Field-reversed Configuration Research Articles

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.

Theoretical Study of Relation between Anomalous Resistivity and Toroidal Spin-Up of Field-Reversed Configurations

Theoretical Study of Relation between Anomalous Resistivity and Toroidal Spin-Up of Field-Reversed Configurations

Radial Compression of a Compact Toroid Caused by Induction of a Paramagnetic Field

Partially ionized and weakly magnetized plasma (typical for MHD generators) flows along the outer spherical chamber, and is placed around the inner chamber where an field reversed configuration (FRC) is injected. Inside the outer chamber, the azimuthal Er × B drift induces a paramagnetic field Bp, with an intensity of tens of Teslas. The intensity of the Bp field is controlled by the inwardly directed radial electric field Er. Inside the inner chamber the Bp field becomes anti-parallel to the external magnetic field Bem. After establishing the magnetic mirror configuration of magnetic field intensity Bp ~ 20T (in the mid-plane), the FRC (target plasma) is injected into the magnetic mirror with the help of a magnetic wave generator. Inside the magnetic mirror (inner chamber), the rotating magnetic field (RMF) induces the azimuthal current jω inside the FRC. This current gives the magnetic field Bj an intensity of dozens of Teslas. This field is antiparallel to the Bp field. Interaction between magnetic fields, Bp and Bj, causes radial compression of the injected FRC. As a result of the magnetic compression, the product of density and the energy confinement time amounts to 1.72 × 1019 s/m3, which is close to the level expected for the working reactor (~1020 s/m3). Detailed analyses reveal that the compressed plasma (compact toroid) is very stable, the kinetic stability condition is fulfilled (S*/e≅0.28), and the ratio α is very low: (~8.6×10-2). This makes the most destructive rotational modes, n=1 and n=2, harmless.

Loss-cone instabilities for compact fusion reactor and field-reversed configuration

Loss-cone instabilities are studied for linear fusion devices. The gyro-kinetic equation for such a configuration is rigorously constructed in terms of action-angle variables by making use of canonical transformation. The dispersion relation, including for the first time, finite bounce frequency is obtained and numerically solved. The loss-cone modes are found near ion-cyclotron frequency. The growth rates are greatly reduced and approaching zero with increasing beta value. The results suggest that loss-cone instabilities are unlikely to be threatening to linear fusion devices since a new longitudinal invariant is found and gives a constraint which helps confinement.

First experimental measurements of a new fast ion driven micro-burst instability in a field-reversed configuration plasma

In modern field-reversed configuration (FRC) experiments (Binderbauer et al 2015 Phys. Plasmas 22 056110) at TAE Technologies, classical FRC instabilities are suppressed by advanced neutral beam injection and edge biasing methods, leading to high plasma confinement and fast ion pressure built-up which is comparable to the bulk plasma pressure. In some of these high performance FRC plasmas, a new macroscopically non-destructive fast ion driven micro-burst instability is observed as periodic small amplitude bursts with frequency down chirping in the diamagnetic drift frequency range, repeating about every 0.1 to 0.5 ms. The occurrence of these micro-bursts and burst-free operation can be controlled by changing the injected neutral beam energy. Major observed characteristics of this new instability are presented. Possible explanation of the phenomenon is suggested.

Formation of field-reversed configuration using an in-vessel odd-parity rotating magnetic field antenna in a linear device.

A Field-Reversed Configuration (FRC) is formed by an in-vessel odd-parity rotating magnetic field (RMF) antenna in a tandem mirror device, Keda mirror with axisymmetricity. The 40-cm diameter antenna is fed independently by four IGBT-based power units with an output current of 1500 A each at 84 kHz, and their phases are adjustable to launch odd or even parity RMFs. A medium-sized washer gun is utilized to generate a highly ionized seed hydrogen plasma. Driven by RMF, the resultant FRC is formed with a separatrix radius of ∼17 cm, external field of ∼50 G, and trapped poloidal flux of ∼0.15 mWb. The formation process of FRCs is evidenced by the measurement of an array of internal two-dimensional probes; a comparison with the rigid rotor model is presented in this paper. In addition, substantial toroidal electron current is found to be driven, despite the partial RMF penetration. Moreover, the dependence of the driven current on the antenna current is reported and is found to be consistent with the RMF current driving model.

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.

