Beam-driven Field-reversed Configuration Research Articles

Fiber Bragg grating sensor array for detecting heat flux in vacuum.

In TAE Technologies' current experimental 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, advanced divertors, edge-biasing electrodes, and an active plasma control system [Gota etal., Nucl. Fusion 61, 106039 (2021)]. A novel diagnostic has been developed by TAE Technologies to leverage an industrial fiber Bragg grating (FBG) sensor array to detect heat flux along the wall of the vacuum vessel from a plasma discharge. The system consists of an optical fiber with FBG sensors distributed along its length, housed in a pressurized steel sheath. Each FBG sensor is constructed to reflect a different wavelength, the exact value of which is sensitive to the strain and temperature at the location of the grating in the fiber. The fiber is illuminated with broadband light, and the data acquisition system analyzes the spectrum of reflected light to determine the temperature at the location of each FBG. We have installed four of these vacuum-rated FBG sensor arrays on the C-2W experiment, each with 30 individual FBG sensors spaced at 0.15m intervals along the 5m fiber, with a 100Hz acquisition rate. The measurement of temperature change due to a plasma discharge provides a single data point at each sensor location, creating a 120-point heat map of the vacuum vessel.

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.

Comprehensive imaging of C-2W plasmas: Instruments and applications.

The C-2W device ("Norman") [Gota et al., Nucl. Fusion 59, 112009 (2019)] has produced and sustained beam-driven field-reversed configuration (FRC) plasmas embedded in a magnetic mirror geometry using neutral beams and end-bias electrodes located in expander divertors. Several discrete vessels comprise this device, and many imaging instruments are required in order to view the plasma throughout. To meet this need, a suite of spatially and radiometrically calibrated, high-speed camera systems have been deployed. Besides global visualization of the plasma evolution and macro-stability, this imaging suite has been used in a variety of applications. One example application is a tomographic reconstruction of passive impurity emission. Calculation of the magnetic field in the equilibrium vessel is complicated by eddy currents in conducting structures and internal currents in the high-β FRC plasma. In addition, thus far non-perturbative measurements of internal field have not been available. The tomographic reconstruction of O4+ impurity emission enables an independent visualization of the plasma geometry, serving as a check on magnetic modeling and indirect evidence for field reversal within the FRC. A second application uses the cameras to view the Balmer-α emission throughout the plasma in order to estimate the ionization rate in each region. These rates can then be incorporated into particle balance calculations and a circuit model for currents from the end-bias electrodes. Finally, arcing on the electrode surfaces is identified through automated image processing of carefully selected spectral line emission.

The integrated diagnostic suite of the C-2W experimental field-reversed configuration device and its applications.

In the current experimental device of TAE Technologies, C-2W (also called "Norman"), record breaking advanced beam-driven field-reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams (15-40 keV, total power up to 20MW), advanced divertors, bias electrodes, and an active plasma control system. This fully operational experiment is coupled with a fully operational suite of advanced diagnostic systems. The suite consists of 60+ individual systems spanning 20 categories, including magnetic sensors, Thomson scattering, interferometry/polarimetry, spectroscopy, fast imaging, bolometry, reflectometry, charged and neutral particle analysis, fusion product detection, and electric probes. Recently, measurements of main ion temperatures via a diagnostic neutral beam, axial profiles of energy flux from an array of bolometers, and divertor and edge plasma parameters via an extensive set of electric probes, interferometers, and spectrometers have all been made available. All the diagnostics work together to provide a complete picture of the FRC, fast-ion inventory, and edge plasma details enabling tomographic reconstruction of plasma parameter profiles and real-time plasma control.

Combination Doppler backscattering/cross-polarization scattering diagnostic for the C-2W field-reversed configuration.

A versatile combination Doppler backscattering and Cross-Polarization Scattering (CPS) diagnostic for the C-2W beam-driven field-reversed configuration is described. This system is capable of measuring density fluctuations and perpendicular magnetic field fluctuations across a wide wavenumber range (2.5 ≤ k θ ρ s ≤ 50), with typical resolution Δk θ/k θ ≤ 0.4-0.8. Four tunable frequencies (26 GHz ≤ f ≤ 60 GHz corresponding to plasma cut-off densities 0.8 × 1019 ≤ n e ≤ 4.4 × 1019 m-3) are launched via quasi-optical beam combiners/polarizers and an adjustable parabolic focusing mirror selecting the beam incidence angle. GENRAY ray tracing shows that the incident O-mode and backscattered CPS X-mode beam trajectories for C-2W plasma parameters nearly overlap, allowing simultaneous detection of ñ and B̃ r or B̃ θ from essentially the same scattering volume.

Jet outflow and open field line measurements on the C-2W advanced beam-driven field-reversed configuration plasma experiment.

Accurate operation and high performance of the open field line plasma surrounding the field reversed configuration is crucial to achieving the goals of successful temperature ramp up and confinement improvement on C-2W. Knowledge and control of the open field line plasma requires extensive diagnostic efforts. A suite of diagnostics, which consists of microwave interferometry, dispersive spectroscopy, and spatial heterodyne spectroscopy, is being developed to measure electron density, ion temperature, and particle outflow velocity at various locations along the open magnetic field lines. A detailed overview of these diagnostics is presented.

