Session UP10: Poster Session VIII: Basic Plasma: Turbulence and Transport, Magnetic Fusion: RF Heating and Current Drive, Sci-DAC 4, Tri-Alpha. Inertial Confinement Fusion: Fast Ignition, Analytical and Computational Techniques, Laser-Plasma Instabilities, Hohlraum and X-Ray cavity Physics, Compression and Burn, Hydrodynamic Instability (2:00pm-5:00pm)

Delayed Onset of Heat Flux by Resonance in Three-Wave Energy Transfer

A saturation theory for toroidal ITG turbulence based on zonal-flow-catalyzed transfer to stable modes successfully recovers scalings of the heat flux with the zonal flow damping rate and plasma beta observed in gyrokinetic simulations. Here the theory is extended to include the physics of the instability threshold in temperature gradient by retaining the appropriate magnetic drift effects in the fluid model. The theory has a quasilinear factor with a flux threshold at the linear value. However, a factor proportional to the inverse triplet correlation time makes the flux very small above this threshold when nonlinear energy transfer is nearly resonant. After a higher threshold in temperature gradient the flux begins to increase at a rate proportional to the gradient. Both features are qualitatively consistent with recent gyrokinetic observations, which show a smooth upturn in flux at the nonlinear threshold and no indication of bifurcation or tertiary instability. The separation of linear and nonlinear thresholds (Dimits shift) is governed by resonance broadening effects. When these arise from finite Larmor radius the shift is small, but it increases to realistic values if the resonance is broadened by nonlinear (eddy damping) effects. Supported by USDOE.   

Analysis of Saturation and Predator-Prey Behavior in ITG Turbulence

Two requirements for realistic modeling of limit cycle oscillations involving ITG turbulence and zonal flows are the inclusion of large-scale stable modes, which are critical for saturation and its scalings, and the energy conserving coupling that links the instability with stable modes through the zonal flow. Models that satisfy these criteria involve wavenumber truncations in the eigenmode decomposition, the simplest of which is a three-wavenumber truncation. We examine truncations that preserve coupling topology between the turbulence and zonal flows, which respectively occupy 2D and 1D spectral domains, showing that this consideration affects the amplitude ratio of turbulence and zonal flows. Truncated models with time dependence are shown to naturally produce predator-prey oscillations. The relation between characteristic oscillation times, phasing and the parameters including the wavenumbers are investigated. Furthermore, the dependence on the zonal flow strength of the characteristic oscillation times and the energy transfer before and after saturation are tested. Dissipation, which breaks the conjugate symmetry of unstable and stable modes, is also examined to further probe saturation physics. Supported by USDOE.   

Dominant Energy Transfer Channels in Toroidal and Slab ITG Branches

Evidence from simulations of ITG turbulence in tokamaks, RFPs, and stellarators suggests that both the slab and the toroidal ITG branches are saturated by three-wave coupling to stable modes, through different intermediaries. In the former the intermediary is a marginally stable mode, while in the latter it is a zonal flow. In a fluid model, this difference is consistent with the elimination of parallel flow physics by strong ballooning, which removes the marginal branch, leaving zonal flows as the best channel for maximizing the triplet correlation time. However, zonal flows and marginal modes coexist in both the slab and toroidal limits in the more general 3-field model that includes parallel flows. We study general saturation physics in this model via parameter orderings that access both limits and allow analytic expressions for the complex mode frequencies and eigenfunctions. This enables a determination of the relative roles played by triplet correlation time and eigenmode overlap in selecting the dominant saturation channel and the role of subdominant instabilities. These results are applied to simulations in MST and quasi-symmetric stellarator configurations to establish an understanding of the physics of dominant energy-transfer channels.   

Collisional Relaxation and Heating in Multi-Ion Species Plasma

Multi-ion species plasma that is immersed in a magnetic field features distinct collisional timescales when external forces are applied to it. We identify and explore intermediate timescales and describe metastable states of such a plasma. In particular, we identify and discuss the temperature gradients that arise in the plasma. We compare plasma to a neutral gas, where related physics, i.e. the piezothermal effect [1], are observed. \newline References: [1] ``Piezothermal effect in a spinning gas" V. I. Geyko and N. J. Fisch, Phys. Rev. E 94, 042113 (2016). \newline [2] ``Strategies for advantageous differential transport of ions in magnetic fusion devices" E. J. Kolmes, I. E. Ochs, and N. J. Fisch, Phys. Plasmas 25, 032508 (2018).   

Analytic theory of the Dimits shift

The Dimits shift is the shift between the linear threshold of the drift-wave primary instability and the actual onset of turbulent transport, and is attributed to the formation of zonal flows (ZFs). We calculate this shift within the modified Terry--Horton [1] and modified Hasegawa--Wakatani [2] model. In agreement with [3], we find that the ZF causes localization of primary modes near the extrema of the zonal velocity $U(x,t)$. We show that these modes can be modeled as quantum harmonic oscillators with complex frequencies, so the growth rate can be calculated analytically and the result agrees with numerical eigenvalues. The local curvature of the velocity, $U''=\partial_x^2 U$, stabilizes the primary modes up to a certain threshold. Beyond that, the primary mode re-emerge with growth rate modified by $U''$, and is also known as the tertiary instability (TI). Notably, the TI mode with the largest rate is the analytic continuation of the Kelvin--Helmholtz mode studied recently in [4]. [1] D. A. St-Onge, J. Plasma Phys. {\bf 83}, 905830504 (2017). [2] R. Numata, R. Ball, and R. L. Dewar, Phys. Plasmas {\bf 14}, 102312 (2007). [3] S. Kobayashi and B. N. Rogers, Phys. Plasmas {\bf 19}, 012315 (2012). [4] H. Zhu, Y. Zhou, and I. Y. Dodin, Phys. Plasmas {\bf 25}, 082121, (2018).   

Maximum-Entropy States for Cross-Field Differential Ion Transport

For a plasma with a collision operator that conserves energy, particle number, and momentum, the Boltzmann distribution is the state of maximum entropy. In a strongly magnetized, quiescent plasma, the motion of net charge across field lines is strongly suppressed. The addition of a constraint on net cross-field charge transport leads instead to the classic impurity pinch relation as the maximum-entropy state. This more general derivation makes it possible to define a broad class of collision operators which will lead to the impurity pinch.   

Magnetic Eddy Viscosity of Mean Shear Flows in 2D Magnetohydrodynamics: Possible Application to Gas Giants' Interiors

Magnetic induction in magnetohydrodynamic (MHD) fluids at magnetic Reynolds number ($\rm Rm$) less than 1 has long been known to cause magnetic drag. Here, we show that when $\rm Rm\gg1$, and additionally in a hydrodynamic-dominated regime in which the magnetic energy is much less than kinetic energy, induction due to a mean shear flow leads to a magnetic eddy viscosity. We derive magnetic viscosity from simple physical arguments, where a coherent response due to shear flow builds up in the magnetic field until decorrelated by turbulence. The dynamic viscosity coefficient is approximately $B_p^2/(2\mu_0) \tau_{\rm cor}$, the poloidal magnetic energy density multiplied by the correlation time. We confirm the magnetic eddy viscosity through numerical simulations of 2D incompressible MHD. We also consider the 3D case, and in cylindrical or spherical geometry we find a nonzero viscosity whenever there is differential rotation. Hence, these results serve as a dynamical generalization of Ferraro's law of isorotation. The magnetic eddy viscosity leads to transport of angular momentum and may be of importance to zonal flows in astrophysical domains. For example, it may explain recent discoveries by Juno and Cassini regarding the depth that zonal flows reach inside Jupiter and Saturn.   

A mechanism of neoclassical tearing modes onset by drift wave turbulence

The evolution of neoclassical tearing modes (NTMs) in the presence of electrostatic drift wave turbulence is investigated. In contrast with anomalous transport effect induced by turbulence on NTMs, a new mechanism that turbulence-driven current can affect the onset threshold of NTMs significantly is suggested. Turbulence acts as a source or sink to exchange energy with NTMs. The turbulence-driven current can change the parallel current in magnetic islands and affect the evolution of NTMs, depending on the direction of turbulence intensity gradient. When the turbulence intensity gradient is negative, the turbulence-driven current enhances the onset threshold of NTMs. When the turbulence intensity gradient is positive, it can reduce or even overcome the stabilizing effect of neoclassical polarization current, leading to a small onset threshold of NTMs. This implies that NTMs can appear without noticeable magnetohydrodynamics (MHD) events. References: [1] Huishan Cai, 2019 Nucl. Fusion 59 026009   

Mathematical equivalence of non-local transport models and broadened deposition profiles

Old and recent experiments show that there is a direct response to the heating power of transport observed in modulated electron cyclotron heating (ECH) experiments both in tokamaks and stellarators, which is commonly known as non-local transport. This is most apparent for modulated experiments in stellarators such as LHD and W7-AS. We show that this power dependence and its corresponding experimental observations such as the so-called hysteresis in flux [Inagaki, NF, 113006, 2013] can be reproduced by broadened ECH deposition profiles. In other words, many mathematical models proposed to describe non-local transport are equivalent to an deposition (effective) profile in its linearized forms [vanBerkel, NF, 106042, 2018]. This also connects with new insights on microwave scattering due to density fluctuations in the edge plasma which shows that in reality the deposition profiles are much broader than expected [Chellai, PRL, 105001, 2018] but it is unclear if this effect is sufficient to explain non-local transport. These relationships can be further studied by separating the transport in a slow (diffusive) and a fast (heating/non-local) time-scale using perturbative experiments.   

DNS and LES of homogeneous MHD turbulence under Hall and FLR effects

Direct numerical simulation (DNS) and Large Eddy Simulation (LES) of homogeneous MHD turbulence under Hall and FLR effects are carried out for some combinations of the ion skin depth and the Larmor radius to the resistive scales in order to study influences of the the scales shorter than the ion skin depth and the Larmor radius to the scales longer than them. Example to show necessity of the LES approach in numerical simulations of plasma instability and turbulence are presented[1,2]. Numerical results by DNS are made use for developing a Sub-Grid-Scale (SGS) model which represents the effects of the scales shorter than the grid width to the scales grid scales and apply the SGS model to LES. We emphasize that the SGS model is developed taking effectss of the Hall and FLR effects into account. Applicability of the SGS model to LES of homogeneous turbulence is examined by a comparison between DNS and LES. \\ $[1]$ H. Miura, F.Hamba, and A.Ito, "Two-fluid sub-grid-scale viscosity in nonlinear simulation of ballooning modes in a heliotron device", Nuclear Fusion 57 076034 (2016). \\ $[2]$ W.Horton, H.Miura, L.Zheng, "Two-fluid simulations of edge-plasma interchange/tearing instability", US-EU TTF workshop (March 17-19, 2019, Austin, U.S.A.)   

2D Drift Wave Turbulence Solved With a Time-Spectral Method

Drift wave turbulence is a universal phenomena in fusion plasma devices, playing a major role for energy confinement. Associated numerical transport modelling poses a difficult task due to the strong non-linearity and chaotic behavior of the turbulence. In order to address the present excessive computational requirements, in particular the small time steps of explicit finite difference methods, a fully time-spectral method (GWRM) has been developed. The GWRM models the 2D spatial domains, \textit{as well as the temporal domain}, using a weighted residual method for approximate solutions in the form of Chebyshev polynomial series. Thus the method gains spectral accuracy in all domains whilst being free of the CFL criteria. Successful benchmarking, employing the 2D Navier-Stokes equations, will be demonstrated for different boundary conditions. The GWRM is currently applied to a 2D fluid drift wave model developed by [1]. This two-fuid model describes fully toroidal ITG mode turbulence including FLR effects. Computational results will be presented and discussed. [1] H. Nordman and J. Weiland, Transport due to toroidal $\eta_i$ mode turbulence in tokamaks, Nucl. Fusion, 29, 251, 1989.   

Anisotropic thermal conduction in the FLASH code

Anisotropic thermal conduction is a diffusive process relevant to applications in plasma physics that use magnetic fields. It is well known that heat is transported more freely parallel to magnetic field lines, and it is constrained perpendicular to field lines. In experiments, such as magneto-inertial fusion experiments, this concept can be utilized to more effectively confine heat. We have implemented anisotropic thermal conduction into the FLASH code, the multi-physics radiation magneto-hydrodynamics code developed and maintained by the Flash Center for Computational Science at the University of Chicago. Our implementation also works with the adaptive mesh refinement in FLASH, which significantly increased the level of complexity of the thermal diffusion code. Here we present our implementation along with verification benchmarks that illustrate the effects of anisotropic thermal conduction.   

