Field-reversed Configuration Plasma Research Articles

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.

High sensitivity far infrared laser diagnostics for the C-2U advanced beam-driven field-reversed configuration plasmas.

A high sensitivity multi-channel far infrared laser diagnostics with switchable interferometry and polarimetry operation modes for the advanced neutral beam-driven C-2U field-reversed configuration (FRC) plasmas is described. The interferometer achieved superior resolution of 1 × 1016 m-2 at >1.5 MHz bandwidth, illustrated by measurement of small amplitude high frequency fluctuations. The polarimetry achieved 0.04° instrument resolution and 0.1° actual resolution in the challenging high density gradient environment with >0.5 MHz bandwidth, making it suitable for weak internal magnetic field measurements in the C-2U plasmas, where the maximum Faraday rotation angle is less than 1°. The polarimetry resolution data is analyzed, and high resolution Faraday rotation data in C-2U is presented together with direct evidences of field reversal in FRC magnetic structure obtained for the first time by a non-perturbative method.

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.

Hanle effect as a magnetic diagnostic for field-reversed configuration plasmas.

Hanle effect is presented as a low magnetic-field diagnostic for field-reversed configuration (FRC) plasmas. The non-perturbative technique is capable of measuring not only magnetic-field profile and direction but also field-null position and its shape. Conditions and configurations for the measurement are discussed. The technique is applicable to other low magnetic-field laboratory plasmas, e.g., magnetic-cusps, where measurements of low field are desirable, and it may also be extended to measure the two-dimensional vector magnetic-field.

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.

Absolute calibration of neutron detectors on the C-2U advanced beam-driven FRC.

In the C-2U fusion energy experiment, high power neutral beam injection creates a large fast ion population that sustains a field-reversed configuration (FRC) plasma. The diagnosis of the fast ion pressure in these high-performance plasmas is therefore critical, and the measurement of the flux of neutrons from the deuterium-deuterium (D-D) fusion reaction is well suited to the task. Here we describe the absolute, in situ calibration of scintillation neutron detectors via two independent methods: firing deuterium beams into a high density gas target and calibration with a 2 × 107 n/s AmBe source. The practical issues of each method are discussed and the resulting calibration factors are shown to be in good agreement. Finally, the calibration factor is applied to C-2U experimental data where the measured neutron rate is found to exceed the classical expectation.

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.

Characterization of compact-toroid injection during formation, translation, and field penetration.

We have developed a compact toroid (CT) injector system for particle refueling of the advanced beam-driven C-2U field-reversed configuration (FRC) plasma. The CT injector is a magnetized coaxial plasma gun (MCPG), and the produced CT must cross the perpendicular magnetic field surrounding the FRC for the refueling of C-2U. To simulate this environment, an experimental test stand has been constructed. A transverse magnetic field of ∼1 kG is established, which is comparable to the C-2U axial magnetic field in the confinement section, and CTs are fired across it. On the test stand we have been characterizing and studying CT formation, ejection/translation from the MCPG, and penetration into transverse magnetic fields.

A mass resolved, high resolution neutral particle analyzer for C-2U.

C-2U is a high-confinement, advanced beam driven field-reversed configuration plasma experiment which sustains the configuration for >5 ms, in excess of typical MHD and fast particle instability times, as well as fast particle slowing down times. Fast particle dynamics are critical to C-2U performance and several diagnostics have been deployed to characterize the fast particle population, including neutron and proton detectors. To increase our understanding of fast particle behavior and supplement existing diagnostics, an E ∥ B neutral particle analyzer was installed, which simultaneously measures H0 and D0 flux with large dynamic range and high energy resolution. Here we report the commissioning of the E ∥ B analyzer, confirm the instrument has energy resolution ΔE/E≲0.1 and a dynamic range Emax/Emin∼30, and present measurements of initial testing on C-2U.

Transport studies in high-performance field reversed configuration plasmas

A significant improvement of field reversed configuration (FRC) lifetime and plasma confinement times in the C-2 plasma, called High Performance FRC regime, has been observed with neutral beam injection (NBI), improved edge stability, and better wall conditioning [Binderbauer et al., Phys. Plasmas 22, 056110 (2015)]. A Quasi-1D (Q1D) fluid transport code has been developed and employed to carry out transport analysis of such C-2 plasma conditions. The Q1D code is coupled to a Monte-Carlo code to incorporate the effect of fast ions, due to NBI, on the background FRC plasma. Numerically, the Q1D transport behavior with enhanced transport coefficients (but with otherwise classical parametric dependencies) such as 5 times classical resistive diffusion, classical thermal ion conductivity, 20 times classical electron thermal conductivity, and classical fast ion behavior fit with the experimentally measured time evolution of the excluded flux radius, line-integrated density, and electron/ion temperature. The numerical study shows near sustainment of poloidal flux for nearly 1 ms in the presence of NBI.

