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Magnetic flux rope versus the spheromak as models for interplanetary magnetic clouds

Magnetic clouds form a subset of interplanetary ejecta with well-defined magnetic and thermodynamic properties. Observationally, it is well established that magnetic clouds expand as they propagate antisunward. The aim of this paper is to compare and contrast two models which have been proposed for the global magnetic field line topology of magnetic clouds: a magnetic flux tube geometry, on the one hand, and a spheromak geometry (including possible higher multiples), on the other. Traditionally, the magnetic structure of magnetic clouds has been modeled by force-free configurations. In a first step, we therefore analyze the ability of static force-free models to account for the asymmetries observed in the magnetic field profiles of magnetic clouds. For a cylindrical flux tube the magnetic field remains symmetric about closest approach to the magnetic axis on all spacecraft orbits intersecting it, whereas in a spheromak geometry one can have asymmetries in the magnetic field signatures along some spacecraft trajectories. The duration of typical magnetic cloud encounters at 1 AU (1 to 2 days) is comparable to their travel time from the Sun to 1 AU and thus magnetic clouds should be treated as strongly nonstationary objects. In a second step, therefore, we abandon the static approach and model magnetic clouds as self-similarly evolving MHD configurations. In our theory, the interaction of the expanding magnetic cloud with the ambient plasma is taken into account by a drag force proportional to the density and the velocity of expansion. Solving rigorously the full set of MHD equations, we demonstrate that the asymmetry in the magnetic signature may arise solely as a result of expansion. Using asymptotic solutions of the MHD equations, we least squares fit both theoretical models to interplanetary data. We find that while the central part of the magnetic cloud is adequately described by both models, the 'edges' of the cloud data are modeled better by the magnetic flux tube. Further comparisons of the two models necessarily involve thermodynamic properties, since real magnetic configurations are never exactly force-free and gas pressure plays an essential role. We consider a polytropic gas. Our theoretical analysis shows that the self-similar expansion of a magnetic flux tube requires the polytropic index gamma to be less than unity. For the spheromak, however, self-similar, radially expanding solutions are known only for gamma equal to 4/3. This difference, therefore, yields a good way of distinguishing between the two geometries. It has been shown recently that the polytropic relationship is applicable to magnetic clouds and that the corresponding polytropic index is approximately 0.5. This observational result is consistent with the self-similar model of the magnetic flux rope but is in conflict with the self-similar spheromak model.

Farrugia, C. 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↗

Pulsed plasmoid electric propulsion

A method of electric propulsion is explored where plasmoids such as spheromaks and field reversed configurations (FRC) are formed and then allowed to expand down a diverging conducting shell. The plasmoids contain a toroidal electric current that provides both heating and a confining magnetic field. They are free to translate because there are no externally supplied magnetic fields that would restrict motion. Image currents in the diverging conducting shell keep the plasmoids from contacting the wall. Because these currents translate relative to the wall, losses due to magnetic flux diffusion into the wall are minimized. During the expansion of the plasma in the diverging cone, both the inductive and thermal plasma energy are converted to directed kinetic energy producing thrust. Specific impulses can be in the 4000 to 20000 sec range with thrusts from 0.1 to 1000 Newtons, depending on available power.

Bourque, Robert F.↗

Progress In Magnetized Target Fusion Driven by Plasma Liners

Magnetized target fusion (MTF) attempts to combine the favorable attributes of magnetic confinement fusion (MCF) for energy confinement with the attributes of inertial confinement fusion (ICF) for efficient compression heating and wall-free containment of the fusing plasma. It uses a material liner to compress and contain a magnetized plasma. For practical applications, standoff drivers to deliver the imploding momentum flux to the target plasma remotely are required. Spherically converging plasma jets have been proposed as standoff drivers for this purpose. The concept involves the dynamic formation of a spherical plasma liner by the merging of plasma jets, and the use of the liner so formed to compress a spheromak or a field reversed configuration (FRC).