Filament dynamics in presence of X-point in turbulence simulations

We investigate the impact on filamentary transport of the presence of X-points with turbulence simulations of the WEST tokamak using the TOKAM3X code. A blob recognition and tracking algorithm resolves the time evolution of the 3D filamentary structures, complemented by 2D and 3D conditional average sampling techniques. As a result, the single blobs exhibit complex trajectories with non-negligible mutual interactions in between filaments and with the turbulent background plasma. On average the blob dynamics are well described by the theoretically derived scalings of blob radial velocities against their size, showing a transition from the sheath connected regime to the ideal interchange one close to the separatrix, where the blobs disconnect from the target plates. In this work, we propose an additional mechanism for blob disconnection, namely the poloidal shear in radial EXB velocity, spontaneously arising in diverted plasmas at the X-point as the topology changes from closed to open field lines, and we compare it with the commonly accepted disconnection through high flux expansion and magnetic shear in the X-point region.   

\textbf{How the self-interaction mechanism affects zonal flow drive and convergence of turbulent transport simulations with system size}

We use gyrokinetic flux-tube simulations to report a decrease in the shearing rate of ExB zonal flows with increasing system size measured by 1/$\rho $*$=$a/$\rho_{\mathrm{i}}$, where a is the tokamak minor radius and $\rho_{\mathrm{i}}$ is the ion Larmor radius. This is done in practice by decreasing k$_{\mathrm{y,min}}\rho_{\mathrm{i\thinspace }}$(\textasciitilde $\rho $*), where k$_{\mathrm{y,min}}$is the minimum wavenumber along the direction y, bi-normal to the magnetic field. The corresponding gyro-Bohm normalised heat and particle fluxes also increase with decreasing k$_{\mathrm{y,min}}$. We find that this results from the non-adiabatic passing electron dynamics and corresponding fine structures at mode rational surfaces associated to each k$_{\mathrm{y\thinspace \thinspace }}$mode. The related strong self-interaction mechanism disrupts resonant 3-wave interactions involving the zonal modes. As a consequence, the different k$_{\mathrm{y}}$ contributions to Reynolds Stress driving the zonal flows tend to get decorrelated, which results in the shearing rate level developing a statistical dependence on k$_{\mathrm{y,min}}$. In adiabatic electron simulations, the scaling is not as severe, owing to a weaker self-interaction mechanism at play.   

Kinetic ballooning mode turbulence in low-magnetic-shear 3D equilibria

Electromagnetic flux-tube simulations of the HSX stellarator using the gyrokinetic code \textsc{Gene} show that the kinetic ballooning mode (KBM) threshold $\beta^\mathrm{KBM}$ is an order of magnitude smaller than the MHD ballooning limit when a strong ion temperature gradient is present. As the ion temperature gradient becomes weaker, $\beta^\mathrm{KBM}$ approaches the MHD ballooning limit. $\beta^\mathrm{KBM}$ is also sensitive to locally-self-consistent modifications of the magnetic shear. Simulations of Heliotron-J also display behavior similar to HSX with respect to $\beta^\mathrm{KBM}$. Finite-$\beta$ ($\approx 0.5 \%$) simulations of HSX exhibit significant nonlinear finite-$\beta$ stabilization when saturation is achieved. We also introduce a fluid model that expands upon a three-field model [C.C.~Hegna et al., Phys.~of Plasmas {\bf 25}, 022511] by including finite-$\beta$ effects. We employ this reduced model to investigate KBM turbulence saturation in 3D magnetic equilibria both when strong ion temperature gradients are present and as the magnetic shear is varied.   

Transport barriers for monotonic and non-monotonic poloidal flows using maps

Test particle EXB transport due to an infinite spectrum of drift waves in two dimensions is studied using a Hamiltonian approach, which can be reduced to a 2D mapping. Finite Larmor radius (FLR) effects are included taking a gyroaverage. The presence of poloidal flows is included which gives rise to transport barrier formation. For large wave amplitudes there is a transition to chaos and the barriers are destroyed. FLR effects tend to restore the barrier, implying that fast particles are better confined. For a thermal FLR distribution, the PDF is non-Gaussian while the transport remains diffusive when there is no flow but becomes ballistic when the flow is strong enough. When the background flow varies linearly with radius, the map can be symplectic but for more general flows a two-step should be used. The stability of transport barriers is analyzed for several types of flow. This is displayed in fractal diagrams wave amplitude, FLR and flow strength.   

The Role of 3D Geometry on Reducing Turbulent Transport in Stellarators

The large space of possible stellarator configurations offers the possibility of changing the magnetic geometry to optimize different physics properties, including turbulent transport. Detailed analysis of the nonlinear three-wave turbulent interactions in a fluid model of ITG turbulence indicates that for the HSX stellarator, energy transfer is strongly influenced by three-wave nonlinear interactions between unstable modes and stable modes at similar scales. This nonlinear model provides a natural optimization metric, as nonlinear energy transfer is quantified by a three-wave interaction time, where the frequencies involved in the interaction time are strongly influenced by geometry. HSX possess the ability to alter its MHD equilibrium by adding a magnetic well or hill component. Both nonlinear GENE simulations and fluid calculations show an ITG turbulence minimum when the magnetic hill is increased and maximum with increased magnetic well, indicating a more prominent role of stable modes with increasing magnetic hill. This picture will be compared against detailed analysis of the spectral gyrokinetic energy transfer, by tracking the evolution of nonlinear energy transfer between different wavenumbers and eigenmodes to expose the role of stable modes in turbulence saturation.   

Link Between Turbulence Properties and Reconnection Dynamics

The interplay between reconnection and turbulence has been the subject of increasing scrutiny. In addition, recent observations of electron-only reconnection in the Earth's turbulent magnetosheath have shown that although turbulence can drive reconnection, the properties of this reconnection may differ from typical large scale laminar reconnection. An important question then is how the global properties of the turbulence affect the nature of the reconnection it drives. We discuss this link using the results from kinetic particle-in-cell simulations of both turbulence and reconnection.   

Ten-Moment Multifluid and Vlasov-Maxwell Modeling of Kelvin-Helmholtz Instability

Anisotropic and non-gyrotropic particle distribution functions are often identified in collisionless plasmas, particularly when there is a sheared background flow and induced Kelvin-Helmholtz Instability (KHI). The dynamic evolution of KHI influenced by such effects was studied in an extended MHD model with the gyrotropic components evolved in time while the non-gyrotropic components determined from analytic formulas. In this work, we present results using the ten-moment model that evolves both gyrotropic and non-gyrotropic pressure components self-consistently. Every species, including electrons, and evolved using their density, momentum, and energy equations. Non-ideal effects like electron inertia and Hall term are naturally contained in these equations. We will first compare the ten-moment simulation results with the so-called five-moment model that retains only an isotropic, gyrotropic scalar pressure for each species. This way we identify the effects introduced by the FLR effects. We will then compare the ten-moment results with those from fully kinetic Vlasov-Maxwell simulations. This serves to further understand the importance of FLR effects and the role of heat flux. All simulations are performed within the PPPL computational plasma physics framework, Gkeyll.   

Regimes of weak ITG/TEM modes for transport barriers without velocity shear

Electrostatic modes (ITG and TEM) usually dominate core transport, but we show there exists a regime where these modes are hugely weakened, enabling transport barriers without velocity shear. This regime has apparently arisen in multiple contexts: high beta poloidal ITB in DIII-D, ITB in JET with pellet injection, ITB observed in Wendelstein 7X, wide pedestal QH-mode pedestals and other pedestals. In all these cases the processes that greatly weaken ITG/TEM modes are similar. Through gyrokinetic simulations in model geometries and actual geometries, and a semi-analytic, Simplified Kinetic Model, we arrive at a clear understanding of these fusion friendly regimes made possible only by specific magnetic geometry characteristics plus substantial density gradients. Comprehensive electrostatic and electromagnetic gyrokinetic simulations with GENE show that for plasmas in this regime, linear modes are weak, and the nonlinear transport can be reduced by two orders of magnitude. Various experimental transport barriers on DIII-D will be used as examples, and stellarator geometries such as Wendelstein 7X, NCSX and HSX will also be considered.   

Numerical studies of multiscale electromagnetic electron-temperature-gradient turbulence

While relevant for transport in the tokamak pedestal, the dynamics and saturation mechanism of the slab branch of the electron-temperature-gradient (ETG) instability with full electromagnetic effects are not fully understood. We report on a set of novel multiscale, reduced-gyrokinetic (Zocco and Schekochihin, 2011) simulations of ETG turbulence in slab geometry. The exponential growth of linearly unstable modes ends in an initial, quasi-saturated state. During this stage, we observe the secular growth via nonlinear excitation of large-scale convective cells, which eventually dominate transport. In electromagnetic simulations, a strong magnetic zonal field is generated and dominates the dynamics. Details of the saturation mechanism are presented for the electrostatic and electromagnetic case.   

Statistical validation of anomalous transport Multi-Mode model for high beta and ITB tokamak scenarios in KSTAR

The Multi-Mode anomalous transport model [1] is validated employing experimental data for superconducting KSTAR NBI heated tokamak discharges that represent a high beta poloidal, high beta normalized, and ITB long pulse scenarios. The Multi-Mode model computes the anomalous transport driven by the ITG, TEM, ETG, KBM, RBM, and PB modes. In addition, recent modification to the model allows the computation of the anomalous transport driven by the microtearing modes [2]. The validation study is carried out using integrated modeling simulations that employ the numerical PT-SOLVER in the TRANSP code and that utilizes the KSTAR experimental boundary and initial conditions. The equilibrium data is interpolated from EFIT reconstruction. NBI heating and current drive are obtained using NUBEAM. Neoclassical transport is calculated using the Chang-Hinton model. The predicted evolving temperature profiles are compared with the corresponding KSTAR experimental data. The comparison is quantified by calculating the RMS deviations and Offsets. \newline [1] T. Rafiq, \textit{et al.} \textit{Phys. Plasmas}, \textbf{20}, 032506, 2013. [2] T. Rafiq, \textit{et al.} Phys. Plasmas \textbf{23}, 062507, 2016.   

Finite Plasma Beta Scaling of ETG Induced Turbulent Transport in Large Laboratory Plasma

Recent success on unambiguous demonstration of excitation of Electron Temperature Gradient (ETG) turbulence in Large Volume Plasma Device (LVPD) has motivated us to investigate turbulent transport induced by ETG turbulence. We investigated particle and heat transport, and compared both electrostatic and electromagnetic components of it with theoretical estimates. We found that convective part is directed radially inward whereas conductive heat flux is radially outward. The EM flux is found finite and non- zero against predicted zero for slab ETG model but its magnitude is found extremely small compared to ES flux. We varied plasma beta between ($\beta $\textasciitilde 0.01- 0.4) and observed that despite reduction in density fluctuations with increasing beta, the contribution to particle flux increases, which is surprising. For this, we carried out investigations for phase angle and temperature fluctuations. Detailed results on plasma beta modifications to phase angle and temperature fluctuations and contribution of ETG induced turbulence on plasma transport will be presented in the conference.   

Experimental Characterization of Three-Wave Coupling in Dipole Plasma Turbulence

Plasmas confined by a strong dipole field exhibit interchange turbulence, which previous experiments have shown respond locally to active feedback [1]. On the Collisionless Terrella Experiment (CTX), this turbulence is characterized by low frequency, low order, quasi-coherent modes with time-varying and intermittent spectral dynamics. We apply bicoherence analysis [2] using both short time fourier transforms and wavelets as basis functions to study nonlinear three-wave coupling and the resulting energy transfer between scales in the naturally occurring turbulence, as well as during active feedback and driven wave scenarios. The drive/feedback system can both amplify and suppress local turbulent fluctuations. During feedback we observe enhancements to the time-averaged bicoherence, while on shorter timescales the bicoherence changes rapidly with variations in fluctuation intensity. [1] Roberts, Mauel, and Worstell, Phys Plasmas (2015). [2] Grierson, Worstell, and Mauel, Phys Plasmas (2009).   

Recent results in suprathermal ion studies in TORPEX.

Suprathermal ion transport in turbulent plasmas has been a main topic of research in TOPREX, a basic plasma physics device located at the Swiss Plasma Center in Lausanne, Switzerland. Through injection of lithium-6 ions using a dedicated miniature source, and detection using a gridded energy analyzer, past experiments have shown that cross-magnetic field transport can in general be non-diffusive. More recently, time-resolved measurements have allowed studying variability features of the detection signals. Theoretical studies have shown that it is possible to predict these features and model experimental observations. We show that the model agrees well with simulations and with an extensive set of experimental data. The experiments encompass configurations with different transport characteristics, including non-diffusive regimes.   