First time-resolved electron density measurements in the C-2W advanced field-reversed configuration plasmas from long-path compact second-harmonic interferometer

Characterization of the plasma structure and density is critical for the diagnosis and control of C-2W plasma equilibria. To this end, two compact, highly portable, turnkey second harmonic interferometers are used to make measurements with greater flexibility than available from other diagnostics, providing important information in areas otherwise inaccessible to more complicated systems. The systems are based on a fiber-coupled 1064 nm Nd:YAG laser and provide a sensitivity of a few 1018 m-2 with a time resolution of a few microseconds. System upgrades were made to allow for beam paths in excess of 5 m. Initial data from two system configurations are presented, showing plasma translation and merged equilibria.

Thomson scattering systems on C-2W field-reversed configuration plasma experiment

TAE Technologies' newly constructed C-2W experiment aims to improve the ion and electron temperatures in a sustained field-reversed configuration plasma. A suite of Thomson scattering systems has been designed and constructed for electron temperature and density profile measurements. The systems are designed for electron densities of 1 × 1012 cm-3 to 2 × 1014 cm-3 and temperature ranges from 10 eV to 2 keV. The central system will provide profile measurements of Te and ne at 16 radial locations from r = -9 cm to r = 64 cm with a temporal resolution of 20 kHz for 4 pulses or 1 kHz for 30 pulses. The jet system will provide profile measurements of Te and ne at 5 radial locations in the open field region from r = -5 cm to r = 15 cm with a temporal resolution of 100 Hz. The central system and its components have been characterized, calibrated, installed, and commissioned. A maximum-likelihood algorithm has been applied for data processing and analysis.

Secondary electron emission detectors for neutral beam characterization on C-2W.

Heating, current drive, and partial fueling from neutral beam injection are essential to sustainment of C-2W field-reversed configuration plasmas. C-2W has eight 2.1 MW neutral beams (16.8 MW of total electrical power), capable of providing a beam of 15 keV hydrogen neutrals for 30 ms. To maximize the effectiveness of neutral beam injection, duct losses must be minimized by maintaining beam alignment and optimizing beam current for minimum divergence. Each beam terminates on a vertical and horizontal array of secondary electron emission detectors (nine in the vertical, seven in the horizontal, and sharing one in the middle). The molybdenum detectors are spatially separated to characterize the beam size and alignment. With knowledge of the geometry of the vacuum ducts and horizontal and vertical beam profiles from test stand measurements, the focal length, divergence, and power loss were calculated. Through characterization, the set of neutral beams are optimized to inject up to 12 MW of power into the confinement vessel throughout the plasma discharge.

Characterization and calibration of the Thomson scattering diagnostic suite for the C-2W field-reversed configuration experiment.

The new C-2W Thomson scattering (TS) diagnostic consists of two individual subsystems for monitoring electron temperature (Te) and density (ne): one system in the central region is currently operational, and the second system is being commissioned to monitor the open field line region. Validating the performance of the TS's custom designed system components and unique calibration of the detection system and diagnostic as a whole is crucial to obtaining high precision Te and ne profiles of C-2W's plasma. The major components include a diode-pumped Nd:YAG laser which produces 35 pulses at up to 20 kHz, uniquely designed collection lenses with a fast numerical aperture, and uniquely designed polychromators with filters sets to optimize a Te ranging from 10 eV to 2 keV. This paper describes the design principles and techniques used to characterize the main components of the TS diagnostic on C-2W, as well as the results of Rayleigh scattering calibrations performed for the whole system response.

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.

Development of a Z eff diagnostic using visible and near-infrared bremsstrahlung light for the C-2W field-reversed configuration plasma.

In C-2W, an elevated impurity concentration can lead to significant degradation of plasma performance and energy losses through radiation. To gauge plasma contamination from impurities, the effective ion charge (Z eff) can be determined from measurements of bremsstrahlung continuum radiation over a small spectral range free from line radiation. To this end, a diagnostic system including visible and near-infrared bremsstrahlung detectors was deployed in C-2W to measure time-dependent radial distributions of Z eff. The system is complemented by an array of survey spectrometers which enable full-range spectroscopic measurements of impurity emission lines from the vacuum ultraviolet to the near infrared, providing a good picture of the plasma composition. Here, the design scheme for this integrated diagnostic system is presented and discussed.

Application of a Hall sensor for pulsed magnetic field measurement in the FAT-CM FRC experiments.

