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Ultrashort Pulse Reflectometry (USPR) is a plasma diagnostic technique involving the propagation and reflection of ultrashort duration (∼few ns) chirps. The reflected packets pass through a multichannel filter with time-of-flight measurements performed on each of the filtered packets. A next generation USPR system is under development, spanning 28-75 GHz, for use on compact, short duration, magnetically confined fusion devices. This system presents a dramatic increase in performance compared with an earlier USPR system employed on the LLNL Sustained Spheromak Physics Experiment device more than a decade ago. The new system replaces upconverting mixers with higher power active multiplier chains to generate mm-wave transmitter chirps, with custom time-of-flight electronics reducing the time per measurement by a factor of 3X. Finally, the system is equipped with a field programmable gate array for data acquisition and analysis.

Reproduced from O'Bryan, J. B., C. A. Romero-Talamas, and S. Woodruff. Simulation of multi-pulse coaxial helicity injection in the Sustained Spheromak Physics Experiment. Physics of Plasma 25, no. 3., Nonlinear, numerical computation with the NIMROD code is used to explore magnetic self-organization during multi-pulse coaxial helicity injection in the Sustained Spheromak Physics eXperiment. We describe multiple distinct phases of spheromak evolution, starting from vacuum magnetic fields and the formation of the initial magnetic flux bubble through multiple refluxing pulses and the eventual onset of the column mode instability. Experimental and computational magnetic diagnostics agree on the onset of the column mode instability, which first occurs during the second refluxing pulse of the simulated discharge. Our computations also reproduce the injector voltage traces, despite only specifying the injector current and not explicitly modeling the external capacitor bank circuit. The computations demonstrate that global magnetic evolution is fairly robust to different transport models and, therefore, that a single fluid-temperature model is sufficient for a broader, qualitative assessment of spheromak performance. Although discharges with similar traces of normalized injector current produce similar global spheromak evolution, details of the current distribution during the column mode instability impact the relative degree of poloidal flux amplification and magnetic helicity content., https://aip.scitation.org/doi/abs/10.1063/1.5018319

To monitor effects of vacuum conditioning, three radiation diagnostics are being built: a Helium–Neon (HeNe) heterodyne interferometer, a Bolometer, and a Hydrogen-alpha (Hα) detector. The interferometer will measure the line-average refractive index of the plasma, enabling us to obtain the line average density. The bolometer is a soft X-ray/UV detector (similar to those used on the Sustained Spheromak Physics Experiment (McLean et al. in Rev. Sci. Instruments 72(1):556–561, 2001) and the High-Beta Tokamak Experiment (Xiao and Navratil. in Rev. Sci. Instrument 67(9):3334–3335, 1996) and is used to directly measure the radiation loss from photons. The Hα detector will detect the amount of Hα being emitted by the plasma as a function of time, thus gauging the neutral density. These same concepts are also applied to astrophysical plasmas, with slightly different approaches. A brief overlap between diagnostics/detectors for laboratory and astrophysical plasmas is discussed.

Nonlinear, numerical computation with the NIMROD code is used to explore magnetic self-organization during multi-pulse coaxial helicity injection in the Sustained Spheromak Physics eXperiment. We describe multiple distinct phases of spheromak evolution, starting from vacuum magnetic fields and the formation of the initial magnetic flux bubble through multiple refluxing pulses and the eventual onset of the column mode instability. Experimental and computational magnetic diagnostics agree on the onset of the column mode instability, which first occurs during the second refluxing pulse of the simulated discharge. Our computations also reproduce the injector voltage traces, despite only specifying the injector current and not explicitly modeling the external capacitor bank circuit. The computations demonstrate that global magnetic evolution is fairly robust to different transport models and, therefore, that a single fluid-temperature model is sufficient for a broader, qualitative assessment of spheromak perfo...

Recent results from investigations using insertable magnetic probes at the Sustained Spheromak Physics Experiment (SSPX) [E. B. Hooper et al., Nucl. Fusion 39, 863 (1999)] are presented. Experiments were carried out during pre-programmed, constant amplitude coaxial gun current pulses, where magnetic field increases stepwise with every pulse, but eventually saturates. Magnetic traces from the probe, which is electrically isolated from the plasma and spans the flux conserver radius, indicate there is a time lag at every pulse between the response to the current rise in the open flux surfaces (intercepting the electrodes) and the closed flux surfaces (linked around the open ones). This is interpreted as the time to buildup enough helicity in the open flux surfaces before reconnecting and merging with the closed ones. Future experimental and diagnostic plans to directly estimate the helicity in the open flux surfaces and measure reconnection are briefly discussed.

Magnetic reconnection in the spheromak changes magnetic topology by conversion of injected toroidal flux into poloidal flux and by magnetic surface closure (or opening) in a slowly decaying spheromak. Results from the Sustained Spheromak Physics Experiment, SSPX, are compared with resistive MHD simulations using the NIMROD code. Voltage spikes on the SSPX gun during spheromak formation are interpreted as reconnection across a negative-current layer close to the mean-field x-point. Field lines are chaotic during these events, resulting in rapid electron energy loss to the walls and the low T e < 50 eV seen in experiment and simulation during strong helicity injection. Closure of flux sufaces (and high T e ) can occur between voltage spikes if they are sufficiently far apart in time; these topology changes are not reflected in the impedance of the axisymmetric gun. Possible future experimental scenarios in SSPX are examined in the presence of the constraints imposed by reconnection physics.