Study of argon impurity transport by X-ray imaging crystal spectrometer on J-TEXT

A tangential X-ray imaging crystal spectrometer (XICS) has been upgraded on J-TEXT tokamak to measure the electron/ion temperature and the plasma toroidal rotation velocity. The XICS has been designed to receive emissions of Ar XVII from $-$13 cm to $+$13 cm region with a spatial resolution of 1.8 cm in the vertical direction. The temporal evolution of argon impurity density profiles after an argon gas puff could be observed with a time resolution of up to 2 ms. The emissions of Ar XVII can be modulated by the resonant magnetic perturbations (RMPs) which indicates that the transport of argon is affected by the RMPs significantly. The 2/1 RMPs can lead to field penetration with enough RMPs amplitude. The XICS provides a tool for the study of the transport of argon impurities during the penetration of RMPs. During the field penetration phase, the emissions of Ar XVII decreased. The phenomena show that the transport of argon impurity at r/a\textasciitilde 0.5 has been enhanced during the field penetration phase. The Ar XVII profile can be changed by the different 2/1 RMP phases. STRAHL can give the ratio between D and v profiles for the argon. The result shows that the argon transport can be affected by 2/1 RMP and its phase.   

Simulation study of nonlinear saturation of cross beam energy transfer in Top9 experiments at the Omega laser facility

In laser-based inertial confinement fusion (ICF), an ensemble of high energy laser beams drives the implosion of a capsule containing nuclear fuel. Ablation of the capsule surface, however, forms a plasma corona apt for laser-plasma instabilities that can limit the performance of the implosion. Among these instabilities, cross beam energy transfer (CBET), or the exchange of energy between overlapped beams mediated by ponderomotively excited ion-acoustic waves, can scatter light away from the capsule surface. At the Laboratory for Laser Energetics (LLE), an experimental platform, TOP9, has been developed for focused studies of CBET in ignition relevant plasmas. These experiments will establish the limits of linear theory, but an understanding of how CBET saturates at these limits requires detailed simulations. Here we will present the results of VPIC particle-in-cell simulations exploring mechanisms for CBET saturation.   

Density dependence of the saturation of stimulated Raman scattering in CBET-amplified multi-speckled beams

Cross-beam energy transfer (CBET) is the process by which two crossing laser beams transfer energy between one another through stimulated Brillouin scattering (SBS). Understanding the nonlinear saturation of CBET, including the effects of wave-particle interaction, the excitation of secondary instabilities such as backward and forward stimulated Raman scattering (BSRS and FSRS, respectively), and speckle geometry, is important to controlling low-mode asymmetry in inertial confinement fusion (ICF) implosions. We perform particle-in-cell simulations using VPIC to characterize the BSRS and FSRS in a CBET-amplified multi-speckled beam across a range of plasma densities that commonly occur in ICF and high energy density experiments. In particular, we quantify the changes in the scattering angle across different densities, the attenuation rates of the beam, and the cascade of energy to lower frequency modes and hot electrons. Tracer electrons demonstrate the particle trapping in electron plasma waves and how multi-speckle communication influences the instability threshold.   

Shock formation in a flowing plasma interacting with crossed laser beams

High power lasers interacting with flowing plasmas can produce a plasma response that leads to beam bending and, by momentum conservation, to slowing down of the plasma flow velocity [1]. In the vicinity of the sonic flow, where this plasma response is the strongest, the flow’s interaction with the laser light can lead to shock formation. We report on numerical and analytical studies of shock formation in the geometry relevant to hohlraum experiments and the interaction of plasma flow with the crossing NIF beams in the vicinity of the laser entrance hole. It was demonstrated [2] that beat waves created by crossing pairs of quads on NIF result in a broad spectrum of low frequency fluctuations that accelerate and heat ions. When the momentum transfer to fast moving ions is in the opposite direction to the plasma flow it can slow down the flow and enhance shock formation. The two scenarios of shock formation are examined in the context of NIF experiment and discussed for the relevant parameters. [1] H.A. Rose, Phys. Plasmas 3, 1709 (1996). [2] P. Michel, W. Rozmus, E.A. Williams, et al. Phys. Plasmas 20, 056308 (2013).   

Hard x-ray source enhancement via tailored plasma interaction

A high fluence source of hard x-rays (30$+$ keV) is desired for extreme radiation effects testing but currently cannot be produced via existing laser-driven K-alpha or pulsed-power bremsstrahlung capabilities. An alternative source under development enhances typically undesired laser-plasma instabilities to generate hot electrons that convert to bremsstrahlung x-ray emission in high-Z target walls. Experiments on Omega and NIF have been performed varying hohlraum plasma conditions to strengthen and enhance plasma waves, most recently using novel foams with density gradients to achieve a 4x increase in hard x-ray emission over single-density counterparts (which themselves emitted 10x greater hard x-rays than a typical target). Further results utilizing solid density structure within the hohlraum preferentially boosts emission of the desired 50-70 keV x-ray spectral range. These experimental results will be discussed along with corroborating simulations that allow extrapolation to ideal conditions on NIF.   

Long Scale-length Plasmas for Studies of LPI Mitigation Via Laser Bandwidth

Experiments at the Nike laser are investigating mitigation of laser plasma instabilities (LPI) via increased laser bandwidth under conditions relevant for inertial confinement fusion. A key step is the creation of a reproducible plasma with long scale-lengths. A previous LPI campaign used a single type of low density foam target to produce large volume plasmas with estimated 5-10x longer density and velocity scale-lengths than solid CH targets. The current study explores a wider range of initial foam densities and utilizes exploding foil targets for comparison to LPI experiments from longer wavelength laser systems. Once the plasma is established and LPI generated, the output spectrum for the Nike laser ($\lambda _{\mathrm{peak}}=$248.5 nm) can be broadened by etalons in the front end or by stimulated rotational Raman scattering after the final amplifier.[Weaver, App. Optics (2017)] The current campaign also uses a 5$^{\mathrm{th}}$ harmonic probe laser (213 nm) to determine the electron density profile around the time of peak pump intensity via a grid image refractometry (GIR) diagnostic.[Oh, Rev. Sci. Instru. (2015)] This poster will present the results from this campaign and simulations (FASTrad3D$^{\mathrm{\thinspace }}$[Gardner, Phys. Plasmas (1998)] and LPSE [Myatt, Phys. Plasmas (2017)]) performed to evaluate LPI growth in these plasmas.   

Petascale kinetic simulations of laser plasma interactions relevant to inertial fusion energy (IFE)

Understanding the roles laser plasma interactions (LPI) play on inertial fusion energy (IFE) experiments is critical for the success of current experiments around the world. And although the physics of Raman and Brillouin scattering is predominantly in one dimension (i.e., the incident and the scattered lights all propagates along the same axis), higher dimensional effects, such as the self-focusing of the plasma waves, or the transverse effects of the lasers due to laser non-uniformities can be important and higher dimensional simulations with kinetic effects are necessary to capture the richness of the LPI problem under IFE relevant conditions. In the past year, we have made numerous improvements to the particle-in-cell code OSIRIS to allow it to perform large simulations with ever increasing realism in 2D, quasi-3D, and 3D. These modifications have allowed us to perform kinetic simulations of laser plasma interactions (including stimulated Raman scattering (SRS), two plasmon decays (TPD) and stimulated Brillouin scattering (SBS)) with ever increasing realism, including phase plates, and temporal smoothing. We will present present and future plans to modify OSIRIS to perform multi-speckle simulations in 2D and 3D with realistic beam smoothing and present 2D and quasi-3D simulations of multi-speckle simulations of the TPD/HFHI instability under shock-ignition relevant conditions.   

Plasma transport and absorption in multiple, overlapping, non-uniform laser beams

In inertial confinement fusion schemes, situations arise in which multiple laser beams overlap in a plasma. For example, on the National Ignition Facility, 96 laser beams overlap as they are focused into the hohlraum. We explore whether the complicated electromagnetic field patterns that arise can affect electron transport and energy absorption via non-linear phenomenon. A 3-dimensional particle-tracking code, which includes Coulomb collisions and 2$^{\mathrm{nd}}$-order magnetic forces, will be described. In particular, we will explore the effect of laser speckles on electron transport, including ponderomotive forces and the plasma response. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. .   

Capsule time dependent drive symmetry in a rugby shaped hohlraum with a 3D laser irradiation drive experiment on OMEGA

Significant calculation benefits can be obtained from a 3D radiation-hydrodynamics code compared to a 2D rad-hydro code. This is the main reason that has encouraged CEA-DAM to develop the 3D radiation-hydrodynamics code TROLL. While the TROLL code has already been challenged by numerous 3D hohlraum experiments, questions remained about its capability to simulate indirect drive implosions with a poor azimuthal irradiation symmetry. In this context, an experiment has been conducted on OMEGA laser facility (LLE, University of Rochester) to validate the 3D radiation-hydrodynamics code TROLL. A rugby hohlraum was driven either by 18 beams at full power (asymmetric radiation drive) or by 30 beams at 3/5 power (symmetric radiation drive) to keep hohlraum energetics constant. We have studied the effects of asymmetry with three types of targets: reemission high-Z spheres for early time, foamballs for intermediate time and D2-filled capsules for late time symmetry measurement. Experimental results will be compared with 3D radiation-hydrodynamics code TROLL.   

\textbf{Characterization of Electromagnetic Fields from Proton Radiographs of Laser-Driven Hohlraums}

A more complete understanding of laser-driven hohlraum plasmas is critical for the continued development and improvement of ICF experiments. For such plasmas, hydrodynamic calculations are very successful in describing the evolution of the plasma at early times. However, at late epochs kinetic effects become dominant and the hydrodynamic description is insufficient. In these hohlraums, self-generated electric and magnetic fields play an important role in determining plasma dynamics and evolution; however, it has largely been uncertain whether electric fields or magnetic fields dominate these systems. To explore this question, we conducted several experiments at the OMEGA laser facility, using monoenergetic proton radiography to probe asymmetrically-driven vacuum-filled gold and plastic hohlraums. In our analysis, we utilized reconstructive methods[1] \textlnot to infer information about the possible structure of electromagnetic fields in the hohlraum, as well as quantify the relative magnitudes of proton deflections due to these electric and magnetic fields. This work was supported in part by the U.S. DOE, NLUF, and LLE. [1] Bott, A., et al. (2017). Proton imaging of stochastic magnetic fields. Journal of Plasma Physics,83(6), 905830614. doi:10.1017/S0022377817000939   

A Model for Radiative Heating of a High-Z Pusher

Current development of Inertial Confinement Fusion (ICF) capsules is moving towards surrounding the fuel with pushers made from High-Z materials. Any radiation emitted by the hot fuel can be absorbed and re-radiated to reduce cooling. While radiation-hydrodynamics codes can model this physics, just performing calculations is not the same as developing a physical picture. For this end, we have developed a set of differential equations from the Hammer and Rosen solution [1] to a Marshak wave [2]. We will present the derivation of the differential equations equivalent to the solutions of Ref. 1, and a set of power-law analytic solutions. We will also discussion numerical implementation of differential equations into a model for burn in ICF capsules [3]. [1] J. H. Hammer and M. D. Rosen, Phys. Plasmas 10, 1829 (2003). [2] R. E. Marshak, Phys. Fluids 1, 24 (1958). [3] C. K. Huang, K. Molvig, B. J. Albright, E. S. Dodd, E. L. Vold, G. Kagan, and N. M. Hoffman, Phys. Plasmas 24, 022704 (2017). LA-UR-19-26058   

Single and Double Shell Ignition Targets for NIF at 527nm

We have expanded Suter's (2004) description of 527nm NIF capabilities with beryllium ablators to include single shell HDC capsules based on the high yield NIF shot N170827, and double shell capsules with aluminum ablators. Both higher laser power and energy are available at 527nm. 2D HYDRA calculations included gold hohlraums with scaled capsules, laser pulses, and beam pointings. A 1.2 hydro scaled version of N170827 requiring 3.1 MJ and 700 TW calculates to yield 3.5e$+$18 neutrons. Increasing power from 450 TW at 351nm to 750 TW at 527nm using 1.8 MJ raises the hohlraum temperature from 310 to 330 eV. This allows a thicker ablator which can reach either higher velocity or carry more remaining mass. LAVALAMP II calculations confirm these are feasible NIF pulses. Drive symmetry changes were accounted for by using a 0.3mg/cc hohlraum gas fill. VPIC simulations of LPI suggest acceptable backwards SBS and SBS, but enhanced forward SRS. Funded by the USDOE. LA-UR-19-25677   

Diagnosing Mix in Double Shell Implosions

Implosions using a high-Z metal pusher, such as in a double shell capsule, promise to achieve thermonuclear burn conditions with low hot spot convergence ratio, CR $\sim$ 10. While the implosions are designed to avoid or minimize mix of the high-Z pusher into the D-T fuel, fusion performance degradation due to mix remains a major concern. Here we discuss the use of secondary D-T neutron yields from D-D fusion, using a CD or CD$_{2}$ foam as a surrogate fuel, to obtain D-D fusion performance, fuel ion temperature, and high-Z mix in early planned implosions on NIF using chromium, molybdenum, or tungsten pushers. Future double shell implosions with D-T fuel will require radiochemical tracers from charged particle reactions, such as 10B($\alpha$, n)13N and 79Br(d, 2n)79Kr, to determine the amount of high-Z mix in the D-T fuel. The reactant products 13N and 79Kr are non-reactive, gaseous, with sufficient half-lives, and can be collected with high efficiency using the Radiochemical Apparatus for Gas Sampling (RAGS) diagnostic on NIF. We will present results from RAGE and HYDRA simulations on mix, and initial results of predicted mix signatures using 1D RAGE results with varying degrees of mix.   