Numerical solutions of Grad-Shafranov equation in a field-reversed configuration

The solution of Grad-Shafranov equation in field-reversed configuration (FRC) is a basic problem. The solution of Grad-Shafranov equation can help to understand most of physical processes in FRC plasma, such as magnetohydrodynamic (MHD) instabilities and plasma transport. In the present paper, based on the FRC asymptotic theory by Barnes D C, the code for solving the two-dimensional Grad-Shafranov equation in FRC is developed. By using the code, the equilibriums of FRC with different elongations and separatrix radii are investigated in the present paper. The one-dimensional numerical results show that the plasma density gradient increases linearly with magnetic flux increasing in the FRC center, while, it steepens due to the high magnetic field distribution at the separatrix. The results also show that the plasma density in the closed field region increases with the density at the separatrix increasing, which implies that FRC embodies the strong confinement ability. It is a key problem to choose equations determining the shape of the separatrix in a two-dimensional numerical investigation. In the present paper, the shape equation is described as rs = rs max (1 - z2a), in which a is the shaping parameter. When a=1, the separatrix shape is elliptical, and when a1, the separatrix shape is like a racetrack. The geometry character of the separatrix appears in the one-order equations (in one-order equations: (0)/(z) = (0)/(rs)(rs)/(z), where (0)/(rs) is determined by lead equations and (rs)/(z) is given by separatrix equation). The two-dimensional numerical results show that O-point moves outward as the sparatrix radius increases. The curvature radius of magnetic flux surface increases with the separatrix radius increasing. The O-point of magnetic flux surface is just at the curvature center. Thus O-point moves outward as the sparatrix radius increases.

Improved Confinement of C-2 Field-Reversed Configuration Plasmas

C-2 is a unique, large compact-toroid (CT) device at Tri Alpha Energy that produces field-reversed configuration (FRC) plasmas by colliding and merging oppositely directed CTs. Significant progress has recently been made on C-2, achieving ~5 ms stable plasmas with a dramatic improvement in confinement, far beyond the prediction from the conventional FRC scaling. This stable, long-lived FRC plasma state is called the high-performance FRC (HPF) regime. The key approaches to achieve the HPF regime are as follows: (i) dynamic FRC formation by collision/merging of super-Alfvénic CTs, (ii) effective control of stability and transport by end-on plasma guns and neutral-beam (NB) injection, and (iii) active wall conditioning using titanium and lithium gettering systems. Moreover, further improvement in FRC confinement has been obtained with improved open-field-line plasma properties such as a lower fluctuation level, reduced transport rates in radial/axial directions, and lower background neutral density as well as recycling. This open-field-line plasma improvement, mainly obtained by higher magnetic fields in the formation and mirror-plug sections, allows for better NB coupling to the core-FRC plasma. In the recent HPF regime there is a sufficiently large fast-ion population that appears to improve FRC confinement properties as well as stability; the FRC particle and global energy confinement times both increased by ~30% and ~80%, respectively, compared to that of the previously obtained HPF regime.

Computed Multiple Tomography for Translated Field Reversed Configuration Plasma

A computed multiple tomography system for the investigation of translated field reversed configuration (FRC) plasmas was established. With this system, we have found that translated FRC plasmas were categorized into three types.

Fusion proton diagnostic for the C-2 field reversed configuration

Measurements of the flux of fusion products from high temperature plasmas provide valuable insights into the ion energy distribution, as the fusion reaction rate is a very sensitive function of ion energy. In C-2, where field reversed configuration plasmas are formed by the collision of two compact toroids and partially sustained by high power neutral beam injection [M. Binderbauer et al., Phys. Rev. Lett. 105, 045003 (2010); M. Tuszewski et al., Phys. Rev. Lett. 108, 255008 (2012)], measurements of DD fusion neutron flux are used to diagnose ion temperature and study fast ion confinement and dynamics. In this paper, we will describe the development of a new 3 MeV proton detector that will complement existing neutron detectors. The detector is a large area (50 cm(2)), partially depleted, ion implanted silicon diode operated in a pulse counting regime. While the scintillator-based neutron detectors allow for high time resolution measurements (∼100 kHz), they have no spatial or energy resolution. The proton detector will provide 10 cm spatial resolution, allowing us to determine if the axial distribution of fast ions is consistent with classical fast ion theory or whether anomalous scattering mechanisms are active. We will describe in detail the diagnostic design and present initial data from a neutral beam test chamber.