Integrated diagnostic and data analysis system of the C-2W advanced beam-driven field-reversed configuration plasma experiment.

The new C-2W experiment (also called Norman) at TAE Technologies, Inc. studies the evolution of field-reversed configuration (FRC) plasmas sustained by neutral beam injection. Data on the FRC plasma performance are provided by a comprehensive suite of diagnostics that includes over 700 magnetic sensors, four interferometer systems, multi-chord far-infrared polarimetry, two Thomson scattering systems, ten types of spectroscopic measurements, multiple fast imaging cameras with selectable atomic line filters, bolometry, reflectometry, neutral particle analyzers, and fusion product detectors. Most of these diagnostic systems are newly built using experience and data from the preceding C-2U experiment to guide the design process. A variety of commercial and custom acquisition electronics collect over 4000 raw signals from the C-2W diagnostics. These data are processed into physics results using a large-scale database of diagnostics metadata and analysis software, both built using open-source software tools.

Calibration and applications of visible imaging cameras on the C-2U advanced beam-driven field-reversed configuration device.

Two filtered, fast-imaging instruments, with radial and axial views, respectively, were used on the C-2U device to visualize line emission from impurities and hydrogenic neutrals. Novel calibration techniques needed to be developed for these instruments because the accelerated pace of C-2U operations precluded access to the interior of the vacuum vessel, targets used in typical calibration methods were not available, and in order to account for effects which have not been sufficiently addressed in the literature. Spatial calibration involved optimizing parameters in a generic camera model: ex situ using a checkerboard target and in situ using the vacuum vessel port geometry. Radiometric calibration was performed ex situ in three stages. First, the camera relative response function was mapped using an algorithm developed for high dynamic-range imaging. Second, the non-uniformity of the optical system was measured using a large LCD monitor with a characterized angular emission pattern. Finally, the absolute photon efficiency of each interference filter was determined using a calibrated uniform radiance source while also accounting for reduction in the filter transmission for off-normal rays. Periodically during the run campaign, line emission from neutral beams fired into a gas target was used as an in situ reference to check for degradation of viewport transmission. One application using calibrated camera data was tomographic reconstruction of passive impurity emission, which provided a sanity check to the excluded-flux radius inferred from wall-mounted magnetic sensors.

Fast-ion D-alpha diagnostic development for the C-2W field-reversed configuration plasma.

TAE Technologies's advanced beam-driven field-reversed configuration device has a large fast-ion population, allowing for fast-ion D-alpha (FIDA) studies. Development of a FIDA spectrometer for the new C-2W device is underway. Previous measurements were combined with C-2W geometry to inform the design [N. Bolte, Rev. Sci. Instrum. 87, 11E520 (2016)]. Measured signal levels led to the purchase of a Phantom Miro 110 high-speed camera that will be paired with a Holospec f/1.8 spectrograph from Kaiser Optical Systems, Inc. The spectrograph utilizes a custom transmission grating centered at 656.0 nm. Simulations were used to choose available ports with large predicted signals. Eight neutral beams and 354 ports were considered. Experimentally obtained 1D plasma profiles from C-2U were mapped onto Q2D [M. Onofri, Phys. Plasmas 24, 092518 (2017)] simulation flux surfaces. For each point on the vessel wall, many lines-of-sight (LOSs) are created to view the entirety of each neutral beam path. FIDA spectra are simulated for each LOS using the FIDA simulation code FIDASIM [http://d3denergetic.github.io/FIDASIM/; W. Heidbrink, Commun. Comput. Phys. 10, 716 (2011); and B. Geiger, "Fast-ion transport studies using FIDA spectroscopy at the ASDEX Upgrade tokamak," Ph.D. thesis, Ludwig Maximilian University of Munich, 2012]. Integrating over wavelength and beam-space allows individual ports to be chosen for their large prospective signals.

Modeling feedback control of unstable separatrix location in beam-driven field-reversed configurations

We present a linear, one-parameter model for rigid displacement of a toroidally symmetric plasma. When the feedback control is feasible, plasma inertia can be neglected, and the instability growth rate is proportional to wall resistivity. We benchmark the linear model against non-linear, hybrid simulations of an axially unstable, beam-driven field-reversed configuration to fix the free parameter of the model. The resulting parameter-free model is validated using linear and non-linear closed-loop simulations with active feedback control by voltage-controlled coils. In closed loop simulations, the predictions of the parameter-free linear model agree satisfactory with the non-linear results. Implications for the feedback control of the positional instability in experiments are discussed. The presented model has been used to guide the design of the feedback control hardware in the C-2W experiment.

Improved density profile measurements in the C-2U advanced beam-driven Field-Reversed Configuration (FRC) plasmas.