Prospects For Magnetic Indirect Drive Inertial Confinement Fusion

Experimental, theoretical, simulation, and technological advances over the past 20 years are motivating a reassessment of the Magnetic Indirect Drive (MID) approach to Inertial Confinement Fusion. We outline the main physics concerns of the MID approach. These include symmetry control, minimum case-to-capsule ratio, radiation coupling into the hohlraum, and pulse-shaping of the radiation drive. A discussion of possible experiments and simulation studies is presented.   

Burn Propagation in ICF and MIF Plasmas.

High energy gain in Inertial Confinement Fusion and Magneto-Inertial Fusion requires the propagation of a burn wave from hot plasma into a cold, dense fuel layer. The speed and efficiency of this propagation determines the energy gain that can be achieved. This work focuses on the physical processes occurring in burn wave propagation and the factors which determine the speed of propagation. Highly resolved hydrodynamic and magneto-hydrodynamic simulations of burn fronts are carried out to study the effects of heat and magnetic field transport at the burn front. It is found that electron heat flow plays an important role in the region behind the burn front, transporting energy from regions in which rapid self-heating is occurring to cooler regions. When a magnetic field is present the suppression of heat flow significantly reduces burn propagation speed. It is also found that magnetic field transport at the burn front is dependent on fuel magnetization. For low values of the electron Hall parameter, the magnetic field can be compressed by the propagating burn front, but for high values rarefaction of the field occurs due to expansion of the heated plasma.   

The Effects of Kinetically Enhanced Interfacial Mix on Reactivity Variation in Omega Capsules

Analyzing the effects of the hydrodynamic mix has been an essential part of designing ICF targets. In contrast, atomic mixing processes due to kinetic effects have largely been overlooked until recent years. Various studies have been performed –both theoretical and computational– to assess the role of these effects on the yield. A particular experiment (amongst many) which has challenged our understanding of both kinetic and hydrodynamic theory is the so-called Rygg experiment [1]. The targets were comprised of a direct drive CH capsule with a D-$^3$He fill that was varied in concentration while ensuring hydro-equivalence (the initial total mass and pressure are kept fixed). In the experiments, anomalous (non-hydrodynamic) yield variations were observed that had eluded explanations thus far. A recent fuel (D-3He) only Vlasov-Fokker-Planck (VFP) simulation [2] of a similar experiment has shown how kinetically enhanced fuel-species separation can partially predict the observational yield trend. In this work, we present our results on similar simulations with the CH pusher partially modeled to assess the interplay of interface dynamics on the yield. [1] J. R. Rygg et al., Phys. Plasmas, 13, 052702 (2006) [2] W. T. Taitano et al., Phys. Plasmas, 25, 056310 (2018)   

Shock-Enhanced Plasma Diffusion at a Gas-Metal Interface

Revolver and Double Shell designs are predicted to ignite at lower temperatures/convergences than conventional single shell capsules. However, any significant mix of the pusher material into the fuel (gas) may have a sizable impact on burn performance. The hydrodynamic stability of the gas-metal interface is an obvious concern, but 1D effects may also be detrimental. Such effects include plasma diffusion at material interfaces; which has been the subject of numerous investigations. However, other 1D mix mechanisms may exist, which have yet to be thoroughly explored. In particular, plasma kinetic effects may drive mix when a shock breaks out of a gas-metal interface. Using the state-of-the-art, hybrid (kinetic-ion/fluid electron), multi-ion Vlasov-Fokker-Planck code, iFP, we show that shock-driven kinetic effects reconfigure the interface, and the inter-facial width subsequently grows proportionally to $M^{5/2}$ with time (where $M$ is the initial shock Mach number in the metal). Finally, we consider any implications for high-Z pusher designs.   

The Best Possible Prediction: statistical inference and uncertainty quantification in predictions for ICF experiments

To make the best possible prediction, we must combine models and data optimally. As an example, we apply a method for inference on large data sets to the problem of ``predicting'' the unknown results, with uncertainties, of 16 direct-drive implosion experiments, using glass and plastic capsules, shot at OMEGA. The method uses the GPM/SA (Gaussian Process Models for Simulation Analysis) code to construct an emulator, based on a rad-hydro code and constrained by data from 22 other ICF implosions carried out under different conditions from the unknown set. Comparing the extrapolative ``predictions'' to the actual observations lets us evaluate the validity of various assumptions and the reliability of the predictions and uncertainty bounds [Osthus et al., SIAM/ASA J. Uncert. Quant. 7, 604 (2019)]. The predictions turn out to be quite reliable: 94{\%} of the predictions agreed with the actual observations to within the 95{\%} uncertainty bounds. This approach will likely also be useful for model calibration and validation, hypothesis testing, and experiment design.   

A Weakly Nonlinear Theory for the Magnetic-Rayleigh--Taylor Instability

The magnetic-Rayleigh--Taylor (MRT) instability is ubiquitous in magnetically-driven cylindrical Z-pinch implosions. In this work, we present a weakly nonlinear theory for the MRT instability. The model is obtained via an asymptotic expansion of a Lagrangian describing the fully nonlinear dynamics. After introducing a suitable choice of coordinates, it is shown that the theory can be casted as a canonical Hamiltonian system, whose Hamiltonian is calculated up to the fourth order in the perturbation parameter. The resulting theory captures harmonic generation, as well as the initial stage of the MRT instability saturation. Comparisons of this theory to fully nonlinear hydrodynamical simulations and to experiment are discussed.   

Using the Bayes Inference Engine to study the deceleration-phase of Rayleigh-Taylor growth rates in laser-driven cylindrical implosions

Hydrodynamic instabilities, such as the Rayleigh-Taylor (R.T.) instability develop in high energy density, inertial confinement fusion (ICF) experiments. These instabilities degrade the implosion due to mixing of the fuel. We study R.T. modes in ICF implosions in order to better understand how they evolve in time. To improve our data analysis, we use the Bayes Inference Engine (BIE). The BIE is a computational framework that takes an iterative forward modeling approach to perform statistical inference. We use the BIE to create a parameterized model of these 2D implosions. This model accounts for blur, alignment and illumination. The parameters are optimized to obtain maximum likelihood estimates for the time-dependent amplitude of the R.T. modes, the returned solution considers weighted statistical likelihood and prior information. This technique has helped improve our ability to quantify uncertainties, establish sensible error bars and guide the refinement of our experimental techniques. When applied to our experiments the BIE has been used to confirm the symmetry of the implosion and understand all asymmetries to be a result of parallax, as well as, improve our error bars and establish a more statistically significant model moving forward. LA-UR-19-21647   

Magneto Rayleigh-Taylor instability growth in magnetically driven cylindrical liners

The magneto Rayleigh-Taylor (MRT) instability grows in magnetically-driven inertial confinement fusion systems and can limit attainable fuel pressures and fusion yields. Here we analyze MRT in cylindrical liners imploded on the Z Machine at Sandia National Laboratories for a wide range of targets and machine configurations. We show that different trends in the MRT amplitude can be understood using the acceleration history applied to linear and non-linear theories for traditional Rayleigh-Taylor instability growth. The acceleration history is determined using a thin-shell implosion model, which allows us to relate the instability amplitude to driver and target properties, including the peak current, risetime and the initial target radius and aspect ratio.   

\textbf{Measurement of ion-electron equilibration rates in hot-spot relevant conditions at OMEGA}

During the thermonuclear-burn phase of an inertial confinement fusion (ICF) implosion, alpha particles primarily deposit energy to the electron which drive the electrons out of thermal equilibrium with the ions. Since the fusion rate is sensitive to the ion temperature, accurate models for ion-electron equilibration are required to capture the thermal evolution of both species. Currently, there are numerous theoretical studies which model the equilibration process in conditions relevant to the hot spot of an ICF implosion. However, there is a lack of experimental data to constrain these models. Here we present precision measurements of ion-electron equilibration rates in the core of exploding pusher implosions at OMEGA. This is indirectly done by measuring the stopping power at low velocities, which is dictated by the same transport coefficient as ion-electron equilibration. The work was supported by DOE, NLUF, CoE and LLE.   

Design of an ultra-long timescale Hydrodynamic Instability platform using the Z pulsed power driver

Here we present the design of a new hydrodynamic instability platform using the Z pulsed power driver. In this platform Z is used to accelerate an exploding cylindrical flyer into a sample that contains an interface between two materials with a pre-machined perturbation. The configuration of the experiment is highly flexible and allows for Richtmeyer-Meshkov and/or Rayleigh-Taylor unstable configurations to be explored. The primary advantage of this configuration is that Z can drive the flyer for very long timescales (\textgreater 100 ns) allowing many e-foldings and potentially probing the transition to turbulence. We explore the impact of material choices, geometry, and pulse shape on the acceleration history of the unstable interface and growth of the perturbation.   

Differences in Turbulence Behavior in Two-Dimensional Versus Three-Dimensional Compressions

In the context of inertial fusion experiments, we examine the behavioral differences between turbulent flow compressed in three dimensions (as in typical laser-driven experiments) and turbulent flow compressed in two dimensions (as in Z-pinch experiments). In particular, we derive a quasi ``equation-of-state'' for the turbulent energy in both cases, and show that a rapid compression in the two-dimensional compression case can preferentially enhance turbulent energy relative to thermal energy, in contrast to the three-dimensional case. Further, we examine the possibilities for viscous dissipation of the turbulence in two-dimensional compressions, and find that complete viscous dissipation of the flow can be more difficult, owing to survival of structure in the non-compressed direction; whether the difficulty is increased is sensitive to the boundary conditions.   

An efficient, time-implicit, conservative solver for the multispecies fully kinetic 1D-2V VFP-Amp\`{e}re system

We discuss the extension of the fluid electron treatment in the hybrid 1D-2V Vlasov-Fokker-Planck (VFP) code iFP to a fully kinetic one. We address the numerical stiffness of kinetic electrons (owing to the presence of fast timescales associated with the plasma frequency, fast electron motion, and electron collisions) by implicit timestepping, accelerated by a multiscale moment-based preconditioner. iFP's mass, momentum, and energy conserving discretization (which is achieved through a Lagrange-multiplier-like approach by using nonlinear constraint functions) is extended to deal with charge separation, while preserving iFP's successful adaptive mesh strategy in physical and velocity space (in which the velocity space of each species is analytically rescaled and shifted by its spatially and temporally varying thermal speed and bulk flow, and a moving mesh in configuration space allows tracking features with sharp spatial gradients, such as shocks and material interfaces). We present results from several benchmark problems, and demonstrate application to a fully kinetic collisional plasma shock in planar geometry.   

A mathematical operator to describe neutron time-of-flight signals from magnetized liner inertial fusion experiments at the Z Pulsed Power Facility

An analytic forward model is required to rapidly simulate the neutron time-of-flight (nToF) signals that result from magnetized liner inertial fusion (MagLIF) experiments for comparison to data. Since the objective functions that model these signals change for various scattering and attenuation geometries and different neutron sources, it is necessary to define a parameterized operator that outputs nToF signals for any MagLIF experiment. The operator was developed from first principles and is described heuristically, hence this technique can serve as a bench mark for other nToF diagnostic methods and can be applied to any inertial confinement fusion experiment. Important parameters describing the source plasma, such as ion temperature and liner areal density, can be extracted from experimental MagLIF data by using this operator in conjunction with a Bayesian inference formalism.   

