is valid for a one-dimensional slab geometry, assumes the plasma remains in quasi-equilibrium throughout its evolution and does not include thermal transport. Scaling laws governing the rate of change of the magnetic energy, particle drift energy, and magnetic flux are calculated. It is found that the magnetic free energy can be substantially larger than the particle drift energy and can be an important energy reservoir in driving plasma instabilities (e.g., the lower-hybrid-drift instability). In addition, the effect of a spatially varying resistivity on the evolution of a reversed-field plasma is studied. The resistivity model used is based upon the anomalous transport properties associated with the nonlocal mode structure of the lower-hybrid-drift instability. The relevance of this research to laboratory plasmas (e.g., theta pinches, reversed-field theta pinches) and space plasmas (e.g., the earth's magnetotail) is discussed.

Drake, J. F.↗

Turbulent relaxation to a force-free field-reversed state

The evolution of nonequilibrium initial conditions of an incompressible magnetohydrodynamic Z pinch is described by a three-dimensional, pseudospectral numerical code. Magnetohydrodynamic turbulence develops in the resistive, nonviscous magnetofluid, resulting in the selective decay of the energy relative to the magnetic helicity, at Lundquist numbers of only a few hundred. An interior force-free region grows with time and achieves spontaneous reversal of the toroidal magnetic field at the wall, without the necessity of an external electric field.

Dahlburg, J. P.↗

Progress on the Plasmoid Thruster Experiment (PTX)

A plasmoid, also called a compact toroid, is a compact plasma structure with an integral magnetic field, that may be categorized according to the relative strength of the poloidal and toroidal magnetic field (Bp and Bt, respectively). An object with Bp/Bt much greater than 1 is called a Field Reverse Configuration (FRC); if Bp = Bt, it is called a Spheromak. The plasmoid thruster is a pulsed inductive device which operates by repetitively producing plasmoids that are accelerated and ejected at high velocity. As the process is inductive, this thruster avoids the problem of electrode erosion. Also, the magnetic structure of the plasmoid should suppress thermal and mass losses to the wall, and improve detachment of the plasma exhaust from the thruster. This concept should be capable of producing an Isp of 5,000 seconds and greater, with thrust densities of order 10(exp 5) N/sq m. The plasmoid thruster consists chiefly of a conical theta-pinch coil. Propellant is introduced onto a bias magnetic field, produced by an auxiliary coil, and is then pre-ionized, freezing in the magnetic field. The theta-pinch coil is then energized producing a field aligned anti- parallel to the bias field. The reversed field reconnects with the bias field to form the plasmoid. The magnetic pressure of the reversed field accelerates the plasmoid out of the thruster . A series of experiments have been conducted on the PTX device, which consisted of a single turn conical theta-pinch coil, driven by a 560 nF, 35 kV capacitor bank, which rang at a frequency of 500 kHz, and served all three functions required for formation: pre-ionization, bias field loading, and field reversal. Initial ionization was found to occur in an annular region at the exit plane of the coil, and was found to be reproducible with a variety of gases, including H2, D2, Ar, and an H2/N2 mixture (75% / 25%). A fast gas valve for injecting propellant has been tested, as well as a ringing pre-ionization circuit (operating at 5 Mhz) to better control the plasmoid formation. Velocities as high as 20 km/s have been measured for a plasmoid propagating into a static back-fill of neutral gas. Magnetic field and density measurements indicate that the plasmoid retains its structure well into the down-stream exhaust region, and that it is capable of pushing a dense cloud of neutral gas in front of it. Further experiments will focus on the effects of coil geometry and bias-field strength on the performance of the device. A high-power solid-state switching system is being developed in order to replace the spark-gap switch.

Martin, Adam↗

Status of fusion research and implications for D/He-3 systems

World wide programs in both magnetic confinement and inertial confinement fusion research have made steady progress towards the experimental demonstration of energy breakeven. However, after breakeven is achieved, considerable time and effort must still be expended to develop a usable power plant. The main program described is focused on Deuterium-Tritium devices. In magnetic confinement, three of the most promising high beta approaches with a reasonable experimental data base are the Field Reversed Configuration, the high field tokamak, and the dense Z-pinch. The situation is less clear in inertial confinement where the first step requires an experimental demonstration of D/T spark ignition. It appears that fusion research has reached a point in time where an R and D plan to develop a D/He-3 fusion reactor can be laid out with some confidence of success.

Miley, George H.↗

Progress on the PT-1 Prototype Plasmoid Thruster

The design and construction of a plasmoid thruster prototype is described. This thruster operates by expelling inductively formed plasmoids at high velocities. These plasmoids are field reversed configuration plasmas which are formed by reversing a magnetic flux frozen in an ionized gas inside a theta-pinch coil. The pinch coil is a unique multi-turn, multi-lead design chosen for optimization of inductance and field uniformity. A table-top bread-board demonstrator has been built at MSFC, and will be delivered to Radiance Technologies Inc. for further testing at the Auburn Space Power Institute.