Thio, Francis Y. C.↗

Magnetized Target Fusion Driven by Plasma Liners

Magnetized target fusion (MTF) attempts to combine the favorable attributes of magnetic confinement fusion (MCF) for energy confinement with the attributes of inertial confinement fusion (ICF) for efficient compression heating and wall-free containment of the fusing plasma. It uses a material liner to compress and contain a magnetized plasma. For practical applications, standoff drivers to deliver the imploding momentum flux to the target plasma remotely are required. Spherically converging plasma jets have been proposed as standoff drivers for this purpose. The concept involves the dynamic formation of a spherical plasma liner by the merging of plasma jets, and the use of the liner so formed to compress a spheromak or a field reversed configuration (FRC). For the successful implementation of the scheme, plasma jets of the requisite momentum flux density need to be produced. Their transport over sufficiently large distances (a few meters) needs to be assured. When they collide and merge into a liner, relative differences in velocity, density and temperature of the jets could give rise to instabilities in the development of the liner. Variation in the jet properties must be controlled to ensure that the growth rate of the instabilities are not significant over the time scale of the liner formation before engaging with the target plasma. On impact with the target plasma, some plasma interpenetration might occur between the liner and the target. The operating parameter space needs to be identified to ensure that a reasonably robust and conducting contact surface is formed between the liner and the target. A mismatch in the "impedance" between the liner and the target plasma could give rise to undesirable shock heating of the liner leading to increased entropy (thermal losses) in the liner. Any irregularities in the liner will accentuate the Rayleigh-Taylor instabilities during the compression of the target plasma by the liner.

Thio, Y. C. Francis↗

Magnetized Target Fusion Driven by Plasma Liners

For practical applications of magnetized target fusion, standoff drivers to deliver the imploding momentum flux to the target plasma remotely are required. Quasi-spherically converging plasma jets have been proposed as standoff drivers for this purpose. The concept involves the dynamic formation of a quasi-spherical plasma liner by the merging of plasma jets, and the use of the liner so formed to compress a spheromak or a field reversed configuration (FRC). Theoretical analysis and computer modeling of the concept are presented. It is shown that, with the appropriate choice of the flow parameters in the liner and the target, the impact between the liner and the target plasma can be made to be shockless in the liner or to generate at most a very weak shock in the liner. Additional information is contained in the original extended abstract.

Thio, Y. C. Francis↗

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.↗

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↗

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 fields. If B(sup p)/B(sub t) is much greater than 1, it is an FRC; if B(sub p) approximately equals B(sub t), it is a Spheromak. A plasmoid thruster would operate by repetitively producing plasmoids that are accelerated to high velocity. The process is inductive, and the magnetic structure of the plasmoid suppresses thermal and mass losses, and improves detachment of the exhaust. This concept should be capable of producing an Isp in the range of 5,000 - 10,OOO seconds, with high thrust density. PTX is a device designed to study this concept. The plasmoid is formed inside of a single turn conical theta-pinch coil, driven by a 560 nF, 35 kV capacitor bank. Experiments conducted with a static-fill of propellant gas (6% H2 in He) demonstrated reliable ionization over a pressure range of 40 - 200 mTorr. A fast gas-puff valve to inject propellant has since been added, and a ringing pre-ionization circuit to independently control ionization has been tested. Hydrogen, deuterium, argon, and an N2/H2 mixture have been tried as propellants. Measurements of the plasmoid shape, mass, and velocity, using a variety of diagnostics will be presented,

Martin, Adam↗

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 fields. If B(sub p/B(sub t) much greater than 1 it is an FRC; if B(sub p) approximately equal to B(sub t), it is a Spheromak. A plasmoid thruster would operate by repetitively producing plasmoids that are accelerated to high velocity. The process is inductive, and the magnetic structure of the plasmoid suppresses thermal and mass losses, and improves detachment of the exhaust, This concept should be capable of producing an Isp in the range of 5,000 - l0,000 seconds, with high thrust density. PTX is a device designed to study this concept. The plasmoid is formed inside of a single turn conical theta-pinch coil, driven by a 560 nF, 35 kV capacitor bank. Experiments conducted with a static-fill of propellant gas (6% H2 in He) demonstrated liable ionization over a pressure range of 40 - 200 mTorr. A fast gas-puff valve to inject propellant has since been added, and a ringing preionization circuit to independently control ionization has been tested, hydrogen, deuterium, argon, and an N2 / H2 mixture have been tried as propellants. Measurements of the plasmoid shape, mass, and velocity, using a variety of diagnostics will be presented.

Martin, Adam↗

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↗