Single-Ion Hall-MHD Formulation and Highly-Coupled Numerical Implementation into Hybrid Particle-in-Cell Code

The rudiments of a particle-based single-fluid two-temperature magnetohydrodynamic (MHD) algorithm have been outlined in C. Thoma, et al., Phys. of Plasmas 20, 082128 (2013). The extension of this algorithm to include the effect of Hall physics is described. An implicit leapfrog version of the algorithm, which allows timesteps large compared to the resistive decay time and other relevant timescales, has recently been added to the hybrid particle--in--cell code Chicago. In standard MHD the Hall term in the generalized Ohm's law can be neglected when the Hall parameter is small. This term must, however, be retained in regimes where it is non-negligible. A highly-coupled implicit Hall-MHD formalism is presented, in which displacement current can either be retained or neglected. A comparison of numerical and analytic dispersion analysis demonstrates the feasibility of this approach and establishes relevant constraints to assure numerical stability. The implementation of the algorithm into Chicago is described, and some preliminary simulation results in 1D and 2D in the high Hall parameter regime are given.   

Hydrodynamic simulation with the hot-electron transport model for shock ignition

In the last phase of the shock ignition scheme, an intense spike laser pulse drives a strong shock in order to ignite the compressed fuel. The generation of strong shock is in a laser-plasma interaction regime where laser-plasma instabilities are expected. For example, generation of hot electron and its non-local transport cannot be ignored. In this study, we focus on the modeling of hot-electron transport generated by the SRS and SBS for hydrodynamic simulations [1]. PIC simulation of LPI in long plasma density scale length generates the time history of distribution of the hot electron. The most dominant hot electron slope temperature produced by the SRS is about 30keV, which is simplified to the hot electron distribution function for the source term of the non-local electron transport model in hydrodynamic simulation. We have implemented a few hot electron transport models [1] in to 2-D radiation hydrodynamic simulation code, PINOCO [2]. Numerical method and some simulation results are shown in this presentation. [1] D. Sorbo, et al., Phys. Plasmas 22, 082706 (2015) [2] H. Nagatomo et al., Nucl. Fusion 57, 086009 (2017)   

Effects of high intensity Laser Plasma Interaction on hydrodynamic simulations

Hydrodynamic simulations of laser plasma do not take account of LPI that are induced by the intense laser($I_{L}$ \textgreater 10$^{\mathrm{15}}$ W/cm$^{\mathrm{2}})$. In order to improve the accuracy of hydrodynamic simulation in LPI regime, development of numerical model of LPI is necessary. We evaluate effects of LPI related to hydrodynamic simulations using a 1-D PIC code. Assuming the laser wavelength and intensity are 0.5 micron and 10$^{\mathrm{16}}$ W/cm$^{\mathrm{2}}$ respectively, intensity exceeds LPI thresholds$^{\mathrm{[1]}}$ and we should think absolute and convective SRS and SBS. We conducted several simulations with the different plasma scale lengths(100, 200, and 300 micron). Laser intensity is set to 10$^{\mathrm{16}}$ W/cm$^{\mathrm{2}}$. In the results, due to the SRS and SBS, reflected light shows periodic behavior and the period depends on the plasma scale length. Scattered light at $n_{cr}$/4 by the SRS is scattered again at $n_{cr}$/16 and a density cavitation is observed there. This procedure is called Raman cascade. In case of 100 micron of the plasma scale length, a density cavitation at $n_{cr}$/16 did not appear. We discuss the detail of characteristics, and implementation into hydrodynamic codes in this presentation.   

Multi-stage simulations of electron transport dynamics in magnetized, imploded cylindrical plasma

Fast isochoric heating of a pre-compressed plasma core is an efficient approach to create extreme high-energy-density states such as those required to trigger ignition. In our studies, a cylinder inside a seed magnetic field is imploded with 1.5 ns OMEGA laser pulses to achieve compression to high density and external B-field strength. Then the high intensity OMEGA EP laser is used to produce relativistic electrons to heat the imploded cylindrical plasma. Here, a multi-stage simulation approach comprehensively describes the two kinds of efficient electron transport guided by the self-generated B-field before the maximum compression and the compressed external B-field after that, respectively.   

Influence of Laser effect on the stopping of He in two-component Plasma Targets

The interaction between charged ion beams composed of atoms and molecules and targets is a subject involving many physical research fields. For example, in the field of ion beam driven inertial confinement fusion, neutral beam heating in magnetic confinement fusion, Astrophysics and fast ignition, etc. In recent years, a scheme has been proposed in the field of inertial confinement fusion, that is, plasma target is irradiated by laser field and ion beam at the same time, and related experiments have been carried out. It is expected that laser field can fundamentally affect the propagation of ion beam through plasma excitation. In this paper, we study the effect of laser field on the stopping of He beam in two-component plasma targets. In particular, the effect of plasma excitation on the behavior of He in intense laser field is discussed. In the absence of laser field, plasma is usually regarded as only electrons participating in the response. However, with the increase of laser field intensity, the behavior of ions becomes more and more important. Therefore, the behavior of ions shouldn't be ignored in the case of strong laser field. Their excitation in the case of strong laser field is considered, especially in the case of low-speed incident ion beam.   

Proton-boron-11 fusion revisited

We revisit the proton-boron-11 (p-B11) nuclear fusion for igniting and sustaining an idealized fusion reactor. The large radiation loss due to electron bremsstrahlung introduces a formidable challenge against harvesting net power in thermalized p-B11 plasmas. However, the recent measurement of the p-B11 cross section provides a new hope. We show that ignition and scientific breakeven can be achieved with the new data. We also discuss the conditions and parameters required for a p-B11 fusion reactor.   

RF current condensation in magnetic islands and associated hysteresis phenomena

The nonlinear RF current condensation effect suggests that magnetic islands might be well controlled with broader deposition profiles than previously thought possible [1]. To assess this possibility, a simplified energy deposition model in a symmetrised 1D slab geometry is constructed. By limiting the RF wave power that can be absorbed through damping, this model describes also the predicted hysteresis phenomena. Compared to the linear model, the nonlinear effects lead to larger temperature variations, narrower deposition widths, and more robust island stabilisation. Although, in certain regimes, the island centre can be disadvantageously shaded because of the nonlinear effects, in general, the RF condensation effect can take place, with current preferentially generated, advantageously, close to the island centre. [1] A. H. Reiman and N. J. Fisch, Phys. Rev. Lett. 121, 225001 (2018).   

{\it FullWave} simulations of ECRH RF beams in DIII-D plasmas

High resolution solution of wave equations in frequency domain in ECR frequency range for realistic Tokamak plasma parameters became feasible with the use of recently formulated hybrid iterative approach [V. A. Svidzinski, et. al. Phys. Plasmas, {\bf 25}, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles and it is implemented in code {\it FullWave}. 2D full wave modeling of ECRH RF beams in DIII-D plasma is performed in the cold and hot plasma models for outboard and top launch scenarios. Full FLR hot plasma response model, based on accurate numerical solution of linearized Vlasov equation is used to model beam propagation and absorption in the 2nd ECR harmonic region. All physics of RF beam propagation, such as diffraction, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams and absorption at the 2nd ECR harmonic is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch nearly a pure X or O mode beam in plasma is developed and tested. Details of RF beams modeling and the results of beams simulations using {\it FullWave} will be presented.   

Recent developments of the $\it FullWave$ code for RF modeling in hot tokamak plasmas

The $\it FullWave$ code is being developed for solving linear wave equations with high resolution in frequency domain in configuration space for Tokamak plasma. $\it FullWave$ finds solution of wave boundary value problem iteratively through hybrid iteration cycles that combine time evolution of the electromagnetic fields and iterative relaxation of the solution. This iteration scheme allows for a much higher resolution of the solution than by using direct solvers. $\it FullWave$ with cold plasma model has been extensively tested for modeling RF beams propagation in 2D in tokamak plasmas in ECR frequency range demonstrating a very high resolution. The development of the code with nonlocal hot plasma dielectric response is underway. This response is formulated by calculating the plasma conductivity kernel based on an accurate numerical solution of the linearized Vlasov equation in inhomogeneous magnetic field. The code is optimized for memory use by interpolating the conductivity kernel from a coarse grid of test points to the fine grid of simulation points at every time and relaxation step. Recent progress of development of the $\it FullWave$ code, including the details of plasma conductivity kernel calculation, will be presented.   

Addressing peripheral damping obstacles for RF stabilization of tearing modes

A recent nonlinear treatment of RF stabilization of tearing modes [1] has identified a current condensation effect which has the potential to increase stabilization efficiency and loosen power localization requirements. Such benefits stem from the cooperative feedback between the RF deposition and resulting island temperature perturbation. However the same nonlinear enhancement effect can lead to complications when considering an RF wave that starts depositing its energy prior to reaching the center. [2] For such a case, the nonlinear enhancement can pull the deposition further into the periphery, counteracting stabilization efforts. Anticipating this difficulty, we address here potential methods of overcoming it. [1] A. H. Reiman and N. J. Fisch, Phys. Rev. Lett. 121, 225001 (2018)~ ~[2] E. Rodriguez et al., this conference   

Suppression of Tearing Modes by RF Current Condensation

We describe a previously unrecognized effect that can significantly facilitate the stabilization of magnetic islands by RF driven currents [1]. Analyses of stabilization have generally assumed that the local electron acceleration is unaffected by the presence of the island. This neglects the sensitivity of the deposition to the temperature, with the temperature in the island perturbed by the power deposition. The nonlinear feedback on the power deposition increases the temperature perturbation, and it can lead to a bifurcation of the solution to the steady-state heat diffusion equation. The combination of the nonlinearly enhanced temperature perturbation with the rf current drive sensitivity to the temperature leads to the rf current condensation effect. A recent calculation has confirmed the appearance of a hysteresis effect, with stabilized islands shrinking to smaller widths than would otherwise be achieved [2]. The threshold for the condensation effect is in a regime that has been encountered in experiments, and will likely be encountered in ITER. The potential impact on disruptivity will be discussed. [1] A. Reiman and N. Fisch, Phys. Rev. Lett. 121, 225001 (2018). [2] E. Rodriguez, A. Reiman and N. Fisch, poster, this meeting.   

Effects of Magnetic Island Geometry on RF Current Condensation

Radio frequency (RF) current drive is a known method for stabilizing magnetic islands in tokamaks. Experimental studies have confirmed the stabilizing effects of RF wave heating and current drive, but corresponding analytic and numerical models have only recently accounted for the effects of nonlinear feedback on the island current and temperature profiles [1]. Recent 1D calculations including wave depletion have confirmed the existence of an associated hysteresis effect [2]. We present the results of numerical solutions of the nonlinear steady-state thermal diffusion equation, including wave depletion, in full magnetic island geometry. The conditions under which there are significant nonlinear effects on the temperature profile are determined, and thresholds for bifurcation and hysteresis are calculated. The cases for both rotating and locked islands are considered. [1] A. H. Reiman and N. J. Fisch, Phys. Rev. Lett. \textbf{121}, 225001 (2018). [2] E. Rodriguez, A. Reiman and N. Fisch, to be submitted.   

Scoping Study of Lower Hybrid Current Drive for CFETR

A scoping study for lower hybrid current drive (LHCD) was performed for the China Fusion Engineering Test Reactor (CFETR) ``hybrid’’ scenario ($R_0 = 7$ m, $a = 2.2$ m, $B_0 = 6.4$ T, $I_p = 7.6$ MA, $n_{e0} = 1.2 \times 10^{20}$ m$^{-3}$, $T_{e0} = 30$ keV). The $\pi$Scope workflow engine was used to set up a large number of parametric scans of the antenna position, launched $n_{||}$, and power balance between low field side (LFS) and high field side (HFS) antennas with a total power of 20MW. Ray tracing/Fokker-Planck simulations predict off-axis current drive with a broad profile near $r/a$ of 0.6-0.9 and high efficiency (1.3 MA per 20 MW, $\eta = 5.5 \times 10^{19}$~AW$^{-1}$m$^{-2}$) for waves launched from the HFS. Waves launched from the LFS damp at larger radius ($r/a \sim 0.9$) with similar efficiency to HFS launch. A modest increase in efficiency (5\%) is found when synergy between the HFS and LFS antennas is considered in single pass damping scenarios. The effect of scattering from density blobs on the LFS is implemented through rotation of the perpendicular wavenumber. This effect can be ignored for HFS launch due to the quiescent nature of the HFS SOL in double null configurations.   

Kinetic Full Wave Analysis of Cyclotron Waves in Tokamak Plasmas Using Integral Form of Dielectric Tensor

In order to describe the wave structure and power deposition profile in ion and electron cyclotron wave heating in tokamak plasmas, a considerable progress has been made in developing full wave codes including kinetic effects. Recently kinetic full wave analysis using integral forms of dielectric tensor and the finite element method was extended to two-dimensional configuration, and mode conversion to Bernstein modes was analyzed. For ion cyclotron range of frequencies, comparison of wave structures in two-ion hybrid resonance heating is carried out with conventional differential operator approach of the finite Larmor radius effects. For electron cyclotron range of frequencies, the O-X-B mode conversion in a small-size spherical tokamak is studied. Density dependence of wave structure and power deposition profile will be reported.   