Data from a recently installed insertable magnetic probe array in the Sustained Spheromak Physics Experiment (SSPX) [E. B. Hooper et al., Nucl. Fusion 39, 863 (1999)] is compared against NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)], a full 3D resistive magnetohydrodynamic code that is used to simulate SSPX plasmas. The experiment probe consists of a linear array of chip inductors arranged in clusters that are spaced every 2 cm, and spans the entire machine radius at the flux conserver midplane. Both the experiment and the numerical simulations show the appearance, shortly after breakdown, of a column with a hollow current profile that precedes magnetic reconnection, a process essential to the formation of closed magnetic flux surfaces. However, there are differences between the experiment and the simulation in how the column evolves after it is formed. These differences are studied to help identify the mechanisms that eventually lead to closed-flux surfaces (azimuthally averaged) and flux amplification, which occur in both the experiment and the simulation.

We present significant advances in the performance and understanding of the sustained spheromak physics experiment (SSPX). High performance discharges are obtained by adjusting the injected current and bias magnetic flux to produce a flat to slightly peaked radial current profile, consistent with reducing the drive for tearing and other MHD modes. Wall conditioning and density control are also essential for obtaining high performance discharges. With these optimizations, plasmas with peak electron temperatures of ~350 eV, edge magnetic fluctuation levels less than 1% and core thermal diffusivities (χe)

In this paper we report on the results of deuterium and hydrogen experiments in the Sustained Spheromak Physics Experiment (SSPX). We have compared ∼500 deuterium discharges with similar discharges in hydrogen. Typically, we produce H 2 plasmas with peak toroidal currents in the range of 0.6 MA, electron temperatures ( T e ) of ∼200 eV and energy confinement times ( τ E ) of ∼200 μs. The D 2 fueled discharges show similar results to those with H 2 fueling with no obvious differences in confinement time. Electron temperatures of ∼200 eV with similar electron densities were observed. Both the deuterium and hydrogen fueled discharges have a calculated thermal diffusivity below χ e 2 /s. However, the D 2 fueled discharges had a factor of ∼5 increase in high- Z (titanium) impurity content suggesting an increase of physical sputtering. We find no significant mass scaling effects.

Theoretical studies aimed at predicting and diagnosing field-line quality in a spheromak are described. These include nonlinear three-dimensional MHD simulations and analyses of confinement in spheromaks dominated by either open (stochastic) field lines or approximate flux surfaces. Three-dimensional nonlinear MHD simulations confirm that field lines are predominantly open when there is a large-amplitude toroidal-mode-number n = 1 mode. However, an appreciable volume of good flux surfaces can be obtained either during the drive-off phase of a scheme with periodic pulsed drive or for an extended period under driven conditions, with oscillating volume, when the odd-n modes are suppressed. If a configuration with radially localized perturbations can be achieved, a scaling analysis for a Rosenbluth?Bussac spheromak equilibrium indicates a favourable (1/Lundquist number) scaling to larger, higher-field devices. A hyper-resistivity analysis, which also assumes small-scale perturbations, reproduces well magnetic probe data in the sustained spheromak physics experiment, while an analysis of the same experiment based on one-dimensional transport along open field lines contradicts experimental observations in several key ways. The scaling analysis is also applied to reversed-field pinches and indicates that a completely determined scaling can be obtained with less approximation to the resistive MHD equations than indicated in the previous literature.

We report here results from power balance measurements for ohmically heated plasmas in the sustained spheromak physics experiment. The plasma is formed inside a close-fitting tungsten-coated copper shell; wall conditioning by baking, glow discharge cleaning (GDC), Ti gettering, and helium shot conditioning produces clean plasmas (Z eff < 2.5) and reduces impurity radiation to a small fraction of the input energy, except when the molybdenum divertor plate has been overheated. We find that most of the input energy is lost by conduction to the walls (the divertor plate and the inner electrode in the coaxial source region). Recently, carborane was added during GDC to boronize the plasma-facing surfaces, but little benefit was obtained.

A broadband, multichannel ultrashort pulse reflectometry (USPR) diagnostic on the Sustained Spheromak Physics eXperiment device has recently undergone a number of system upgrades, which has resulted in significant improvements in the signal-to-noise ratio of the USPR signals and a dramatic reduction in the number of “lost signals” in which the amplitude of the reflected wave form drops below detection threshold. This has greatly enhanced the ability of USPR to study relatively fast density profile modifications, and allows the simultaneous monitoring of multiple density layers with as short as a 3 μs pulse repetition rate. This article provides details of the upgraded USPR system together with density profiles and fluctuation data.

Current drive by coaxial helicity injection in the Sustained Spheromak Physics Experiment (SSPX) is modeled by a hyper-resistive term in Ohm's law for discharges in which magnetic fluctuations are small (1–3%). The current on the open magnetic field lines from the applied vacuum bias flux is assumed completely relaxed; interior to the spheromak, the helicity flux balances the ohmic losses. The poloidal area of the spheromak is found to depend on the strength of the hyper-resistive diffusion coefficient, allowing potentially large amplifications of the vacuum flux and discharge current. One discharge is examined in detail; the best fit to the experimental data finds that a limited fraction of the helicity injected into the flux conserver is effectively applied to current drive interior to the spheromak.

