Session PO07: Magnetic Confinement: Self-Organized Configurations

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Gyrokinetic simulations of ion temperature gradient (ITG) in the scrape-off layer (SOL) of the field-reversed configuration (FRC) find that ITG saturates by self-generated zonal flows, which reduce ITG saturation amplitude, turbulence eddy size, and the ion heat flux. Zonal flows are mostly generated by nonlinear coupling of high-n modes (n is toroidal mode number) rather than modulational instability. Turbulence intensity and transport level continue to drop to very low level in the nonlinear phase since zonal flows are undamped in collisionless simulations with adiabatic electrons. Zonal flows can be damped by collision operators with pitch-angle and gyro-angle scatterings that induce ion guiding center random walk. Steady state ITG turbulence has been observed in simulations with collisions. The turbulence intensity and transport level are found to increase with higher collision frequency. Furthermore, the shear of equilibrium radial electric fields are found to reduce ITG linear growth rate, nonlinear fluctuation amplitude, and ion heat conductivity by tilting the turbulence eddies.   

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High current amplification (CA) sustained spheromaks with pressure confinement ($\beta =$ 2$\mu _{\mathrm{o}}$P/B$^{\mathrm{2}}_{\mathrm{\thinspace }}$\textgreater 0) are of interest for fusion energy applications to enable sufficiently low recirculating power fractions, high fusion power densities, and relaxed reactor engineering requirements. Driven resonant CA has been previously studied in both fully and partially relaxed force-free spheromak states (\textbf{J}\textbar \textbar \textbf{B}) using an axisymmetric, ideal MHD equilibrium model described by the Grad-Shafranov equation. In this work, this previous analysis has been extended beyond force-free states to now allow for non-zero plasma pressure gradients. An analytical treatment shows that pressure gradients can impact CA under particular profile assumptions, with the ability to enhance or suppress the expected CA relative to comparable force-free states. Computational results with varying poloidal current and pressure profiles suggest a modification of the regularization of Jensen-Chu resonances shown in previous works when calculating nonlinear force-free spheromak equilibria in which $\lambda $ $=$\textbf{ }$\mu_{\mathrm{o}}$\textbf{J}/\textbf{B }spatially varies. The results from this work suggests the persistence of driven resonant CA in sustained spheromaks with pressure confinement, adding further support for the continued research and development of these configurations for fusion energy applications.   

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The Helicity Injected Torus – Steady Inductive 3 (HIT-SI3) is a spheromak experiment that uses three AC transformer and solenoid pairs, known as helicity injectors, to form and sustain a spheromak with DC toroidal current. Changing the injector frequency and temporal phasing between injectors changes the toroidal Fourier spectrum of the applied perturbations. Biorthogonal Decomposition (BD) performed on data from a surface array of Mirnov probes reveals $n=2$ activity not associated with the spheromak or injector currents. Past work has shown differences in this activity between different injector frequencies. The NIMROD xMHD code is used to simulate HIT-SI3 in an axisymmetric domain, with the injector fields modeled as boundary conditions on $\vec{E}$ and $\vec{B}$ at the injector locations. Linear NIMROD simulations of undriven equilibria generated from experimental data are used to attempt to find a linear growth rate for this $n=2$ activity. Experimental data is also used to estimate this growth rate directly, and growth rates between frequencies will be compared. NIMROD simulations using constant, single and two-fluid temperature models at injector frequencies of 5, 15, 30, 45, 60, 75, and 100 kHz will be examined to investigate differences at low and high frequencies.   

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The presented research considers electron confinement and heating on the Steady-Inductive Helicity-Injected Torus (HIT-SI3). Specifically, the mechanisms that determine how input energy is distributed in the spheromak plasma are examined. Thomson Scattering measurements of the HIT-SI3 electron temperature and relative density are used to inform the discussion for discharges driven by steady inductive helicity injection at 15.6 kHz. These measurements are compared to simulation. They also guide the parameter choices in a 0-D energy balance model to further elucidate the confinement and heating in HIT-SI3. Results suggest that, if the heat flux is assumed to be diffusive, a Rechester-Rosenbluth stochastic field formulation for the electron thermal diffusion coefficient may be most appropriate.   

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In TAE Technologies’ current experimental device, C-2W (also called “Norman”)\footnote{H. Gota et al., Nucl. Fusion \textbf{59}, 112009 (2019).}, record breaking, advanced beam-driven field-reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams, advanced divertors, end-biasing electrodes, and an active plasma control system. Combining unmatched operating capabilities with a unique diagnostic suite\footnote{M.C. Thompson et al., Rev. Sci. Instrum. \textbf{89}, 10K114 (2018).}, the C-2W machine remains the world’s premier venue for studying fast-ion-dominated FRC plasmas. C-2W’s diagnostic suite is being further expanded to measure and understand key factors of stability and confinement. These new additions include: ChERS with neutral beam, an IR camera, upgraded bolometer systems, Hall probes, Doppler-free saturation spectroscopy, and more. The suite consists of 20 separate categories and a total of 50+ individual systems all producing data for every plasma shot. The synthesis of the data produced by these systems coupled with sophisticated analysis and advanced reconstruction techniques lead to a comprehensive understanding of C-2W plasmas and guide us toward an emerging reactor design.   