Estimation of the O-X-B and X-X-B mode conversion rates with taking into account the electric field profile of the launched wave by using full wave analysis

The electron Bernstein (B) wave is excited via the mode conversion process from the slow extraordinary (SX) wave. Considering the wave launching from the low field side, mode conversions from the fast X (FX) and/or the ordinary (O) wave to the SX wave occur beyond the cutoffs before the X-B mode conversion. There are several analytic forms to calculate the O-X and/or X-X mode conversion rates considering the plane wave propagation in the slab geometry. However, in the experiments electromagnetic waves are launched by waveguide or quasi-optical antenna and cannot be assumed to be plain waves. We can calculate the electric field vector by the TASK/WF2D code that solves the Maxwell's equation by finite element method in the two-dimensional space. Plasma parameter profiles and the electric field profile at the calculation boundary can be input arbitrary. In addition to obtain a precise view of the wave propagation across the cutoffs, the O-X and/or X-X mode conversion rates can be estimated qualitatively from the Poynting fluxes of launched and transmitted/reflected waves. With introducing the kinetic full wave analysis using an integral form of dielectric tensor, the X-B mode conversion rate can be also estimated from the absorbed power of the B wave.   

\textbf{Measurement of ion energies in a magnetized RF sheath}

The interaction between an ion cyclotron resonant heating (ICRH) antenna and the near-field plasma can lead to rectified high-voltage sheath formation and subsequent material erosion on surfaces that are magnetically connected to the antenna. This issue is being studied in a magnetized plasma by measuring the ion energy distribution function (IEDF) on magnetic field lines that are connected to or pass near an RF-driven electrode that is inserted into an electron cyclotron resonant (ECR) plasma source. The 13.56MHz RF-driven electrode is DC grounded to simulate the RF potential that exists on the ICRH antenna surfaces. Microwaves at 2.45 GHz are used to produce hydrogen and helium ECR plasmas at densities of \textasciitilde 10$^{\mathrm{18}}$/m$^{\mathrm{3}}$, with T$_{\mathrm{e}}$ of 3-5 eV, in magnetic fields of \textasciitilde 0.1 T. A retarding-field energy analyzer is radially scanned to measure the spatial variation of IEDF profiles. Results show that the IEDF, measured 0.35 m from the electrode, becomes broader and extends to higher energies as the RF voltage increases. These results are compared to theoretical predictions of a magnetized RF sheath. Scaling as a function of RF-driven voltage and implications for material erosion on surfaces magnetically connected to an antenna will be presented.   

Coupling of Lower-Hybrid Full Wave and 3D Fokker-Planck Codes in Weak Damping Scenarios

In the simulation of lower-hybrid current drive in tokamaks ray-tracing is currently the workhorse simulation tool used to design experiments. However, ray-tracing has yet to be extensively validated against full-wave simulations. Due to recent advancements in computation it is now possible to simulate lower-hybrid wave propagation in medium-sized tokamaks by a direct solve of the wave equation after it has been Fourier analyzed for a single frequency. Simulations such as these are of significant interest since they are capable of simulating weak-damping scenarios in modern tokamaks where current ray-tracing techniques’ assumptions could possibly break down. However, calculations of the non-Maxwellian damping of the lower-hybrid wave requires an iteration between the full-wave solver and a 3D Fokker-Planck solver in order to self-consistently model the wave fields. Techniques for iteration between the TORLH full wave and the CQL3D Fokker Planck codes by coupling the two codes with a quasi-linear RF diffusion coefficient will be shown and the results of these iterations and their implications for lower-hybrid current drive theory will be discussed.   

Parasitic excitation of the slow mode by an ICRH antenna in the LAPD

Recent work on ICRF physics at the Large Plasma Device (LAPD) at UCLA has focused on deleterious near-field antenna effects, such as RF rectification, sputtering, convective cells and power lost to the plasma edge. Plasma parameters in LAPD are similar to the scrape-off layer of current fusion devices. The machine has a 17 m long, 60 cm diameter magnetized plasma column with typical plasma parameters $n_{e,core} \sim 10^{12} - 10^{13} \mbox{cm}^{-3}, T_e \sim 1 - 10 $ eV and $B_0 \sim 1 -2 $ kG. A single-strap fast wave antenna has been developed for LAPD, with the ability to rotate the angle of the strap with respect to the background field. This poster will focus on low power experiments, in which the parasitic coupling to slow waves in the low density region in front of the antenna is being studied. Detailed wave field measurements show coupling to both the short wavelength slow wave and the long wavelength fast wave if the density at the antenna is low enough. Coupling to lower hybrid waves was demonstrated for a range of normalized frequencies, from $1 < f / f_{ci} < 30$. The coupling was studied both with and without Faraday screen, as well as the dependence of the coupling on the angle of the antenna.   

Mitigation of RF sheaths with insulating side walls

A single strap, high-power ($\sim $150kW), RF (2.4MHz) antenna was used to study RF sheaths in a magnetized helium plasma with plasma parameters n$_{\mathrm{e}}$ \textasciitilde 10$^{\mathrm{18}}$ -- 10$^{\mathrm{19}}$ m$^{\mathrm{-3}}$, T$_{\mathrm{e}}$ \textasciitilde 1 -- 10 eV and B$_{\mathrm{0}}$ \textasciitilde 0.1 T. The experiment was conducted on the Large Plasma Device (LAPD). This presentation will draw a comparison between two experiments carried out at the LAPD with different antenna strap enclosures. The two different enclosure consisted of different materials for enclosure side walls- copper and electrically insulating, macor. Both experiments had similar plasma density, temperature, magnetic field and fast wave amplitude. In the case of the copper enclosure, formation of convective cells as a result of plasma potential rectification was observed and reported$^{\mathrm{1}}$. In the experiments with the macor enclosure we observe a lack of plasma potential rectification as well as no evidence of convective cells. The results are reminiscent to the results obtained in ASDEX-U with the 3-strap antenna optimized to reduce image currents on the antenna limiters$^{\mathrm{2}}$. $^{\mathrm{1}}$ M. Martin \textit{et al}, Phys. Rev. Lett. \textbf{119}, 205002 (2017) $^{\mathrm{2}}$ V. Bobkov \textit{et al}, Nucl. Fusion \textbf{56}, 084001 (2016)   

50 kV Klystron Driver for Fusion Science Applications

Eagle Harbor Technologies, Inc. (EHT) is developing a new, solid-state klystron driver for use in fusion science applications. EHT is using high-frequency SiC MOSFET-based full bridges, previously developed with support of the DOE SBIR program. These full bridges drive a resonant circuit that allows for zero current switching, reducing the stress on the solid-state switches. The high frequency operation allows a more compact system, which can be placed closer to the klystrons. The Phase I program focused on a demonstration of 50 kV operation with low output voltage ripple (\textless 1{\%}) and minimizing stored energy in the output filter (\textless 2 J). During a klystron fault, this energy is deposited into the klystron. Minimizing the stored energy is a more robust, passive solution that allows for the removal of additional switching components to protect the klystron. EHT will present the Phase I results. In a potential Phase II program, EHT will build and deliver a 50 kV, 600 kW klystron driver to MIT for testing.   

A Pulsed Magnetron Driver for the Lithium Tokamak Experiment

Eagle Harbor Technologies (EHT), Inc. has designed and built a pulsed magnetron driver that will be delivered to the Lithium Tokamak Experiment (LTX) at the Princeton Plasma Physics Laboratory. Earlier in the program, EHT developed and tested a 10-kV solid-state switch. To build the magnetron driver, EHT has stacked four of the 10-kV switches in series to achieve the 40-kV output. The driver can produce 40 kV for 5 ms and source up to 100 A. The rise time of the output pulse has been tailored for the specific magnetron at LTX. EHT has also developed short-circuit protection that will shut down the magnetron driver in less than 1 \textmu s. EHT will present results of the development of the pulsed magnetron driver during the Phase II program.   

Nonlinear electron cyclotron current drive by high intensity, pulsed, beams

There have been significant advances in the technology of high-powered microwave sources since free-electron lasers were used in the Microwave Tokamak Experiment (MTX) in 1990s. These advances have led us to reexamine nonlinear current drive by high intensity, pulsed beams. We have been studying the relativistic nonlinear interaction of electrons with Gaussian beams in the electron cyclotron range of frequencies. The Gaussian beam is analytically constructed so as to satisfy Maxwell's equations for a cold, magnetized plasma. The electrons are initially distributed homogeneously in space while having a Maxwell-Juttner distribution in momentum space. As the electrons interact with the beam, the components of their momenta, along and across the magnetic field, vary with beam power and its direction of propagation. The electron motion is affected by the ponderomotive force due to the spatial variation of the beam, and by trapping within the beam. Results for the gain in energy and momentum of the electrons, as a function of beam parameters and wave polarization will be presented. The impact of the ponderomotive force and of trapping on the efficiency of current drive is evaluated.   

Recent Results from the SciDAC Center for Simulation of Fusion Relevant RF Actuators

An overview is given of recent research results related to the self-consistent interaction of RF power with the scrape-off layer (SOL). We will discuss the development and application of RF wave solvers based on the open-source scalable Modular Finite Element Framework (MFEM), including the implementation of a RF sheath boundary, work on pre-conditioners for matrix solves, and grid adaptivity. We will discuss the development of a far-SOL fluid transport solver for equilibrium (Braginskii MFEM mini-app) and turbulent (SOLT-3D code based on BOUT$++)$ models. The turbulent transport model includes the presence of a RF ponderomotive force term which can be calculated directly from the results of the VSim FDTD plasma wave code. Results from full-wave RF solvers utilizing SOL turbulence data from an edge turbulence code will also be presented. Results in plasma-material-interactions will be presented on benchmarking of kinetic vs fluid sheath models, parameterization of a sub-grid RF sheath model, results from a 1D RF sputtering model, and results for fast ion impact at the plasma wall from an RF Monte Carlo code.   

Development of a scalable 3D full wave RF simulation (1): Petra-M platform

In this and the following paper, we discuss the recent progress in developing the scalable 3D full wave RF simulation in the RF SciDAC center. A goal of the center is to develop an integrated RF full wave simulation to accurately predict RF actuator performance. Such a simulation needs to include 1) RF wave propagation/absorption physics in hot core region, 2) SOL turbulence effects on the wave propagation 3) interactions with background plasma profiles, and 4) RF rectified potential formation and resultant impurity generation in a seam-less, integrated manner. As the simulation model involves multi-physics coupling in the complicated 3D SOL geometry, a highly scalable RF wave field solver is required. Petra-M (Physics equation translator for MFEM) is an open source FEM analysis platform based on the scalable MFEM finite element library, allowing for FEM analysis from geometry/mesh generation, FEM assembly, equation solution, and visualization. Petra-M has been used for modeling various RF plasma wave problems in fusion devices including C-Mod, DIII-D, LAPD, and NSTX. It is also used on non-RF problems, such as the quench dynamics on HTS magnets. In this paper, we discuss the code structure and various capabilities Petra-M provides.   

Development of a scalable 3D full wave RF simulation (2): Applications to NSTX-U/LAPD/C-Mod/DIII-D

In this paper we report on the main applications of Petra-M, a recently developed open source code, based on the scalable MFEM C++ finite element library (see previous paper), on different experiments, such as NSTX-U, LAPD, Alcator C-Mod, and DIII-D. The first full torus 3D HHFW simulations for NSTX-U plasmas including the SOL region with realistic antenna geometry and core plasma is presented. A scan of the antenna phasing is performed showing a strong interaction between FWs and the SOL plasma for lower antenna phasing. A first attempt to couple the 3D RF solver with the full-orbit following particle code SPIRAL will be discussed with the aim to show the impact of the effect of the 3D wave field on the fast ion population from NBI beams in NSTX-U. An initial comparison between Petra-M simulations for a HHFW 4-strap antenna mounted on LAPD and its RF wave field measurements for LAPD plasma shows a qualitative agreement in the magnetic wave field pattern. The integration of TORIC hot core wave physics model with Petra-M was demonstrated using the Alcator C-Mod field-aligned ICRF antenna, showing the toroidal mode coupling. Petra-M models DIII-D HFS launcher to verify the RF antenna design based on smaller simplified models computed using COMSOL.   

Simulation Workflow for Adaptive High-Performance FR Fusion System Simulations

Accurate RF simulations of fusion systems like ITER require the definition of high-fidelity analysis geometries that include detailed antenna, reactor wall and physics region representations. This poster will describe a workflow for the execution of adaptive high-performance FR fusion system simulations. The steps in the simulation workflow include; defeaturing of un-needed details from antenna CAD models; combining the antenna, reactor wall and physics components into a single analysis model geometry; applying physical attributes to the analysis model; automatically generating a graded mesh; and executing an adaptive finite element analysis that includes the application of a iterations of finite element solve, a posteriori error estimation, and mesh enrichment.   