New types of toroidally rotating fluctuations (toroidal mode numbers n = 1 and n = 2) of line-integrated electron density and Hα emission, with frequencies ranging from 10 to 100 kHz, are observed in the sustained spheromak physics experiment (SSPX). The rotating directions of these fluctuations are the same as the direction determined by E×B, while the E and B directions are determined by the gun voltage and gun magnetic flux polarities, respectively. These results take advantage of one distinctive signature of spheromaks, i.e. it is possible to observe toroidal MHD activity during decay and sustainment at any toroidal angle. A theoretical constraint on line-integrated measurement is proposed and is found to be consistent with experimental observations. Fluctuation analysis in the time and frequency domains indicates that the observed density and Hα fluctuations correlate with magnetic modes. Observation of Hα fluctuations correlating with magnetic fluctuations indicates that, at least in some cases, MHD n = 1 modes are due to the so-called `dough-hook' current paths that connect the coaxial gun to the flux conserver, rather than internal kink instabilities. These results also show that electron density and Hα emission diagnostics complement other tools for spheromak mode study.

In this paper we report on density and impurity measurements in the Sustained Spheromak Physics Experiment (SSPX) which has recently started operation. The SSPX spheromak plasma is sustained by coaxial helicity injection for a duration of 2msec with peak toroidal currents of up to 0.5MA. The plasma-facing components consist of tungsten-coated copper to minimize sputtering. The surfaces are conditioned by a combination of baking at 150 C, glow discharge cleaning, Titanium gettering, and pulse-discharge cleaning with helium plasmas. In this way we can achieve density control so that the plasma density ({approx} 1-4 x 10{sup 20}m{sup -3}) matches the gas input. Low-density operation is presently limited by breakdown requirements, but we hope that new gas valves with supersonic nozzles will allow for a further reduction in density. We find that the conditioning reduces the impurity radiation to the point where it is no longer important to the energy balance, and long-lived spheromak plasmas are obtained (decay times of 1.5msec).

The Sustained Spheromak Physics Experiment (SSPX) will examine the confinement properties of spheromak plasmas sustained by DC helicity injection. Understanding the plasma-surface interactions is an important component of the experimental program since the spheromak plasma is in close contact with a stabilizing wall (flux conserver) and is maintained by a high current discharge in the coaxial injector region. Peak electron temperatures in the range of 400 eV are expected, so the copper plasma facing surfaces in SSPX have been coated with tungsten to minimize sputtering and plasma contamination. Here, we report on the characterization and conditioning of these surfaces used for the initial studies of spheromak formation in SSPX. The high pressure plasma-sprayed tungsten facing the SSPX plasma was characterized in situ using β-backscattering and ex situ using laboratory measurements on similarly prepared samples. Measurements showed that water can be desorbed effectively through baking while the removal rates of volatile impurity gases during glow discharge and shot conditioning indicated a large source of carbon and oxygen in the porous coating.

The nonlinear time-dependent equations of resistive magnetohydrodynamics are solved in simply connected domains to investigate spheromak formation and sustainment with electrostatic current drive. Spheromak magnetic fields are generated in three-dimensional computations as the nonlinear state resulting from an unstable pinch. Perturbations convert continuously supplied toroidal magnetic flux into poloidal magnetic flux, leading to “flux amplification” of field embedded in the electrodes. Relaxation of the axisymmetric component of the parallel current profile can be substantial, and the final nonlinear state is steady over a wide range of parameters. However, for sufficiently large values of Lundquist number or sufficiently large applied potential, nonsteady final states are observed with periodic relaxation events in some cases. Under most conditions, the saturated configuration exhibits chaotic scattering of the magnetic field lines. Conditions just above the marginal point of pinch instability sustain ...

A newly installed density diagnostic using CO2 laser interferometry and an Hα diagnostic using interference filters and photomultiplier tubes for the recently constructed sustained spheromak physics experiment (SSPX) are described. First diagnostic results of the Hα diagnostic were useful to understand the breakdown physics in the new SSPX experiments. Low-noise density data validates techniques to reduce vibration and electronic pickup. The data-processing electronics of the new interferometer can yield unambiguous density data that is equivalent to 16 fringe shifts. Density data is also critical to understand the particle source, and the J/ne parameter for SSPX.

In this article we discuss the measurement of the field profile in the sustained spheromak physics experiment (SSPX). We have built a transient internal probe (TIP) diagnostic to measure the internal field profile in a SSPX plasma sustained by dc coaxial helicity injection. TIP is a diagnostic that makes a spatially resolved (i.e., not chord averaged) measurement of the local magnetic field using Faraday rotation. A 1-cm by 4-mm-diameter verdet probe is fired through the plasma at about 2 km/s by a two-stage light gas gun. The probe is illuminated by an argon ion laser throughout the traverse of the plasma—the retro-reflected light is then analyzed with an ellipsometer to determine the field at each location. The speed, small size of the probe, and the probe cladding make this measurement possible even in hot plasmas (100 s of eV). The measurement is accurate enough (1 MHz, ±7 G, 1-cm spatial resolution) to map out magneto hydrodynamic (MHD) mode amplitudes from the edge to the magnetic axis.