Overview of C-2 field-reversed configuration experiment plasma diagnostics.

A comprehensive diagnostic suite for field-reversed configuration (FRC) plasmas has been developed and installed on the C-2 device at Tri Alpha Energy to investigate the dynamics of FRC formation as well as to understand key FRC physics properties, e.g., confinement and stability, throughout a discharge. C-2 is a unique, large compact-toroid merging device that produces FRC plasmas partially sustained for up to ∼5 ms by neutral-beam (NB) injection and end-on plasma-guns for stability control. Fundamental C-2 FRC properties are diagnosed by magnetics, interferometry, Thomson scattering, spectroscopy, bolometry, reflectometry, and NB-related fast-ion/neutral diagnostics. These diagnostics (totaling >50 systems) are essential to support the primary goal of developing a deep understanding of NB-driven FRCs.

Design of a fully-fiber multi-chord interferometer and a new phase-shift demodulation method for field-reversed configuration.

A 633 nm laser interferometer has been designed based on a novel concept, which, without the acousto-optic modulator or the demodulator circuit, adopts the fibers to connect all elements except photodetectors and oscilloscope in this system to make it more compact, portable, and efficient. The noteworthy feature is to mathematically compare the two divided interference signals, which have the same phase-shift caused by the electron density but possess the different initial phase and low angular frequencies. It is possible to read the plasma density directly on the oscilloscope by our original mathematic demodulation method without a camera. Based on the Abel inversion algorithm, the radial electron density profiles versus time can be obtained by using the multi-chord system. The designed measurable phase shift ranges from 0 to 2π rad corresponding to the maximum line integral of electron density less than 3.5 × 10(17) cm(-2), and the phase accuracy is about 0.017 rad corresponding to the line integral of electron density accuracy of 1 × 10(15) cm(-2). After the construction of eight-chord interferometer, it will provide the detailed time resolved information of the spatial distribution of the electron density in the field-reversed configuration (FRC) plasma target produced by the "Yingguang-1" programmed-discharge device, which is being constructed in the Key Laboratory of Pulsed Power, China Academy of Engineering Physics.

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

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

Mitigation of rotational instability of high-beta field-reversed configuration by double-sided magnetized plasmoid injection

Active control of destructive rotational instability in a high-beta field-reversed configuration (FRC) plasma was demonstrated by using double-sided plasmoid injection technique. The elliptical deformation of the FRC's cross section was mitigated as a result of substantial suppression of spontaneous spin-up by the plasmoid injection. It was found that the injected plasmoid provided better stability against the rotational mode, suggesting that the compensation of the FRC's decaying magnetic flux might help to suppress its spin-up.

Ball Lightning Events Explained as Self-Stable Spinning High-Density Plasma Toroids or Atmospheric Spheromaks

Spinning plasma toroids, or spinning spheromaks, are reported as forming in partial atmosphere during high-power electric arc experiments. They are a new class of spheromaks because they are observed to be stable in partial atmosphere with no confining external toroidal magnetic fields, and are observed to endure for more than 600 ms. Included in this paper is a model that explains these stable plasma toroids (spheromaks); they are hollow plasma toroids with a thin outer shell of electrons and ions that all travel in parallel paths orthogonal to the toroid circumference - in effect, spiraling around the toroid. These toroids include sufficient ions to neutralize the space charge of the electrons. This model leads to the name Electron Spiral Toroid Spheromak (ESTS). The discovery of this new class of spheromaks resulted from work to explain ball lightning. A comparison is made between the experimental observations of spheromaks in partial atmosphere and reported ball lightning observations; strong similarities are reported. The ESTS is also found to have a high ion density of ~ 1019 ions/cm3 without needing any external toroidal magnetic field for containment, compared, for example, to tokamaks, with ion density limits of ~ 1015 ions/cm3. This high ion density is a defining characteristic and opens the potential to be useful in applications. The ESTS is a field reversed configuration plasma toroid.