Scattering of radio frequency waves by plasma turbulence

In order to optimize the heating of plasmas, or the generation of non-inductive plasma currents, it is necessary to assess the effect of edge turbulence in fusion devices on the propagation of radio frequency (RF) waves. We will present a set of theoretical and computational studies that model the propagation of RF waves through turbulent plasma. The theoretical models are mathematically tractable, and provide physical and intuitive insight into the scattering phenomena. The computational studies provide support for the theoretical models. We use two complementary approaches - geometrical optics and physical optics - for magnetized plasmas with a tensor permittivity. The former, an approximation to the latter full-wave approach, illustrates several important physical aspects of scattering. The physical optics method is the basis for studying scattering from blobs and filaments. Besides refraction and reflection, the spatial uniformity of power flow into the plasma is affected by side-scattering, diffraction, shadowing, and interference. Also, the incident wave can couple power to other plasma waves in the presence of fluctuations.   

Generalization and Verification of RF Sheath Microscale Models

RF sheaths in the ICRF range of frequencies are studied on the micro- (Debye length) scale with the goal of improving the RF sheath boundary conditions used in macroscale global RF wave codes. Previous microscale models based on nonlinear fluid theory are extended in parameter space to higher frequencies for oblique magnetized sheaths that carry net DC current. Results for the rectified (DC) sheath potential and sheath impedance are compared with PIC simulations from the hPIC and Vorpal codes. In addition to their role in verification, the PIC codes also provide additional information such as the role of finite ion temperature, sources and the particle impact energy and angle distributions for sputtering and surface interaction physics.   

Development of Impedance Sheath Boundary Conditions in Finite Element RF Codes

Ion cyclotron radio frequency range (ICRF) power plays an important role in heating and current drive drives in fusion devices. Experiments show that in under the ICRF regime there is a formation of a radio frequency (RF) sheath at the material and antenna boundaries that influences sputtering and power dissipation. Given the size of the sheath relative to the scale of the device, it can be approximated as a boundary condition (BC). RF codes, like the MFEM-based [http://mfem.org] finite element code Petra-M (Physics Equation Translator for MFEM)~\footnote{S. Shiraiwa et al., EPJ Web of Conference Services 157, 03048 (2017)}, implement a conducting wall as this BC, however the use of a finite impedance sheath BC based on the work of J. Myra 2015~\footnote{J. Myra et al., Phys. Plasmas 22, 062507 (2015)} provides a more accurate representation of the RF sheath. This research will discuss the results from the development of a parallelized cold-plasma wave equation solver that implements this sheath impedance BC through the method of finite elements in pseudo-1D and pseudo-2D using the MFEM library with the eventual aim to incorporate the same BC into Petra-M.   

Using Ponderomotive Force from the VSim RF Code in the SOLT3D and NIMROD Codes

The VSim software [1] is a fast time-scale time-domain code that can be used to model accurate 3D antenna geometry, and the coupling to, and propagation of RF energy in fusion plasmas. It now computes a Ponderomotive Force source term intended for use in slow time-scale codes for equilibrium and turbulence calculations. This includes source terms for electron and ion momentum equations, and also source terms for the vorticity equation, in addition to the more typical energy source terms. In this paper we look specifically at coupling to the SOLT3D code built on the BOUT$++$ framework [2], and the NIMROD code[3]. We discuss the various data formatting and mesh interpolation issues relating to transferring data between VSim and these codes. We are primarily interested in applications of the codes to tokamak configurations with ICRF, helicon, and/or LH RF sources, and we look at examples of these cases. The analysis includes tensor force terms contributing in both the poloidal plane and in the toroidal plane. [1] Nieter and Cary, Journal of Computational Physics 196(2):448--473 (2004). [2] Umansky et al., Computer Physics Communications 180, pp. 887-903 (2009). [3] Sovinec et al., Journal of Computational Physics, 195, 355 (2004).   

Modeling LH wave refraction through SOL blobs using synthetic turbulence data

Lower hybrid (LH) waves are an efficient means to drive off-axis current in a tokamak. LH wave and scrape-off-layer (SOL) interactions may affect wave propagation, leading to altered core power absorption and decrease in current drive (CD). Previous wave-scattering models assume non-intermittent turbulence and have yet to explain experimental measurements of CD efficiency. Synthetic SOL turbulence that account for intermittent blob-like structures [1] is coupled to the ray-tracing/Fokker-Planck model GENRAY/CQL3D. In a slab geometry, refraction through blob-like turbulence is shown to result in increased wave scattering compared to previous models. This model is next used to study the effects of SOL refraction on power deposition and CD in an Alcator C-Mod geometry. Initial results show that the presence of SOL blobs lead to broadening of the power deposition profile caused by refraction at the edge and the subsequent change in evolution of $N_{||}$. Increasing blob packing fraction and density can also decrease fraction of LH power coupled to core, implying waves are trapped in the highly collisional SOL. [1] J. M. Sierchio et al., RSI. 87, 023502 (2016).   

Including RF Antenna Effects in Scrape-Off-Layer-Turbulence Simulati\textbf{ons}

Capabilities for including RF-sheath boundary conditions and ponderomotive forces associated with RF launching structures on turbulent solutions such as those from SOLT3D, a 3D BOUT$++$-based extension of the SOLT model [1], are being developed. Inclusion of ponderomotive effects involves a straightforward implementation of appropriate source terms in the model equations. The simplest implementation of RF-sheath boundary conditions involves regions on the outer flux surface biased at an effective potential relative to other parts of the surface and other boundary surfaces. In order to apply this capability to more complicated domains, e.g., with indentations representing antenna and shielding structures and boundaries not conformal with flux surfaces, a Finite-Element-Method (FEM) calculation of steady solutions of the SOLT3D model has been implemented. The values of fields on a flux surface in the FEM-based solutions can be used as boundary conditions in SOLT3D or other BOUT$++$-based simulations. Progress on developing such a simulation workflow will be discussed, and results from verification studies and initial simulations will be presented. [1] J. R. Myra, D. A. Russell, D. A. D'Ippolito, Phys. Plasmas \textbf{15}, 032304 (2008)   

Adaptive time-stepping in fusion plasma simulations with MFEM

The simulation of magnetized plasma transport using the fluid approximation is ubiquitous in the study of fusion devices. However, the extreme anisotropy of the diffusion coefficients and their non-linear dependence on state variables make time-step selection both very important and non-trivial. The nature of the diffusion equation suggests that small time-steps are needed whenever small scale structure must be captured by the simulation and much larger time-steps can be appropriate as the solution approaches a steady state. Unfortunately, the non-linear character of the diffusion coefficients make these general rules-of-thumb difficult to use in practice. We investigate time-step selection based on a proportional-integral-derivative controller (PID controller) which is a type of feedback control system. The controller makes use of an estimate of the solution error and attempts to choose the largest time-step which restricts this error below some target. Here we present progress on using this technique coupled with a high-order finite element simulation of a non-linear advection-diffusion transport equation.   

A 1.5D coupled RF / transport model for ponderomotive density modification of the SOL near high power RF actuators.

Efficient coupling of RF power to a magnetically confined fusion plasma is essential for robust operation of future devices (e.g. ITER). The scrape off layer density profile directly affects RF wave propagation, where the RF waves themselves can also modify the plasma density via the ponderomotive force. A 1D (parallel to the confining magnetic field), coupled full-wave RF and plasma transport solver was previously developed. Here we present an extension of this work via the inclusion of perpendicular components of the ponderomotive force in a 1.5D plasma transport code. Simulation results are compared with experimental data from the LArge Plasma Device (LAPD). The description of perpendicular flows driven by the ponderomotive force necessitates extension to higher dimensions, and progress on the development of this capability will be discussed.   

CQL3D Simulations of Suppression of Impurity-Induced Current Quench Using LH Current Drive in C-Mod

In C-Mod lower hybrid current drive experiments (LHCD), Reinke [1] has examined rare discharges which undergo an abrupt thermal quench (TQ) to low Te due to radiation from incoming tungsten flake material. Surprisingly, the TQ did not lead to a runaway electron (RE) current quench (CQ) which normally would be expected to follow the TQ. Rather, the plasma toroidal current continued at its pre-TQ value without large enhancement of the toroidal electric field, implying the LH is instrumental in maintaining the current. We simulate the driven LHCD and compare with experiment using the CQL3D Fokker-Planck code [2] with GENRAY ray tracing and LH collisional damping, based on experimental traces of the background densities, temperatures, Zeff, and one-turn voltage. Self-consistent internal toroidal electric field is included. A major problem for this theory to explain is how the very large spectral gap between the c\textunderscore light/2 injected LH wave and the post TQ plasma with Te \textless 50 eV, is filled, thereby driving LH current? [1] M.L. Reinke, S. Scott, R. Granetz, et al, Nucl. Fusion 59 066003 (2019). [2] R.W. Harvey and M.G. McCoy, ``The CQL3D Fokker Planck Code,'' \underline {www.compxco.com/cql3d.html}.   

The Centrifugally-Confined Mirror Machine as a Fusion Reactor

There is renewed interest in the broader fusion community for examining alternative routes to fusion reactors. Here we present a new look at one promising configuration -- the centrifugally-confined mirror. Initial explorations of this concept were performed on the Maryland Centrifugal Experiment (MCX) [Ellis et. al. Phys. Plasmas 8, 2057]. These experiments demonstrated sustained supersonic rotation and good momentum confinement [J. Ghosh et. al. Phys. Plasmas 13, 022503]. This is a promising concept because of its simple magnetic configuration, low recirculating power, and long-pulse capability. We present theoretical analyses of a reactor design based on this concept. We provide kinetic equilibrium calculations including collisional end-losses and magnetic equilibria that incorporate the effects of both supersonic rotation and pressure anisotropy. We also calculate profiles based on classical confinement of particles, heat, and momentum. Confinement of and self-heating by fusion products is taken into account in these calculations. With these theoretical tools, we design a reactor operating point. We present both a high-density, high-temperature design and a conservative design. We use these to predict the most important physics for a next-step experiment to resolve.   

Progress on the Madison Mirror Helicon

The Madison Mirror Helicon (MadMiriCon) is revitalizing US mirror research with possible applications in fusion research, basic plasma physics and as a cost-effective neutron source for medical isotope production and fusion material testing. The plasma is confined inside a quartz tube connected to stainless steel expansion tanks on both ends with a total plasma length of 3.5 m and a central plasma diameter of 7 cm. Fully steady-state plasmas are created using a right-handed helicon antenna at 10 kW RF power. The solenoid guiding field can reach 0.3 T and has very strong flaring inside the expanders. Experimental goals include demonstration of MHD stability in a plasma with strongly magnetized ions and high electron temperature and density, suitable for NBI absorption. We give an overview of how to achieve 10 kW input power while maintaining control over the various machine subsystems and diagnostics in a high EMI environment. Efforts to stabilize the helicon mode in lieu of the strong field flaring are shown. We present measurements for electron density scaling with RF power and magnetic field and a comparison to the helicon dispersion relation. An outline of upcoming developments, e.g. installation of two 15-20 Tesla range HTS mirror coils is given.   

Study of an axisymmetric mirror-based volumetric neutron source

A dedicated neutron source is required to develop and test materials with both a long lifetime and minimal activation when subjected to a high neutron flux. We revisit the long-studied magnetic mirror concept for this application, including recent breakthroughs in both physics (stable high $\beta$, high Te plasmas in the GDT) and technology (high fields produced by HTS coils). Stability is achieved by a combination of plasma escaping the mirror into a region of good magnetic curvature, sloshing fast ions, and non-paraxial end cell effects. Plasma heating and fueling is via neutral beam injection at modest energy (25kV); synergistic application of high-harmonic fast waves that damp primarily on the beam ions dramatically increases the fusion neutron yield. Electron temperature is a key parameter in fusion yield; studies of 110GHz ECH show complete absorption of fundamental X mode high field side launch. With the expected 2MW of available power, a large range of Te is available and allows fusion neutron flux exceeding $10^{13}$ n/s before $\beta=1$ is reached. A higher field central cell is investigated for achieving materials-testing-relevant fusion flux levels.   