In this article we present an overview of the plasma diagnostics operating or planned for the sustained spheromak physics experiment device now operating at Lawrence Livermore National Laboratory. A set of 46 wall-mounted magnetic probes provide the essential data necessary for magnetic reconstruction of the Taylor relaxed state. Rogowski coils measure currents induced in the flux conserver. A CO2 laser interferometer is used to measure electron line density. Spectroscopic measurements include an absolutely-calibrated spectrometer recording extended domain spectrometer for obtaining time-integrated visible ultraviolet spectra and two time-resolved vacuum monochrometers for studying the time evolution of two separate emission lines. Another time-integrated spectrometer records spectra in the visible range. Filtered silicon photodiode bolometers provide total power measurements, and a 16 channel photodiode spatial array gives radial emission profiles. Two-dimensional imaging of the plasma and helicity injec...

Spheromaks sustained by coaxial helicity injection differ from unsustained spheromaks in the profiles of the ratio of current to magnetic field and of the safety factor. Ideal MHD modelling with Taylor relaxed profiles in the injector predicts that the safety factor in the confined region will generally lie between 0.5 and 1, with a divergence on the separatrix since the open field lines carry current from the injector. The safety factor can be single or double valued, depending on the current profile. The modelling predicts that there are no mode rational surfaces with m = 1 except very near the separatrix; this is expected to determine the unstable resistive tearing modes associated with the dynamo which drives the discharge current. The resulting low magnetic shear has a beta (~2%) at the Mercier limit, which can be improved by current profiles differing significantly from the Taylor state or by other effects such as plasma flow. Examples are presented for the Sustained Spheromak Physics Experiment recently constructed at LLNL.

Pulsed reflectometry using both ordinary (O) and extraordinary (X) modes can provide time- and space-resolved measurements of the electron density, the magnitude of the magnetic field, the magnetic shear as a function of radius, and information on density and magnetic fluctuations. Such a diagnostic also yields the current profile from the curl of the magnetic field. This research addresses theoretical issues associated with the use of pulsed reflectometry with particular emphasis on applications in the Sustained Spheromak Physics Experiment (SSPX) at the Lawrence Livermore National Laboratory [E. B. Hooper et al., “Sustained Spheromak Physics Experiment,” in Proceedings of the 17th International Atomic Energy Agency (IAEA) Fusion Energy Conference, Yokohama, Japan, October 19–24, 1998, Lawrence Livermore National Laboratory Report UCRL-JC-132034 (September 29, 1998)]. Simulation results are presented for O- and X-mode mixed-polarization reflectometry and linear mode conversion in two spatial dimensions. The profile reconstruction algorithms depend on Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) formulae for group delays and linear mode conversion, which agree reasonably well with direct numerical solutions of the wave equation. Reconstructions of the electron density and modulus of the magnetic field are relatively robust in the presence of two-dimensional electron density and magnetic perturbations of the plasma.

A broadband ultrashort pulse reflectometry (USPR) diagnostic has been developed for measuring electron density profiles of the sustained spheromak physics experiment (SSPX) device. In USPR, an extremely short pulse or chirped wave form is propagated which contains a broad range of frequency components spanning the desired plasma density profile (or a significant fraction thereof). Upon reflection, each frequency component in the incident waveform reflects from a different spatial location (density layer) in the plasma, thus spreading out the reflected wave packet in time. By simultaneously collecting double-pass time delay data at many distinct frequencies, the time delay data may then be inverted to generate plasma density profiles using a single source and a single set of measurements. On SSPX, wideband mixers are utilized to up- and downconvert 6–18 GHz chirp signals to millimeter-wave frequencies (33–158 GHz) to form a 48 channel O-mode reflectometer system. In this article we describe details of the new USPR system installed on the SSPX device and provide preliminary time-of-flight results.

Options for a spheromak fusion-energy reactor are described and provide examples of the attractive opportunities which this magnetic configuration offers. However, the ability of the spheromak to confine plasma energy has not yet been demonstrated. The physics issues, including confinement in the presence of current drive by a magnetic dynamo driven by helicity injection, are summarized. These are being studied in the Sustained Spheromak Physics Experiment at LLNL.

We describe the design and operation of the SPHEX spheromak device and present an overview of its behaviour. The plasma is formed by ejection from a magnetized Marshall gun, and can be sustained as long as the gun is energized. The plasma is divided into the annulus comprising the closed toroidal flux, linked with the open flux forming the central column. The column current is driven directly by the central gun electrode, and the toroidal current in the annulus is driven indirectly by a mechanism associated with a coherent n = 1 oscillation of the column. The configuration exemplifies the operation of the process of relaxation to a state of minimum magnetic energy, which leads to magnetic configurations similar to those observed; to sustain these configurations requires some mechanism of toroidal current drive. Associated with this is the amplification of the poloidal flux, which is typically a factor of about five larger than the flux generated by the gun solenoid; the constancy (to a first approximation) of this factor plays a controlling role in spheromak behaviour. In standard operating conditions there is a `hard' limit, set by the solenoid flux, on the current carried by the column; any current driven by the external circuit above this apparently does not emerge from the gun. Evidence is presented that the column current is carried largely (> 50%) by accelerated ions with energy up to the gun voltage ( for a typical gun current of 60 kA). These ions are poorly magnetized and can escape across the magnetic field to the wall, a likely mechanism for the observed `loss' of current. Hydrogen is the normal operating gas: other gases ( and He) have been used, but the current drive is found to be less effective than in , with lower toroidal current maintained in the annulus.

