Theta Pinch Research Articles

A Historical Perspective of Controlled Thermonuclear Research at Los Alamos: 1946–1990

The following historical account highlights the evolution of controlled thermonuclear research (CTR) at Los Alamos (the singular entity denoted Los Alamos Laboratory/Los Alamos Scientific Laboratory/Los Alamos National Laboratory at different times in its evolution is designated “Los Alamos”) following the Manhattan Project. It focuses on magnetic fusion energy research performed by the Physics Division, Theory Division, and CTR Division from 1946 through 1990. It chronicles a compelling story, including the first laboratory demonstration worldwide of thermonuclear D-D fusion in 1960 by James Leslie Tuck and colleagues with the Scylla 1 theta pinch. Neither the rich history of Los Alamos research into inertial confinement fusion nor a summary of the historical breadth of fusion energy research worldwide is included. These subjects have been well researched and well documented in numerous publications, some of which are referenced herein.

Observation of plasma dynamics in a theta pinch by a novel method

A novel experimental method is proposed for observing plasma dynamics subjected to magnetic fields based on a newly developed cylindrical theta-pinch device. By measuring simultaneously the temporal profiles of multiple parameters including the drive current, luminosity, plasma density, and plasma temperature, it provides a basis for observing the plasma dynamics of the theta pinch, such as shock transport and magnetohydrodynamic instability. We show that the plasma evolution can be distinguished as three phases. First, in the radial implosion phase, the trajectories of the current sheath and shock wave are ascertained by combining experimental data with a snowplow model (Lee model) in a self-consistent way. Second, in the axial flow phase, we demonstrate that m = 0 (sausage) instability associated with the plasma axial flow suppresses the plasma end-loss. Third, in the newly observed anomalous heating phase, the lower-hybrid-drift instability may develop near the current sheath, which induces anomalous resistivity and enhanced plasma heating. The present experimental data and novel method offer better understanding of plasma dynamics in the presence of magnetic fields, thereby providing important support for relevant research in magneto-inertial fusion.

Automated signal classification in the C-2W fusion experiment.

In TAE Technologies' current experimental fusion device, C-2W (also called "Norman"), record breaking, advanced beam-driven field-reversed configuration plasmas are produced and sustained in steady state utilizing variable-energy neutral beams, expander divertors, end-bias electrodes, and an active plasma control system. With a rapid shot-pace and an extensive number of data channels, the amount of data generated necessitates automated signal processing. To this end, a machine learning algorithm consisting of a multi-layered neural network as well as other data processing software has been designed for signal feature identification, allowing for accurate and fast signal classification, anomalous condition detection, and providing for signal pre-processing. With a small set of training data, the neural network can be "bootstrapped" to provide a robust classification system while minimizing human oversight. An example using data from the theta pinch plasma formation pulsed power system is presented. With an overall accuracy of ∼97%-having classified more than 5 × 106 pulsed power signals-the classification scheme is more than sufficient to fine-tune machine set points. However, this technique can be used for near-real-time preprocessing of any plasma physics signal and has wide ranging application in fusion experiments for the varied data produced by plasma diagnostics.

Experimental evidence for super-Alfvénic acceleration of the field-reversed configuration due to a magnetic pressure gradient

The super-Alfvénic acceleration of an extremely high beta plasmoid due to a magnetic pressure gradient is evidenced in translation experiments involving the field-reversed configuration (FRC) in the FRC amplification via the translation-collisional merging (FAT-CM) device. Inside the FRC, there is a population of unmagnetized particles that forms a volume with extremely high beta. Formed using the field-reversed theta pinch method, the FRC is accelerated and injected into a quasi-static confinement magnetic field that is weaker than the formation and acceleration fields. Because the FRC is injected with nonzero axial translation speed and cannot slow down, its speed exceeds the Alfvénic and sonic speed upon entering the confinement field. This phenomenon is predicted from two-dimensional resistive magnetohydrodynamic simulations, and experimental results that are consistent with the magnetohydrodynamic approximation show that the FRC acceleration process is due mainly to magnetic pressure on the thin magnetized layer.