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In the C-2W Field Reversed Configuration (FRC), the radial \textbf{\textit{E}}x\textbf{\textit{B}} velocity shear has been controlled via divertor biasing, applied in the scrape-off layer mirror plasma just outside the FRC excluded flux radius via annular electrodes. Doppler Backscattering measurements show that the \textbf{\textit{E}}x\textbf{\textit{B}} flow shearing rate is comparable to the plasma-frame turbulence decorrelation rate, and reduced density fluctuations levels are observed with increased flow shear. The measured \textbf{\textit{E}}x\textbf{\textit{B}} velocity at the separatrix agrees with the impurity (oxygen IV) toroidal velocity from active Charge Exchange Recombination Spectroscopy (CHERS). Automated analysis of Doppler Backscattering data has been implemented, using GENRAY ray tracing based on Far Infrared Interferometry (FIR) density profile reconstruction. Measurements of the toroidal wavenumber spectrum confirm core FRC stability to longer wavelength ion-scale modes $k_{\mathrm{\theta }}\rho _{\mathrm{s}}\le $ 5, in agreement with previous measurements on the C-2U FRC [1], and Gyrokinetic simulations of the coupled core FRC/mirror scrape-off layer plasma. The first measurements of magnetic field fluctuations perpendicular to the confining magnetic field are presented, obtained via Cross Polarization Scattering [2]. [1] L. Schmitz et al., Nature Comm. 7 13860 (2016). [2] X.L. Zou et al., Phys. Rev. Lett. 75 1090-93 (1991).   

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In TAE Technologies’ experimental device, C-2W (also called “Norman”), record breaking, advanced beam-driven field-reversed configuration (FRC) plasmas are produced. Long-lived, hot FRCs with excluded flux radius up to 50 cm are sustained in steady state in the central confinement vessel by utilizing several advanced subsystems. These subsystems include variable energy neutral beams, advanced divertors, end bias electrodes, variable axial magnetic field and mirrors, fueling setup, and an active plasma control system. In this presentation, we discuss the effect of these external parameters on various C-2W plasma parameters. Preliminary analysis shows that plasma temperature is strongly correlated with the biasing voltage, $V_{bias}$ and hence, to the biasing power at low biasing currents, $I_{bias}$. Plasma density increases with $I_{bias}$ in a limited range. An upper limit on gas fueling required to form a hot, dense plasma is observed. Gas fueling above this limit leads to higher $I_{bias}$ and reduction in $V_{bias}$. Effect of gas fueling location will also be discussed.   

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In TAE Technologies' current experimental device, C-2W (also called ``Norman'')\footnote{H. Gota, et al. Nuclear Fusion 59, 112009 (2019)}, beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady-state using neutral beams (up to 20 MW, 15--40 keV), advanced divertors, end bias electrodes, and an active plasma control system. Particle injection throughout the discharge is necessary to maintain electron density, since titanium deposited on the walls and cryogenic surfaces adsorb incident particles. Gas injection in various locations complements fueling from neutral beam injection, which is insufficient alone. Unfortunately, neutrals from gas fueling can also be a charge-exchange target for fast-ions. DEGAS2 neutral particle modeling is used to estimate the neutral distribution from each source, followed by Monte Carlo fast-ion modeling to calculate charge-exchange losses. Results are compared to images of Balmer-$\alpha$ emission from filtered, high-speed cameras and other diagnostics. Fast ions are found to be particularly sensitive to gas injection near the midplane, while minimally affected by gas injection in the mirror throat. Other observations and further improvements to reduce fast-ion charge-exchange will also be discussed.   

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TAE Technologies' current experimental device, C-2W (also called ``Norman'')~[1], produces and sustains advanced beam-driven field reversed configuration (FRC) plasmas in steady state utilizing variable energy neutral beams (15 -- 40 keV, total power up to 20 MW), among other systems. Charge exchange collisions with neutral gas are a~substantial~loss mechanism for beam-derived fast ions. We installed an array of collimated pyroelectric bolometers to measure fast neutral charge exchange losses. The bolometers measure power losses with high time resolution and moderate spatial and pitch-angle resolution. The pyroelectric crystals, which are the active element in the bolometers, were calibrated optically on the bench top as well as in-vessel by exposure to the exhaust from the open field line plasma and comparison to an adjacent gridded ion energy analyzer. [1]~H. Gota et al., Nucl. Fusion~\textbf{59}, 112009 (2019)   

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In TAE Technologies' current experimental device, C-2W, beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams, advanced divertors, end bias electrodes, and an active plasma control system. Diagnosis of fast ions, which are born from neutral beam injection and responsible for heating, current drive, and stabilization, is critical for understanding the FRC behavior. Interpreting fast ion diagnostics in an FRC provides unique challenges, driven by the non-local nature of fast ion orbits. We present Monte Carlo methods for the forward modeling of measured fast ion signals, including the energy spectrum of charge exchange neutrals, heat flux to the wall, fast ion pressure, Doppler-shifted line emission and neutron production.~ These modeled signals are used to investigate fast ion physics topics, including fast ion transport and ion acceleration. Collaborations with Google AI have yielded high-fidelity Bayesian reconstructions of plasma mode activity, which have been used to model mode-induced fast ion transport. Theoretical and experimental evidence for thermal ion acceleration due to fast ion driven waves, as seen in C-2U, is also presented. This includes comparisons to alternative accelerating mechanisms, including collisional effects and inductive electric fields.   

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Current-vorticity MHD model has direct application to plasma control in the C-2W device~[1]. The model and 2D code possesses remarkable features: written in the state space form dx/dt$=$ f(x,t)$+$u(t) with voltage/current control input; semi-implicit time integration scheme with analytic/symbolic Jacobian and adaptive stepping; triangulation of computational domain including curving wall shape and adaptation if needed; flexible filtering technique restricting the frequency bandwidth to the bandwidth of control system interest; code is verified with 1D analytic solution and can run on coarse grid. Control system maintains macroscopic plasma parameters such as shape, position, elongation, etc. at prescribed values. The plasma model can be applied to control system design, training as well as to simulation and reconstruction of plasma parameters. Details of the model, its applications and simulations will be presented. \newline [1]~H. Gota et al., Nucl. Fusion 59, 112009 (2019).