The structure of the n = 1 mode in the SPHEX spheromak, which plays a central role in relaxation during sustainment, is investigated by analysing the measured voltage fluctuations in the central plasma column. By combining these results with a suitably defined helical magnetic flux function, the mode is found to be due to a rotating helical distortion of the open linked flux. We propose that the distortion is due to a saturated current-driven kink mode of the open flux tube. The prolongation of this `helical column' on its return around the outside of the closed flux is found to be strongly asymmetric. Previously published measurements of the Poynting flux and -profile are re-analysed in the light of these results, and implications for the mechanism of relaxation and non-inductive current drive are discussed.

Time-resolved density profiles on the Sustained Spheromak Physics Experiment device are now generated automatically from data collected by an ultrashort-pulse reflectometry (USPR) diagnostic comprised of 24 frequency channels spanning 34–75 GHz. Upgrades in USPR timing electronics and reconstruction software, coupled with new low noise amplifiers and reduced bandwidth filters, have significantly decreased amplitude and timing jitter enabling simultaneous density profile and multilayer density fluctuation operation. Hardware and software components of the upgraded USPR system are described, and sample profile and fluctuation data are presented. A new system layout is proposed to increase the USPR dynamic range by 8–10 dB.

Impurities play a critical role in magnetic fusion research. In large quantities, impurities can cool and dilute plasma creating problems for achieving ignition and burn; however in smaller amounts the impurities could provide valuable information about several plasma parameters through the use of spectroscopy. Many impurity ions radiate within the extreme ultraviolet (EUV) range. Here, we report on spectra from the silver flat field spectrometer, which was implemented at the Sustained Spheromak Physics experiment (SSPX) to monitor ion impurity emissions. The chamber within the SSPX was made of Cu, which makes M-shell Cu a prominent impurity signature. The Spect3D spectral analysis code was utilized to identify spectral features in the range of 115–315 A and to more fully understand the plasma conditions. A second set of experiments was carried out on the compact laser-plasma x-ray/EUV facility “Sparky” at UNR, with Cu flat targets used. The EUV spectra were recorded between 40–300 A and compared with results from SSPX.

Spheromak research from 1979 to the present is reviewed including over I60 references. Emphasis is on understanding and interpretation of results. In addition to summarizing results some new interpretations are presented. An introduction and brief history is followed by a discussion of generalized helicity and its time derivative. Formation and sustainment are discussed including five different methods, flux core, theta -pinch z-pinch, coaxial source, conical theta -pinch, and kinked z-pinch. All methods use helicity injections. Steady-state methods and rules for designing spheromak experiments are covered, followed by equilibrium and stability. Methods of stabilizing the tilt and shift modes are discussed as well as their impact on the reactor designs. Current-driven and pressure-driven instabilities as well as relaxation in general are covered. Energy confinement is discussed in terms of helicity decay time and and beta s limits. The confinement in high and low open-flux geometries are compared and the reactor implications discussed.

We present measurements of the magnetohydrodynamic ``dynamo'' due to correlated fluctuations of velocity and magnetic field in the SPHEX spheromak. We show that there are both single-mode and turbulent dynamo processes present, although the single-mode process is in this case an ``antidynamo'' opposing the externally applied electric field. The size of the turbulent dynamo at the magnetic axis is close to that required to drive the toroidal current there.

The silver flat field spectrometer (SFFS) is a high-resolution grazing-incidence diagnostic for magnetically confined plasmas. It covers the wavelength range of 25-450 A with a resolution of Delta lambda=0.3 A full width at half maximum. The SFFS employs a spherical 1200 lines/mm grating for flat-field focusing. The imaging is done using a backilluminated Photometrics charge-coupled device camera allowing a bandwidth of around 200 A per spectrum. The spectrometer has been used for atomic spectroscopy on electron beam ion traps and for plasma spectroscopy on magnetic confinement devices. Here we describe the design of the SFFS and the spectrometer setup at the sustained spheromak physics experiment in Livermore.

Electrostatic (dc) helicity injection has previously been shown to successfully sustain the magnetic fields of spheromaks and tokamaks. The magnitude of the injected magnetic helicity balances (within experimental error) the flux lost by resistive decay of the toroidal equilibrium. Hence the problem of optimizing this current drive scheme involves maximizing the injected helicity (the voltage‐connecting‐flux product) while minimizing the current (which multiplied by the voltage represents the energy input and also possible damage to the electrodes). The impedance (voltage‐to‐current ratio) and energy efficiency of a dc helicity injection experiment are studied on the CTX spheromak [Phys. Fluids 29, 3415 (1986)]. Over several years changes were made in the physical geometry of the coaxial magnetized plasma source as well as changes in the external electrical circuit. The source could be operated over a wide range of external charging voltage (and hence current), applied axial flux, and source gas flow rate...