Kinetic simulations of anomalous resistivity in high-temperature current carrying plasmas

Anomalous resistivity caused by lower hybrid drift instabilities (LHDIs) has been extensively studied in the literature, and has been invoked to explain the rates of magnetic diffusion and plasma profile evolution in the low-density plasma periphery of theta and screw pinch plasmas. This article presents a fully kinetic simulation study of LHDIs with a realistic mass ratio using the particle-in-cell code Chicago over a large range of drift speeds, 0.5<vdi2/vti2<14.5, plasma β, β≥2×10−5, and temperature ratios, 0.1<Te/Ti<10. The resistivity quantified from the simulations is compared with the analytic estimates from the literature and a generalized resistivity expression is presented, which can be applied over the entire range of plasma environments that were simulated in this study. This expression uses the amplitude of the LHDI fluctuations resulting from instability saturation by electron resonance broadening rather than plateau formation, current relaxation, or ion trapping. The generalized resistivity expression is appropriate for full-scale fluid simulations that encounter a large range of plasma conditions, and has better agreement with the resistivity quantified from kinetic simulations than previous expressions in the literature, particularly at low plasma β. Anomalous resistivity has also been considered as an explanation of the rapid magnetic field dissipation during magnetic reconnection events at large plasma β. At a large β, the magnetic field fluctuations of LHDIs can dominate the electrostatic fluctuations and this article investigates enhanced collisionality due to the nonlinear magnetic force, δJ×δB/c.

Study on a dense theta pinch plasma for ion beam stripping application for FAIR

Study on a dense theta pinch plasma for ion beam stripping application for FAIR

Estimation of the Current Sheath Dynamics and Magnetic Field for Theta Pinch by Snow Plow Model Simulation

The snowplow model and shock wave equation are used to simulate theta pinch plasma experiment. The model calculates the sheath velocity, radial position, plasma current, plasma temperature, and the induced magnetic field of the current sheath. The model uses two phases: the radial inward phase and the reflected shock phase. The governing equations are derived by using the current factor and the mass factor. The model calculates the induced magnetic field of the plasma by the deriving equation and the magnetic field of the coil. Also, the model is operated by using the Hydrogen, Deuterium and Tritium gases at the same of the mass density. The results illustrate that the temperature and the induced magnetic field are higher for tritium gas, which has a higher molecular weight, while the current sheath velocity of tritium is lower. Some results of the model were compared with Lee model and other paper.

Study on the Theta Pinch Plasmas for Applied as Ion Stripper

Study on the Theta Pinch Plasmas for Applied as Ion Stripper

Topology of the Magnetic Field and Resistivity of a Compact Torus Generated in a Mirrorless Theta Pinch

The mapping of the magnetic field and analysis of the plasma resistivity were used to study the change of magnetic field topology during the formation of a reversed field configuration. Using a theta pinch with straight coil, the formation of the torus was observed during the early time of the plasma radial implosion, in scale comparable to Alfven’s time and shorter than the resistive diffusion. The non-intrusive excluded flux probe also indicated the formation of the torus even in the absence of mirror coils in the system. The plasma at the end region of the coil has distributed in the entire cross section of the tube, slightly peaked at the null field region. The anomalous plasma resistivity at the reconnection site was close to the prediction given by numerical calculation using numerical hybrid code with anomalous collision frequency either calculated using Chodura’s algorithm or evolution of microinstabilities, particularly the lower hybrid drift instability.

Determining the ion temperature and energy distribution in a lithium-plasma interaction test stand with a retarding field energy analyzer.

The ThermoElectric-driven Liquid-metal plasma-facing Structures (TELS) experiment at the University of Illinois is a gas-puff driven, theta-pinch plasma source that is used as a test stand for off-normal plasma events incident on materials in the edge and divertor regions of a tokamak. The ion temperatures and resulting energy distributions are crucial for understanding how well a TELS pulse can simulate an extreme event in a larger, magnetic confinement device. A retarding field energy analyzer (RFEA) has been constructed for use with such a transient plasma due to its inexpensive and robust nature. The innovation surrounding the use of a control analyzer in conjunction with an actively sampling analyzer is presented and the conditions of RFEA operation are discussed, with results presented demonstrating successful performance under extreme conditions. Such extreme conditions are defined by heat fluxes on the order of 0.8 GW m-2 and on time scales of nearly 200 μs. Measurements from the RFEA indicate two primary features for a typical TELS discharge, following closely with the pre-ionizing coaxial gun discharge characteristics. For the case using the pre-ionization pulse (PiP) and the theta pinch, the measured ion signal showed an ion temperature of 23.3 ± 6.6 eV for the first peak and 17.6 ± 1.9 eV for the second peak. For the case using only the PiP, the measured signal showed an ion temperature of 7.9 ± 1.1 eV for the first peak and 6.6 ± 0.8 eV for the second peak. These differences illustrate the effectiveness of the theta pinch for imparting energy on the ions. This information also highlights the importance of TELS as being one of the few linear pulsed plasma sources whereby moderately energetic ions will strike targets without the need for sample biasing.