Eskridge, Richard H.↗

Gradient Field Imploding Liner Fusion Propulsion System: NASA Innovative Advanced Concepts Phase I Final Report

The advancement of human deep space exploration requires the continued development of energetic in-space propulsion systems, from current chemical engines to nuclear thermal rockets to future high energy concepts such as nuclear fusion. As NASA embarks on a program to develop near-term nuclear thermal propulsion, this NASA Innovative Advanced Concepts (NIAC) Phase I activity was funded to investigate the feasibility of an innovative approach toward highly energetic pulsed fusion propulsion. Previous concept studies have proposed the conversion of fusion energy for in-space propulsion, ranging from laser-ignited fusion systems such as Gevaltig and VISTA, to the British Interplanetary Society's Daedalus concept and its more recent incarnation under Project Icarus, to steady-state spherical torus fusion systems. Recent NIAC studies have also evaluated several innovative fusion concepts, including the acceleration and compression of field reversed configuration plasmas in time-changing magnetic fields, magnetically driven liners imploding onto plasma targets, and high current z-pinch compression of material liners onto fission-fusion fuel targets. While each of these studies firmly established the potential benefits of fusion systems for interplanetary travel, they also identified significant challenges in successfully engineering such systems for spacecraft propulsion. The concept outlined in this Technical Publication (TP) builds on the lessons learned from these prior activities, approaching the quest for fusion-powered propulsion through an innovative variation of magneto-inertial fusion concepts developed for terrestrial power applications.

Lapointe, M. R.↗

A Plasmoid Thruster for Space Propulsion

There are a number of possible advantages to using accelerated plasmoids for in-space propulsion. A plasmoid is a compact plasma structure with an integral magnetic field. They have been studied extensively in controlled fusion research and are classified according to the relative strength of the poloidal and toroidal magnetic field (BP and Bt, respectively). An Object with B P t >> 1 is classified as a Field Reverse Configuration (FRC); if B, = Bt, it is called a Spheromak. The plasmoid thruster operates by producing FRC-like plasmoids, and subsequently ejecting them from the device at high velocity. The plasmoid is formed inside of a single turn conical theta-pinch coil. As this process is inductive, there are no electrodes. Similar experiments have yielded plasmoid velocities of at least 50 km/s (l), and calculations indicate that velocities in excess of 100 km/s should be possible. This concept should be capable of producing Isp s in the range of 5,000 - 10,000 s with thrust densities of order 10(exp 5) N/sq m. The current experiment is designed to produce jet powers in the range of 5-10 kW, although the concept should be scalable to several MW s. The plasmoids mass and velocity will be measured with a variety of diagnostics, including internal and external B-dot probes, flux loops, Langmuir probes, high-speed cameras, and a laser interferometer. Also of key importance will be measurements of the efficiency and mass utilization. Simulations of the plasmoid thruster using MOQUI, a time dependent MHD code, will be carried out concurrently with experimental testing.

Koelfgen, Syri J.↗

A Plasmoid Thruster for Space Propulsion

There are a number of possible advantages to using accelerated plasmoids for in-space propulsion. A plasmoid is a compact plasma structure with an integral magnetic field. They have been studied extensively in controlled fusion research and are classified according to the relative strength of the poloidal and toroidal magnetic field (B(sub p), and B(sub t), respectively). An object with B(sub p), / B(sub t) much greater than 1 is classified as a Field Reversed Configuration (FRC); if B(sub p) approximately equal to B(sub t), it is called a Spheromak. The plasmoid thruster operates by producing FRC-like plasmoids and subsequently ejecting them from the device at a high velocity. The plasmoid is formed inside of a single-turn conical theta-pinch coil. As this process is inductive, there are no electrodes. Similar experiments have yielded plasmoid velocities of at least 50 km/s, and calculations indicate that velocities in excess of 100 km/s should be possible. This concept should be capable of producing Isp's in the range of 5,000 - 15,000 s with thrust densities on the order of 10(exp 5) N per square meters. The current experiment is designed to produce jet powers in the range of 5 - 10 kW, although the concept should be scalable to several MW's. The plasmoid mass and velocity will be measured with a variety of diagnostics, including internal and external B-dot probes, flux loops, Langmuir probes, high-speed cameras and a laser interferometer. Also of key importance will be measurements of the efficiency and mass utilization. Simulations of the plasmoid thruster using MOQUI, a time-dependent MHD code, will be carried out concurrently with experimental testing.