In the Sustained Spheromak Physics Experiment, (SSPX) ['Improved operation of the SSPX spheromak', R.D. Wood, D.N. Hill, E.B. Hooper, S. Woodruff1, H.S. McLean and B.W. Stallard, Nucl. Fusion 45 1582-1588 (2005)], plasmas with core electron temperatures reaching up to 500 eV at densities of 10{sup 20}/m{sup 3} have been sustained for several milliseconds, making them suitable as targets for neutral beam injection. High performance and further progress in understanding Spheromak plasma physics are expected if neutral beams are injected into the plasma. This paper presents the results of numerical 1.5 D modeling of the plasma to calculate neutral beam current drive and ion and electron heating. The results are presented for varying initial conditions of density, temperatures and profiles and beam energy, injection angle and power. Current drive efficiency (Ampere/Watt of absorbed power) of up to 0.08 can be achieved with best performance SSPX shots as target. Analyses of neutral beam heating indicate that ion temperatures of up to 1.5 keV and electron temperatures of up to 750 eV can be obtained with injection of about 1 MW of neutral beam for 5-10 ms and with diffusivities typically observed in SSPX. Injection targeting near the magnetic axis appears to bemore » the best for heating and current drive. Effect of the current drive and evolution of SSPX equilibrium are discussed.« less

Software routines developed to prepare NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] results for three-dimensional visualization from simulations of the Sustained Spheromak Physics Experiment (SSPX ) [E. B. Hooper et al., Nucl. Fusion 39, 863 (1999)] are presented here. The visualization is done by first converting the NIMROD output to a format known as legacy VTK and then loading it to VisIt, a graphical analysis tool that includes three-dimensional rendering and various mathematical operations for large data sets. Sample images obtained from the processing of NIMROD data with VisIt are included.

The Sustained Spheromak Physics Experiment (SSPX) shows considerable sensitivity to the value of the injected (''gun'') current, I{sub gun}, parameterized by the relative values of {lambda}{sub gun} = {mu}{sub 0}I{sub gun}/{Psi}{sub gun} (with {Psi}{sub gun} the bias poloidal magnetic flux) to the lowest eigenvalue of {del} x B = {lambda}{sub FC}B in the flux conserver geometry. This report discusses modeling calculations using the NIMROD resistive-MHD code in the SSPX geometry. The behavior is found to be very sensitive to the profile of the safety factor, q, with the excitation of interior MHD modes at low-order resonant surfaces significantly affecting the evolution. Their evolution affects the fieldline topology (closed flux, islands, stochastic fieldlines confined by KAM surfaces, and open fieldlines), and thus electron temperature and other parameters. Because of this sensitivity, a major effect is the modification of the q-profile by the current on the open fieldlines in the flux core along the geometric axis. The time-history of a discharge can thus vary considerably for relatively small changes in I{sub gun}. The possibility of using this sensitivity for feedback control of the discharge evolution is discussed, but modeling of the process is left for future work.

A new 5 kV, 1.5 MJ modular capacitor bank has been designed for the Sustained Spheromak Physics Experiment (SSPX) at LLNL. The new bank consists of thirty 4 mF capacitors that are independently controlled by light-triggered thyristors. By closing all switches simultaneously, the bank will provide a mega-ampere discharge. The new bank will also allow additional capabilities to SSPX, including higher peak gun current, longer current pulses, and multi-pulse plasma buildup. Experiment results for a single stage prototype will be presented.

Nonlinear plasma simulations of the Sustained Spheromak Physics Experiment demonstrate the role of transient effects in establishing a toroidal magnetic structure that confines internal energy. Magnetohydrodynamics modeling with temperature-dependent transport coefficients compares well with experimental measurements and shows that the second current pulse improves confinement by keeping the $q$ profile from falling below the value of $1/2$, suppressing resonant $m=1$, $n=2$ fluctuations.

By operating a magnetized coaxial gun in a pulsed mode it is possible to produce large voltage pulses of duration $\ensuremath{\sim}500\text{ }\ensuremath{\mu}\mathrm{s}$ while reaching a few kV, giving a discrete input of helicity into a spheromak. In the sustained spheromak physics experiment (SSPX), it is observed that pulsing serves to nearly double the stored magnetic energy and double the temperature. We discuss these results by comparison with 3D MHD simulations of the same phenomenon.

Summary form only given, as follows. Summary form only given. New physics understanding of the ultrashort pulse reflectometry (USPR) diagnostic technique has been achieved with a series of receiver bandwidth studies on the Sustained Spheromak Physics Experiment (SSPX) device at the Lawrence Livermore National Laboratory. This new understanding, together with a number of transmitter and receiver modifications suggested by this new understanding, has resulted in significant increases in both dynamic range and signal-to-noise ratios of the USPR signals. This in turn has translated to a significant reduction in receiver timing jitter and the number of lost signals in which the received power has dropped below the detection threshold USPR involves the propagation of short duration (/spl sim/2-3 ns) chirps of moderate frequency bandwidth. These chirps axe upconverted to millimeter-wave frequencies, reflected from the plasma, and downconverted for detection and analysis. Each received chirp is analyzed at a number of simultaneous frequencies, with multiple chirps required to provide broad frequency coverage. Commercial time-to-amplitude converters convert the receiver time delays into easily acquired analog voltages with 25 ps resolution. On SSPX, four mixers (LO frequencies are 27, 44, 57 and 75 GHz) are utilized to up- and down-convert 7-16 GHz chirped waveforms to millimeter-wave frequencies (34-91 GHz). Four mixer operation provides 32 frequency channels of timing data with 12 /spl mu/s resolution, while operation with only the lowest frequency mixer provides 8 frequency data with 3 /spl mu/s resolution. In addition to edge density profile information, the system is also capable of simultaneously monitoring density fluctuations on as many as 32 distinct density layers. Details of the upgraded USPR system axe described together with USPR profile and fluctuation data.