Parallel Triggering and Conduction of Rail-Gap Switches in a High-Current Low-Inductance Crowbar Switch

The field-reversed configuration heating experiment (FRCHX) was designed to form closed-field-line magnetized target plasmas for magnetoinertial fusion and other high energy density plasma research. These plasmas are in a field-reversed configuration and are formed via a reversed-field theta pinch on an already magnetized background plasma. To extend the duration and temporal uniformity of the pinch, the capacitor bank driving the reversed-field discharge is crowbarred near the current peak. Four parallel rail-gap switches are used on the FRCHX for this application to ensure a low-inductance crowbar discharge path and to accommodate the large magnitude of the discharge current (often greater than 1 MA). Historically, parallel operation of spark gap switches in a crowbarring arrangement has often proved to be difficult due to the very low voltage present on the bank and across the switches at the time of peak current. In a low-inductance design, triggering can be further complicated by the rapid collapse of what little voltage there is across the switches as soon as the first spark gap begins conduction. This paper reports on the efforts that were made to develop a low-inductance crowbar switch for the FRCHX and to ultimately enable successful triggering and operation of the four parallel rail-gap switches used in the crowbar. The design of the low-inductance parallel switch assembly is presented first, followed by a description of the triggering scheme employed to ensure conduction of all four switches.

Time-Resolved Electron Temperature in an Argon Theta Pinch by Line Ratio Methods

Pulsed inductive argon plasma in an 80-J, 15-kV, 490-kHz theta pinch is interrogated using spectroscopic methods. Time-resolved electron temperature is obtained by coupling line intensity ratios with steady-state corona and collisional-radiative (CR) models. Neutral excited state argon transitions from the 2p to 1s subshells were utilized. The backfill pressures of 50 and 100 mtorr are of primary focus. Time-resolved electron temperature estimates are presented ranging from 1 to 11.1 eV for the corona model up to an excess of 80 eV for the CR model. Near-IR spectral emission is seen to increase rapidly near the first zero crossing of the oscillating discharge current while electron temperature increase lags by roughly one full discharge cycle later near the third zero crossing. An analysis of long exposures provides an account of substantial second-order diffracted spectra. Weak spectral signal quality for the short exposures of 0.25-μs yielded time-resolved spectral intensity trend lines of a low accuracy with an average percent difference of 69% between raw data and trend lines.

Magnetohydrodynamic simulation of conical plasma compression

Low density gas conical implosion can produce high density plasmas with a volume compression ratio of 106 to 109, and a temperature over 10 eV. As the temperature is limited by the plasma-wall interaction, to further increase the density and temperature and confine the plasma energy, we use a theta pinch at the top of the imploding cone. A conical magnetohydrodynamic simulation method is used to calculate the properties of the plasma, in which three cases, i.e., pure conical fluid compression, pure theta pinch, and synergic compression of fluid compressing and theta pinch, are calculated in a two-dimensional conical geometry. Simulation shows that synergic compression can improve the energy confinement and efficiently raise the temperature of the plasma. Different parameter combinations are calculated to find the optimum performance.

Study of the Theta Pinch Plasma Numerically by Varying β Parameter and Applied Current

The implosion dynamics of theta pinch is studied by simulation technique through snow plow model with the help of MATHEMATICA software. The differential equation of motion for plasma implosion is derived and solved numerically by using this software. The variation effects of β parameter (plasma kinetic pressure to plasma magnetic pressure ratio) and applied current is examined on normalize radius of imploded plasma by variations in normalized time. The graphs between normalized radius and normalized time of imploded plasma indicates that theta pinching effect can be improved by decreasing β value and increasing in the magnitude of applied current.

Hydrogen plasma dynamics in the spherical theta pinch plasma target for heavy ion stripping

Due to the superior ability of dense and highly ionised plasmas to ionise penetrating heavy ion beams to degrees beyond those reachable by common gas strippers, many experiments have been performed to find suitable plasma generators for this application. In the field of gas discharges, mainly z-pinch devices have been investigated so far, which are known to be limited by the nonlinear focusing effects of the plasma columns sustaining current and by electrode erosion. The spherical theta pinch has therefore been proposed as a substitution for the z-pinch, promising progress by inductive rather than capacitive coupling and displacement of the outer magnetic field by the dense, diamagnetic discharge plasma. As yet mainly experiments with argon/hydrogen mixture gas have been performed, which is not suitable for the application as a plasma stripper, this paper describes the first detailed analysis of the plasma parameters and dynamics of a hydrogen plasma created by the spherical theta pinch. These include the time integrated and time resolved electron density, the dynamics of the plasma in the discharge vessel, the comparison with the argon dominated plasma, and an outlook to reachable characteristics with similar devices.