Collisional merging experiments of a field-reversed configuration (FRC) plasma at the super-Alfvénic velocity have been conducted in the FAT (FRC Amplification via Translation)-CM (Collisional Merging) device. In the experiments, two FRCs are collided and merged in a confinement section with a quasi-static confinement magnetic field. Therefore, it is necessary to measure the high-frequency pulsed magnetic field superposed on a quasi-stationary signal. The magnetic field is generally measured by a magnetic coil probe in the pulse discharge experiments; however, in such measurements, errors arise in the low-frequency band in the conducted FRC experiments. Therefore, a Hall sensor has been applied for low-frequency magnetic field measurements in the FAT-CM experiments. Calibration of the Hall sensor involves confirming that the sensor has a sufficient response speed and linear characteristics for the magnetic field with a rising time of approximately 240 µs and that its output voltage does not saturate up to a magnetic field of 0.7 T. Combination of the Hall sensor and the magnetic coil probe ensures a comprehensive measurement of the magnetic field in the range of FAT-CM experiments. In this study, accurate magnetic measurements were performed in a collisional merging experiment in the FAT-CM device by using a combined magnetic diagnostic system.

A combined millimeter wave and CO2 interferometer on the C-2W Jet plasma.

A two wavelength tangentially viewing multi-chord interferometer has been built for the Jet plasma of the C-2W experiment at TAE Technologies. A novel 1 mm wavelength interferometer has been developed to be used simultaneously with a CO2 laser interferometer to provide full coverage of the Jet plasma and the translating field-reversed configuration (FRC) plasma before merging. With CO2 and millimeter wave sources, the interferometer proposes to cover a combined dynamic range of line integrated density of more than 1000 although the CO2 interferometer sub-system is not yet operational. Sited at the axial location of the mirror field of C-2W, the interferometer will play a pivotal role in assessing the FRC before merging and the operation of the inner and outer divertors and particle outflow. The performance of the millimeter wave interferometer and recent measurements is discussed.

Development of a three-wave far-infrared laser interferometry and polarimetry diagnostic system for the C-2W field-reversed configuration plasmas.

Great advancements in modern field-reversed configuration (FRC) experiments motivated the development of a 14-chord three-wave far infrared (FIR) laser interferometry and polarimetry diagnostic system, which can provide simultaneous high temporal resolution measurements of density and Faraday rotation profiles with high accuracy. The unique challenges facing FIR diagnostics in high beta FRC plasmas are the extremely small (<0.5°) Faraday rotation angles, and severe laser beam refraction effects due to high density gradient and choice of long wavelength. The diagnostic system design and development are described with methods to overcome the challenges, and initial experimental data are also presented.

Internal magnetic field measurements of translated and merged field-reversed configuration plasmas in the FAT-CM device.

Field-reversed configuration (FRC) Amplification via Translation-Collisional Merging (FAT-CM) experiments have recently commenced to study physics phenomena of colliding and merged FRC plasma states. Two independently formed FRCs are translated into the confinement region of the FAT-CM device, collided near the mid-plane of the device with a relative speed of up to ∼400 km/s, and a final merged FRC plasma state is achieved. To measure internal magnetic field profiles of the translated and merged FRC plasmas as well as to understand its collisional-merging process, an internal magnetic probe array, developed by TAE Technologies, has been installed in the mid-plane of the FAT-CM device. Initial magnetic field measurements indicate that both the translated and the merged FRC plasma states exhibit a clear field-reversed structure, which is qualitatively in good agreement with 2D MHD simulation. It is found and verified that a sufficient mirror field in the confinement region is required for colliding FRCs to be fully merged into a single FRC plasma state.

Design of a custom insertable probe platform for measurements of C-2W inner divertor plasma parameters.

A custom motor controlled probe system has been designed to make spatially resolved measurements of temperature, density, flow, and plasma potential in the C-2W inner divertors. Measurements in the inner divertors, which have a 1.7 m radius and are located on either end of the confinement vessel, are critical in order to gauge exactly how local settings affect the plasma conditions, confinement, and stability in the field-reversed configuration core. The inner Divertor Insertable Probe Platform (iDIPP) system consists of a custom motor controlled linear rack and pinion transporter that has a 1.9 m travel length in order to reach the center of the divertor. Mounted to the end of the transporter is a 1 m long segmented probe shaft made of individually floating stainless steel rings to prevent shorting out the electrode plates, which are biased up to 5 kV/m. A variety of interchangeable probe tips, including a triple Langmuir probe, a baffled probe, and a Gundestrup probe, can plug into the end of the probe shaft. Custom UHV coiled cabling comprised of 9 shielded conductors expands/retracts with the motion of the transporter in/out of the divertor. The physics motivating plasma parameter measurements in the inner divertors and the details of the design of the iDIPP system will be discussed.

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.