A multichannel ultrashort pulse reflectometry (USPR) system has been upgraded to enhance the performance of simultaneously measuring electron density profiles and fluctuations on the sustained spheromak physics experiment device (SSPX). In addition to the use of a high power frequency multiplier in the transmitter subsystem, the optimization of filter bandwidths in the receiver subsystem results in significant improvement of the dynamic range and signal-to-noise ratios of the USPR signals, thereby dramatically reducing the number of "lost" signals. Details of the upgraded USPR system are described together with USPR profile and fluctuation data.

Tangled magnetic field lines are common in laboratory and space plasmas, but determining the geometrical structure of magnetic fields in the presence of plasma is a difficult and still unresolved problem. To address this open question we developed and tested a new technique for measuring the magnetic field-line topology in magnetically confined plasmas. Our field-line tracing diagnostic (FLIRT) uses a high-power, short-pulse laser to launch a burst of energetic ({approx}100 keV) electrons from a target passing through the plasma. These electrons then generally follow magnetic-field lines until they strike a solid surface, where a burst of x-rays is produced. The field-line connection length can be determined from the time delay between the laser pulse and the burst of x-rays. The topology of the field lines can be inferred by measuring the connection length as a function of initial target location inside the plasma. Measuring the spatial distribution of x-ray production provides further information on the field topology, including the effects of magnetic field fluctuations and stochasticity. The goals of this experiment were to test the appropriate x-ray detectors; measure the background x-ray emission in a spheromak plasma; measure the energetic electron production by a short-pulse, high-power laser; make preliminary measurementsmore » of the edge field line topology in the Sustained Spheromak Physics Experiment (SSPX), and perform analytic studies of electron production. These results are reported in detail in three publications listed. A brief summary is given.« less

Magnetic fluctuations have been reduced to approximately 1% during discharges on the Sustained Spheromak Physics Experiment by shaping the spatial distribution of the bias magnetic flux in the device. In the resulting quiescent regime, the safety factor profile is nearly flat in the plasma and the dominant ideal and resistive MHD modes are greatly reduced. During this period, the temperature profile is peaked at the magnetic axis and maps onto magnetic flux contours. Energy confinement time is improved over previous reports in a driven spheromak.

This is the final report on LDRD SI-funded research to determine the Effect of Magnetic Field Configurations on Spheromak Performance for the years FY2000-FY2001, during which a new set of bias magnetic field coils was used to change the vacuum magnetic field configuration of the SSPX spheromak at LLNL. The USDOE Office of Fusion Energy Science funded the routine operation of the SSPX facility during FY00 and FY01. A photo of the SSPX facility as it appeared in mid-FY01, appears in this report. The main distinctive feature of the spheromak is that currents in the plasma itself produce the confining toroidal magnetic field, rather than a complex set of external coils. The Sustained Spheromak Physics Experiment (SSPX) device was designed and built study how well the spheromak can contain plasma energy while dynamo processes in the plasma maintain the confining magnetic fields. The spheromak potentially offers advantages over other fusion reactor concepts because it is compact, has no field coils linking the vacuum vessel, and can be operated in a steady state with voltage applied to external electrodes. It is predicted that the ability of the SSPX to contain the plasma thermal energy will increase with increasing plasma electron temperature;more » that is, the hotter it is, the better it will work. Our near-term goal for the SSPX facility is to determine which of several magnetic field configurations works best to produce hot, well-confined spheromak plasmas. We also want to verify the predicted inverse relation between plasma temperature and heat loss, and to use these results to design an even higher-temperature follow-on experiment that will push closer to fusion conditions. New features of the SSPX spheromak include a large-radius coaxial plasma injector to improve efficiency, a conformal flux conserver to minimize open field lines around the plasma, a divertor to aid in cold-particle exhaust, and the programmable-bias magnetic field coils to vary the magnetic geometry. The effect of operating SSPX with the bias magnetic-field coils is the subject of this LDRD research project.« less

The Ion Doppler Spectrometer instrument on the Sustained Spheromak Physics experiment is described, along with background about it's operation. Results are presented from recent experimental runs, and the data is compared to the results of simple statistical models of heat exchange in two species gasses.

The Sustained Spheromak Physics Experiment is proposed for experimental studies of spheromak confinement issues in a controlled way: in steady state relative to the confinement timescale and at low collisionality. Experiments in a flux - conserver will provide data on transport in the presence of resistive modes in shear-stabilized systems and establish operating regimes which pave the way for true steady-state experiments with the equilibrium field supplied by external coils. The proposal is based on analysis of past experiments, including the achievement of T{sub e} = 400 eV in a decaying spheromak in CTX. Electrostatic helicity injection from a coaxial ``gun`` into a shaped flux conserver will form and sustain the plasma for several milliseconds. The flux conserver minimizes fluxline intersection with the walls and provides MHD stability. Improvements from previous experiments include modem wall conditioning (especially boronization), a divertor for density and impurity control, and a bias magnetic flux for configurational flexibility. The bias flux will provide innovative experimental opportunities, including testing helicity drive on the large-radius plasma boundary. Diagnostics include Thomson scattering for T{sub e} measurements and ultra-short pulse reflectrometry to measure density and magnetic field profiles and turbulence. We expect to operate at T{sub e} of several hundred eV, allowing improved understanding of energy and current transport due to resistive MHD turbulence during sustained operation. This will provide an exciting advance in spheromak physics and a firm basis for future experiments in the fusion regime.