In the prior C-2 experiment, electron density was measured using a two-color 6-chord CO2/HeNe interferometer. Analysis shows that high-frequency common mode phase noise can be reduced by a factor of 3 by constructing a reference chord. In the system upgrade from C-2 to C-2U a 4-chord far-infrared laser interferometer was developed, which demonstrated superior sensitivity (1 × 1016 m-2 at >1 MHz bandwidth) and solved the under spatial sampling issue of the C-2 interferometer system. Improved density-profile measurement results are presented in this paper, including evidence of fast-ion modified density profile and stabilization of the n = 1 plasma wobble mode.

Jet outflow and open field line measurements on the C-2U advanced beam-driven field-reversed configuration plasma experiment.

Knowledge and control of the axial outflow of plasma particles and energy along open-magnetic-field lines are of crucial importance to the stability and longevity of the advanced beam-driven field-reversed configuration plasma. An overview of the diagnostic methods used to perform measurements on the open field line plasma on C-2U is presented, including passive Doppler impurity spectroscopy, microwave interferometry, and triple Langmuir probe measurements. Results of these measurements provide the jet ion temperature and axial velocity, electron density, and high frequency density fluctuations.

First fast-ion D-alpha (FIDA) measurements and simulations on C-2U.

The first measurements of fast-ion D-alpha (FIDA) radiation have been acquired on C-2U, Tri Alpha Energy's advanced, beam-driven field-reversed configuration (FRC). These measurements are also forward modeled by FIDASIM. This is the first measurement and simulation of FIDA carried out on an FRC topology. FIDA measurements are made of Doppler-shifted Balmer-alpha light from neutralized fast ions using a bandpass filter and photomultiplier tube. One adjustable line-of-sight measured signals at eight locations and eight times during the FRC lifetime over 26 discharges. Filtered signals include only the highest energy ions (>6 keV) and share some salient features with the FIDASIM result. Highly Doppler-shifted beam radiation is also measured with a high-speed camera and is spatially well-correlated with FIDASIM.

Fast imaging diagnostics on the C-2U advanced beam-driven field-reversed configuration device.

The C-2U device employed neutral beam injection, end-biasing, and various particle fueling techniques to sustain a Field-Reversed Configuration (FRC) plasma. As part of the diagnostic suite, two fast imaging instruments with radial and nearly axial plasma views were developed using a common camera platform. To achieve the necessary viewing geometry, imaging lenses were mounted behind re-entrant viewports attached to welded bellows. During gettering, the vacuum optics were retracted and isolated behind a gate valve permitting their removal if cleaning was necessary. The axial view incorporated a stainless-steel mirror in a protective cap assembly attached to the vacuum-side of the viewport. For each system, a custom lens-based, high-throughput optical periscope was designed to relay the plasma image about half a meter to a high-speed camera. Each instrument also contained a remote-controlled filter wheel, set between shots to isolate a particular hydrogen or impurity emission line. The design of the camera platform, imaging performance, and sample data for each view is presented.

Dual wavelength imaging of a scrape-off layer in an advanced beam-driven field-reversed configuration.

A dual wavelength imaging system has been developed and installed on C-2U to capture 2D images of a He jet in the Scrape-Off Layer (SOL) of an advanced beam-driven Field-Reversed Configuration (FRC) plasma. The system was designed to optically split two identical images and pass them through 1 nm FWHM filters. Dual wavelength images are focused adjacent on a large format CCD chip and recorded simultaneously with a time resolution down to 10 μs using a gated micro-channel plate. The relatively compact optical system images a 10 cm plasma region with a spatial resolution of 0.2 cm and can be used in a harsh environment with high electro-magnetic noise and high magnetic field. The dual wavelength imaging system provides 2D images of either electron density or temperature by observing spectral line pairs emitted by He jet atoms in the SOL. A large field of view, combined with good space and time resolution of the imaging system, allows visualization of macro-flows in the SOL. First 2D images of the electron density and temperature observed in the SOL of the C-2U FRC are presented.

Enhanced magnetic field probe array for improved excluded flux calculations on the C-2U advanced beam-driven field-reversed configuration plasma experiment.

External flux conserving coils were installed onto the exterior of the C-2U [M. W. Binderbauer et al., Phys. Plasmas 22, 056110 (2015)] confinement vessel to increase the flux confinement time of the system. The 0.5 in. stainless steel vessel wall has a skin time of ∼5 ms. The addition of the external copper coils effectively increases this time to ∼7 ms. This led to better-confined/longer-lived field-reversed configuration (FRC) plasmas. The fringing fields generated by the external coils have the side effect of rendering external field measurements invalid. Such measurements were key to the previous method of excluded flux calculation [M. C. Thompson et al., Rev. Sci. Instrum. 83, 10D709 (2012)]. A new array of B-dot probes and Rogowski coils were installed to better determine the amount of flux leaked out of the system and ultimately provide a more robust measurement of plasma parameters related to pressure balance including the excluded flux radius. The B-dot probes are surface mountable chip inductors with inductance of 33 μH capable of measuring the DC magnetic field and transient field, due to resistive current decay in the wall/coils, when coupled with active integrators. The Rogowski coils measure the total change in current in each external coil (150 A/2 ms). Currents were also actively driven in the external coils. This renders the assumption of total flux conservation invalid which further complicates the analysis process. The ultimate solution to these issues and the record breaking resultant FRC lifetimes will be presented.