New model of calculating the energy transfer efficiency for the spherical theta-pinch device

Ion-beam-plasma-interaction plays an important role in the field of Warm Dense Matter (WDM) and Inertial Confinement Fusion (ICF). A spherical theta pinch is proposed to act as a plasma target in various applications including a plasma stripper cell. One key parameter for such applications is the free electron density. A linear dependency of this density to the amount of energy transferred into the plasma from an energy storage was found by C. Teske. Since the amount of stored energy is known, the energy transfer efficiency is a reliable parameter for the design of a spherical theta pinch device. The traditional two models of energy transfer efficiency are based on assumptions which comprise the risk of systematical errors. To obtain precise results, this paper proposes a new model without the necessity of any assumption to calculate the energy transfer efficiency for an inductively coupled plasma device. Further, a comparison of these three different models is given at a fixed operation voltage for the full range of working gas pressures. Due to the inappropriate assumptions included in the traditional models, one owns a tendency to overestimate the energy transfer efficiency whereas the other leads to an underestimation. Applying our new model to a wide spread set of operation voltages and gas pressures, an overall picture of the energy transfer efficiency results.

Analysis on the formation of a FRC by flux measurements and MHD simulations

The evolution of the separatrix and excluded flux radius was investigated in a mirror-less theta pinch with external magnetic and loop probes and by numerical simulation. In the numerical hybrid code the anomalous effect was taken as evolution of lower hybrid drift instability. At mid-plane of the coil the experimental and theoretical values of lift-off time, implosion time and equilibrium plasma radius were very close. The implosion time is 5 ± 1 cm/ps and the separatrix radius at mid-plane is around one half of the discharge tube radius. Within the experimental uncertainty the excluded flux radius has the same value along the coil, suggesting an elongated configuration with closed magnetic field lines.

A model code for the radiative theta pinch

A model for the theta pinch is presented with three modelled phases of radial inward shock phase, reflected shock phase, and a final pinch phase. The governing equations for the phases are derived incorporating thermodynamics and radiation and radiation-coupled dynamics in the pinch phase. A code is written incorporating correction for the effects of transit delay of small disturbing speeds and the effects of plasma self-absorption on the radiation. Two model parameters are incorporated into the model, the coupling coefficient f between the primary loop current and the induced plasma current and the mass swept up factor fm. These values are taken from experiments carried out in the Chulalongkorn theta pinch.

Review of the State-of-the-Art Development of the Spherical Theta Pinch Plasma Source

After the spherical theta pinch had been developed at the Institute of Applied Physics in Frankfurt, considerable progress in creating high efficiency and long lifetime plasma sources had been made. Several devices have been built to study the characteristics of the spherically confined plasma. Scaling rules and investigated setups are presented, showing devices with electron densities of up to some $10^{23}~{\rm m}^{-3}$ , electron temperatures of several eV and confinement times of ${\sim}{\rm 10}~\mu{\rm s}$ . Typical dimensions are: discharge vessel radius $R=10~{\rm cm}$ , radius of the pinched plasma $r=2~{\rm cm}$ , initial gas pressures of 1–200 Pa at currents of up to 35 kA and resonance frequencies of 10–40 kHz. During the harmonic discharge of the stored energy, the plasma periodically pinches and expands again as long as the current rise rate creates sufficient electrical field strengths for ionization, which allows for pinching sequences in the millisecond range. The principles, improvements, theoretical approaches, and applications including pulsed ion source, plasma ion stripping, and vacuum ultraviolet flash lighting are discussed.

Addressing Short Trapped-Flux Lifetime in High-Density Field-Reversed Configuration Plasmas in FRCHX

The objective of the field-reversed configuration heating experiment (FRCHX) is to obtain a better understanding of the fundamental scientific issues associated with high-energy density laboratory plasmas (HEDLPs) in strong, closed-field-line magnetic fields. These issues have relevance to such topics as magneto-inertial fusion, laboratory astrophysical research, and intense radiation sources, among others. To create HEDLP conditions, a field-reversed configuration (FRC) plasma of moderate density is first formed via reversed-field theta pinch. It is then translated into a cylindrical aluminum flux conserver (solid liner), where it is trapped between two magnetic mirrors and then compressed by the magnetically driven implosion of the solid liner. A requirement is that, once the FRC is stopped within the solid liner, the trapped flux inside the FRC must persist while the compression process is completed. With the present liner dimensions and implosion drive bank parameters, the total time required for implosion is ${\sim}{\rm 25}~\mu{\rm s}$ . Lifetime measurements of recent FRCHX FRCs indicate that trapped lifetimes following capture are now approaching ${\sim}{\rm 14}~\mu{\rm s}$ (and therefore, total lifetimes after formation are now approaching ${\sim}{\rm 19}~\mu{\rm s}$ ). By separating the mirror and translation coil banks into two so that the mirror fields can be set lower initially, the liner compression can now be initiated 7–9 $\mu{\rm s}$ before the FRC is formed. A discussion of FRC lifetime-limiting mechanisms and various experimental approaches to extending the FRC lifetime will be presented.