This report summarizes the state of theoretical knowledge of several physics issues important to the spheromak. It was prepared as part of the preparation for the Sustained Spheromak Physics Experiment (SSPX), which addresses these goals: energy confinement and the physics which determines it; the physics of transition from a short-pulsed experiment, in which the equilibrium and stability are determined by a conducting wall (``flux conserver``) to one in which the equilibrium is supported by external coils. Physics is examined in this report in four important areas. The status of present theoretical understanding is reviewed, physics which needs to be addressed more fully is identified, and tools which are available or require more development are described. Specifically, the topics include: MHD equilibrium and design, review of MHD stability, spheromak dynamo, and edge plasma in spheromaks.

The spheromak is a Magnetic Fusion Energy (MFE) configuration, which is a leading alternative to the tokamak. It has a simple geometry which offers an opportunity to achieve the promise of fusion energy if the physics of confinement, current drive, and pressure holding capability extrapolate favorably to a reactor. Recent changes in the US MFE program, taken in response to budget constraints and programmatic directions from Congress, include a revitalization of an experimental alternative concept effort. Detailed studies of the spheromak were consequently undertaken to examine the major physics issues which need to be resolved to advance it as a fusion plasma, the optimum configuration for an advanced experiment, and its potential as a reactor. As a result of this study, we conclude that it is important to evaluate several physics issues experimentally. Such an experiment might be appropriately be named the Sustained Spheromak Physics Experiment (SSPX). It would address several critical issues, the solution to which will provide the physics basis to enable an advanced experiment. The specific scientific goals of SSPX would be to: * Demonstrate that electron and ion temperatures of a few hundred electron volts can be achieved in a steady-state spheromak plasma sustained by a magnetic dynamo (``helicity injection``). * Relate energy confinement quantitatively to the magnetic turbulence accompanying the dynamo and use this knowledge to optimize performance. * Measure the magnetic field profiles and magnetic turbulence in the plasma and relate these to the science of the magnetic dynamo which drives the current in the plasma. * Examine experimentally the pressure holding capability (``beta limit``) of the spheromak. * Understand the initial phases of the transition of the plasma from an equilibrium supported by a magnetic-flux conserving wall to one supported by external coils. These goals could be achieved in an experiment with duration of a few milliseconds, and can consequently be addressed at a relatively low cost. There are additional goals which would be addressed in a larger, follow-up experiment, the Advanced Spheromak Physics Experiment. These include the achievement of temperatures in the multi-kev range, the control of low mode-number instabilities (perhaps with a feedback system), and the technology of long-pulse current drive. This document reviews past work in the field and describes a number of new results. Recent publications which complement this report are also referenced. These publications also describe the characteristics of an experiment to examine the important spheromak physics issues.

The Sustained Spheromak Physics Experiment (SSPX) was a high-temperature (Te up to 0.5 keV) spheromak formed by coaxial helicity injection (CHI) and with plasma duration of a few milliseconds following the high-current formation stage. Clean walls and low impurity operation were obtained by a combination of baking, discharge cleaning and titanium deposition on the walls, allowing the generation of high-quality plasmas. Resistive-magnetohydrodynamic simulations, benchmarked to the experiment, were used to elucidate the physics. The detailed characteristics of the nφ = 1 toroidal mode associated with CHI were determined as was the physics of the nonlinear current drive and magnetic reconnection that formed and sustained the spheromak. If the helicity injection rate was reduced following formation the plasma became relatively quiescent and magnetic surfaces formed. The measured thermal diffusivity in the core was as low as ∼1 m2 s−1. However, reconnection events during buildup or sustainment of the plasma current by CHI were found to open magnetic surfaces throughout the plasma allowing rapid energy loss to the walls. As a result, experiments and simulations in SSPX found no path to simultaneous sustainment by CHI and good energy confinement. Additional physics results are also presented in this review.

The possibility of using extreme ultraviolet emission from low charge states of tungsten ions to diagnose the divertor plasmas of the ITER tokamak has been investigated. Spectral modelling of Lu-like W3+ to Gd-like W10+ has been performed by using the Flexible Atomic Code, and spectroscopic measurements have been conducted at the Sustained Spheromak Physics Experiment (SSPX) in Livermore. To simulate ITER divertor plasmas, tungsten was introduced into the SSPX spheromak by prefilling it with tungsten hexacarbonyl prior to the usual hydrogen gas injection and initiation of the plasma discharge. The tungsten emission was studied using a grazing-incidence spectrometer.

For the reconstruction of electron density profiles in the Sustained Spheromak Physics Experiment plasma, ultrashort-pulse reflectometry signals are numerically generated solving a one-dimensional wave equation by means of the central difference scheme. The signals cover an O-mode cutoff frequency range of 33–93 GHz. The lower frequencies (6–18 GHz) of a chirped waveform are up-converted to higher frequencies using four mixers. The reflected signals are down-converted to the lower frequency signals, thereby permitting band-pass filters to compute the time delays of different frequency components. A variety of density profiles are assumed to examine the performance of density profile reconstruction.