Koelfgen, Syri J.↗

The Plasmoid Thruster Experiment (PTX)

A plasmoid is a compact plasma structure with an integral magnetic field. They have been studied extensively in controlled fusion research and are categorized according to the relative strength of the poloidal and toroidal magnetic field (B(phi), and B(tau), respectively). An object with B(phi)/B(tau) >> 1 is classified as a Field Reverse Configuration (FRC); if B(phi) = B(tau), it is called a Spheromak. There are a number of possible advantages to using accelerated plasmoids for in-space propulsion. A thruster based on this concept would operate by repetitively producing plasmoids and ejecting them from the device at high velocity. The plasmoid is formed inside of a single turn conical theta-pinch coil; as this process is inductive, there are no life-limiting electrodes. Similar experiments have yielded plasmoid velocities of at least 50 km/s (l), and calculations indicate that velocities in excess of 100 km/s are possible. A thruster based on this concept would be capable of producing an I(sp) in the range of 5,000 - 10,OOO s, with thrust densities of order 10(exp 5) N/m(exp 2). The current experiment is designed to produce jet powers in the range of 5-10 kW, although the concept should be scalable to higher power. The purpose of this experiment is to determine the feasibility of this plasma propulsion concept. To accomplish this, it will be necessary to determine: a.) specific impulse and thrust, b.) efficiency and mass utilization, c.) which type of plasmoid (FRC-like or Spheromak-like) gives the best performance, and d.) the characteristics required of actual thruster components (i.e., switch and capacitor technology). The plasmoid mass and velocity will be measured with a variety of diagnostics, including internal and external B-dot probes, flux loops, Langmuir probes, high-speed cameras, and an interferometer. Simulations of the plasmoid thruster using MOQUI, a time dependent MHD code, will be carried out concurrently with experimental testing. The PTX device is currently undergoing initial testing and preliminary experimental results are presented.

Eskridge, Richard↗

The FRC Acceleration Space Thruster (FAST) Experiment

The objective of the FRC (Field Reversed Configuration) Acceleration Space Thruster (FAST) Experiment is to investigate the use of a repetitive FRC source as a thruster, specifically for an NEP (nuclear electric propulsion) system. The Field Reversed Configuration is a plasmoid with a closed poloidal field line structure, and has been extensively studied as a fusion reactor core. An FRC thruster works by repetitively producing FRCs and accelerating them to high velocity. An FRC thruster should be capable of I(sub sp)'s in the range of 5,000 - 25,000 seconds and efficiencies in the range of 60 - 80 %. In addition, they can have thrust densities as high as 10(exp 6) N/m2, and as they are inductively formed, they do not suffer from electrode erosion. The jet-power should be scalable from the low to the high power regime. The FAST experiment consists of a theta-pinch formation chamber, followed by an acceleration stage. Initially, we will produce and accelerate single FRCs. The initial focus of the experiment will be on the ionization, formation and acceleration of a single plasmoid, so as to determine the likely efficiency and I(sub sp). Subsequently, we will modify the device for repetitive burst-mode operation (5-10 shots). A variety of diagnostics are or will be available for this work, including a HeNe interferometer, high-speed cameras, and a Thomson-scattering system. The status of the experiment will be described.

Martin, Adam↗

Progress on the Plasmoid Thruster Experiment (PTX)

A plasmoid is a compact plasma structure with an integral magnetic field, that may be categorized according to the relative strength of the poloidal and toroidal magnetic field (B(sub p) and B(sub t), respectively). An object with B(sub p)/B(sub t), much much more than 1 is called a Field Reverse Configuration (FRC); if B(sub p) approximately equal to B(sub t), it is called a Spheromak. The thruster operates by repetitively producing plasmoids that are accelerated and ejected at high velocity. As this process is inductive, there are no electrodes. Also, the magnetic structure of the plasmoid should suppress thermal and mass losses to the wall, and improve detachment of the plasma exhaust from the thruster. This concept should be capable of producing an Isp in the range of 5,000 - 10,000 s with thrust densities of order 10(exp 5) N per square meters. The current experiment is designed to produce jet powers in the range of 5-10 kW, although the concept should be scalable into the MW range. In PTX, the plasmoid is formed inside of a single turn conical theta-pinch coil (17.58 cone angle). The coil is driven by a 640 nF, 35 kV capacitor bank, which rings at a frequency of 500 kHz. Previous experiments on PTX were conducted with a static-fill of propellant gas (6% H2 in He), and demonstrated reliable ionization over a pressure range of 40 - 200 mTorr. We are now adding a fast gas-puff valve to load the propellant, and a ringing pre-ionization circuit (f = 5 Mhz) to better control the plasmoid formation. An alternate coil (8.58 cone angle) will also be used, so as to investigate the effect of coil shape on performance. In addition, a variety of propellants will be used, including hydrogen, nitrogen, and argon. The plasmoid mass and velocity will be measured with a variety of diagnostics, including external B-dot probes and flux loops, a high-speed framing camera, and a HeNe laser interferometer. Internal B-dot probes and a quadruple Langmuir probe will provide additional measurements of the plasmoid shape and structure, as well as density, and will be described in a companion paper. The experimental results will be compared to calculations made using a 0-D coil-gun model and also a 2-D time dependent MHD code.

Martin, Adam↗