Diagnostic Development for the Lockheed Martin Compact Fusion Reactor Project

The T4B experiment is a linear, encapsulated ring cusp confinement device, designed to develop a physics and technology basis for a follow-on high beta machine as part of the compact fusion reactor program. Three non-invasive laser diagnostics have been developed to investigate confinement, neutral beam heating, and source behavior on the T4B device, including (1) a Thomson scattering system employing a 532 nm Nd:YAG laser to measure electron density and temperature, (2) a dispersion interferometer utilizing a continuous-wave CO2 laser (10.6 $\mu $m) to measure time resolved, line-integrated electron density and (3) a dispersion interferometer utilizing a continuous-wave, 532 nm Nd:YAG laser to measure time resolved, line-integrated electron density. An overview of laser systems, detection schemes, and data analysis techniques is presented, including up to date results obtained from the T4B experimental campaign. We also present a suite of non-invasive diagnostics for the T4B experiment looking at several aspects of the plasma performance including plasma emissions (bolometry, spectroscopy), stability, and magnetic field perturbations. \copyright 2019 Lockheed Martin Corporation. All Rights Reserved.   

\textbf{Neutral Beam Development for the Lockheed Martin Compact Fusion Reactor }

The Compact Fusion Reactor project at Lockheed Martin Skunk Works is developing a neutral beam injection system for plasma heating. The neutral beam plasma source consists of a high current lanthanum hexaboride (LaB6) hollow cathode which drives a ring cusp discharge similar to gridded ion thrusters. The beam is extracted with a set of focusing grids and is then neutralized in a chamber pumped with Titanium gettering. The design, testing, and analyses of individual components are presented along with the most current full system results. The design and development of an imaging calorimeter for beam profile characterization is also presented. The goal of this project is to advance in-house neutral beam expertise at Lockheed Martin to aid in operation, procurement, and development of neutral beam technology. \copyright 2019 Lockheed Martin Corporation. All Rights Reserved.   

Plasma Source Development for Lockheed Martin's Compact Fusion Reactor Program

A multipronged plasma source development effort supports the Lockheed Martin Compact Fusion Reactor (CFR) program. The objective of the plasma source development effort is to build a plasma source that can provide a sufficiently dense plasma target for neutral beam heating in the CFR geometry (a linear encapsulated ring cusp). An ideal source would allow for high mirror ratios in the expansion regions (divertors) of the device, have a very high ionization fraction, have very low impurity levels, and create sufficiently dense plasma (\textgreater 5 x 10$^{\mathrm{19}}$ m$^{\mathrm{-3}})$. In addition to the arc-reflex thermionic source currently employed on the T4B linear encapsulated ring cusp experiment, we are developing three alternative technologies: a high power (\textgreater 2 MW) MagnetoPlasmaDynamic source (MPD), a cross-field (ExB) homopolar type source, and a high power (\textgreater 300 kW), high field (up to 1 T) RF source. We present the performance of these high power plasma sources and plans for incorporation onto the next experiment, T5. \copyright 2019 Lockheed Martin Corporation. All Rights Reserved.   

Magnet Support Shielding for T4B

The linear encapsulated ring cusp topology of Lockheed Martin's Compact Fusion Reactor (CFR) concept requires electromagnetic field coils internal to the plasma. These coils have supports that pass through the confined plasma volume. To reduce plasma losses and protect the coil supports, we are pursuing magnetic guarding. While magnetic guarding can invariably reduce plasma losses directly to supports, magnetic guard fields introduce cross-field plasma drifts (predominately grad B drifts). Depending on the ratio of the guard field to background magnetic field, these drifts can be negligible or become dominant loss mechanisms. As part of the T4B experimental campaign, various forms of magnetic guarding have been investigated. We present the experimental results for prototype magnetically guarded supports and demonstrate total plasma loss reduction due to the supports of greater than 55{\%} in comparison with unshielded supports. \copyright 2019 Lockheed Martin Corporation. All Rights Reserved.   

Simulation Support of the T4B Experiment

The Lockheed Martin Compact Fusion Reactor concept utilizes magnetic cusps to confine plasma. Simulations are carried out in support of the T4B experiment. Grad-Shafranov simulations are used to explore equilibrium stability. PIC simulations are conducted to understand the evolution of particle distribution functions, neutral beam heating efficiency and plasma confinement. Zero-Dimensional models are used predict plasma evolution. Finally, collision radiative models are used to determine plasma density and temperature. \copyright 2019 Lockheed Martin Corporation. All Rights Reserved.   

Hybrid Simulations of Low-frequency Oscillations in Field-Reversed Configurations

We report on progress in developing a kinetic-ion, fluid-electron simulation code to simulate low-frequency ($\sim \omega_{ci}$) phenomena in field-reversed configuration (FRC) plasmas. The code retains inductive and electrostatic fields, but neglects radiation and advances electrons implicitly to allow for longer timesteps. The phenomena of interest include fast-ion-driven Alfvenic modes as well as the interaction of an FRC with an external rotating magnetic field (RMF).   

Particle simulation of field reversed configuration

We have developed a GTC-X code (based on GTC) to study global turbulent transport in FRC. A coupled simulation of scraped-off-layer (SOL) and core regions is realized in the code with the help of a carefully designed grid system, and the ITG instability in SOL has been verified. Drift kinetic electron (DKE) model has been implemented to understand the influence of trapped electrons on drift waves. We will implement the gyroaveraging algorithm as in previous GTC code and study the influence of radial electric field to the linear ITG mode. Furthermore, to simulate high frequency waves, we have developed a fully kinetic ion (FKI) model to examine the weak magnetic field region and the beam ions. Finally, we have derived the self-consistent equations for FKI with fluid elections, which is used to produce the numerical equilibrium ion distribution of FRC in GTC-X.   

Development of Integrated Modeling for Field-Reversed Configuration Design

An integrated modeling suite for Field-Reversed Configuration (FRC) design is being developed at ENN, consisting of (1) coils and magnetic field design module; (2) fixed and free boundary MHD Grad-Shafranov equilibrium solver; (3) nonlinear 2D resistive MHD solver; (4) 1D linear gyrokinetic drift instability code; (5) magnetic and liner compression module; (6) 1D Finite-Lamor-Radius (FLR) and 2D MHD linear instability solvers; (7) single particle full kinetic orbit solver; and (8) other fusion relevant modules. In addition to these modules listed above, a powerful general kinetic dispersion relation solver BO [H. S. Xie , BO: A unified tool for plasma waves and instabilities analysis, Computer Physics Communications, 2019, https://doi.org/10.1016/j.cpc.2019.06.014.] has also been developed to study the physics issues in FRC, such as the high frequency loss-cone instability and lower-hybrid drift instability in FRC.   

Status and plans for the PFRC-2 device

The PFRC-2 is magnetized, steady-state, RF-heated plasma device on which research is performed to develop small, clean fusion reactors suitable for mobile power plants or propulsion of spacecraft throughout the solar system. With a duty of factor near 1{\%}, the PFRC-2 forms high-beta plasmas of up to 300 ms duration and radius to 8 cm with line-average electron density exceeding 5e12/cc and a minority electron temperature exceeding 600 eV. Up to 70 kW of RF heating power at 6 MHz has been applied using the RMF\textunderscore o method. The present maximum vacuum magnetic field is 300 G. Plans for the next year focus on ion heating to an average energy of 600 eV at a peak density of 1e13/cc. To achieve this, the vacuum magnetic field will be increased to in excess of 600 G, the RMF frequency reduced to below 2 MHz, and the RMF power increased to 200 kW corresponding to B\textunderscore RMF $=$ 15 G. At these parameters stochastic ion heating is predicted.   

Energy-dependent electron heating processes during high-power operation of the PFRC-2 experiment, as obtained using inversion of X-ray spectra

As part of an experimental program to investigate ion heating via odd-parity rotating magnetic field (RMF-O), the PFRC-2 device was operated at lower frequency and higher power to achieve higher density and enhanced electron heating. The electron heating was measured by SDD pulse-height x-ray detectors in multiple locations. These experiments have produced minority populations of electrons whose effective temperature -- to above 600 eV -- is many times larger than previously reported. The predicted classical ion heating by these warm and the cooler bulk electrons is evaluated. Also, the energy distribution functions of these electrons disagree with that expected from a single-particle Hamiltonian model, indicating collisional or collective effects affecting electron heating. By using a previously described Poisson-regularized spectral inversion to obtain full Electron Energy Distribution Functions (EEDFs) from x-ray pulse-height spectra, we are able to characterize these processes in an energy-resolved way.   

Density and magnetic flux measurements on the PFRC-2

Understanding the core plasma of the PFRC-2 is essential to achieving ion heating. Line-integrated density from a 170~GHz microwave interferometer and excluded magnetic flux from an axial array of diamagnetic loops allow a detailed look at the time evolution of the core plasma and magnetic field strength during a rotating magnetic field (RMF) pulse. We have measured the variations in time of density and excluded flux with the axial magnetic field, the RMF power, and the neutral fill pressure. At the midplane, excluded flux values to 2 $\mu$Wb have been observed, consistent with an FRC with separatrix radius ranging from 2 to 5~cm in an axial magnetic field of 75~G. The plasma current is then estimated as 500~A. The hot electron densities and energies obtained via x-ray diagnostics broadly agree with the flux measurements. The evolution of discharges shows periodic and well as chaotic density behavior, correlated with the flux measurements.   

Spectroscopic Line Ratio Determination of Electron Density, Electron Temperature, and H$_2$ Dissociation Fraction in PFRC-2 Pulsed Hydrogen Plasmas

The degree of H$_2$ dissociation in a hydrogen plasma affects the relative intensities of H I spectral lines and is therefore an important parameter in the interpretation of H I spectra. Line ratio spectroscopy using an iCCD spectrometer and a high time resolution monochromator is used to determine the electron temperature, electron density, and degree of H$_2$ dissociation in PFRC-II pulsed hydrogen plasmas. Ratios of impurity helium I spectral line intensities yield measurements of the electron temperature and density via a collisional-radiative (CR) model.\footnote{S. Sasaki, S. Takamura, S. Watanabe, S. Masuzaki, T. Kato, and K. Kadota, Review of Scientific Instruments \textbf{67}, 3521 (1996).} Similar CR calculations for hydrogen then relate the observed Balmer line ratio H-$\beta$/H-$\alpha$ to the degree of H$_2$ dissociation.\footnote{T. Fujimoto, K. Sawada, and K. Takahata, Journal of Applied Physics 66, 2315 (1989).} Results are presented at various axial and radial positions in the plasma as parameters such as RF input power, axial magnetic field, and initial gas pressure are varied.   

0.2-10 keV X-Ray measurements on the PFRC-2: EEDF, heating, and confinement

Time and spatially resolved X-Ray spectra from odd-parity RMF-heated hydrogen plasma in the PFRC-2 were obtained with in-house-calibrated silicon-drift detectors (SDD). Both Bremsstrahlung and line radiation were observed. Maxwellian-fit electron density and temperature were extracted from the Bremsstrahlung segment of the spectra using a Poisson-regularized inversion method. Temperatures of a minority component exceeded 600 eV. The rate-of-rise of the electron energy was used as a proxy for the effectiveness of the heating process and quality of confinement. Line emission showed the presence of carbon, oxygen, iron, and nitrogen. The brightness values of these line emissions were sensitively dependent upon applied magnetic field strength, gas fill pressure, pumping method, and boundary conditions.~Conditions were found where the SDD viewing through the axial midplane of the plasma measured an X-ray brightness as much as 100x greater than that measured by an SDD viewing 5 cm away from the midplane. Possible causes, including non-uniform electron energization, plasma shape changes, and plasma-wall interactions, for this disparity are discussed.   

A feasibility study of RFX-mod2 tokamak equilibria scenarios with DEMO-like shape conditions and negative triangularity

RFX-mod device has been operated as circular and shaped tokamak. An upgrade of the machine assembly is now being implemented, dubbed RFX-mod2. The vessel will be removed, graphite tiles will be attached to the stabilizing shell and the support structure will be vacuum tight. Thus, shell-plasma radius ratio decreases and the shell will be the conducting structure nearest to the plasma. An improved diagnostic system would allow a better control of both plasma shape and H-mode transition. We present a feasibility study on new operational scenarios with the aim of increasing plasma performances by acting on the plasma shape. Thus, new D-shaped plasma equilibria with DEMO-like plasma shape parameters (i.e. $\delta $\textgreater 0.3, $\kappa $\textgreater 1.5) are investigated with the IET (Inverse Equilibrium Tool) code, including the option of single/multiple X-points. In the same way, we investigated the possibility of reversing the triangularity of such plasmas. Thanks to its engineering flexibility, RFX-mod2 would allow to explore a wide window of shape parameters with low requirements on active coil currents.   

Study on Stabilization of Plasma Vertical Position of Tokamak Plasma with Local Helical Coils in TOKASTAR-2

Elongated plasmas are suitable for the high beta values and high confinement in tokamaks, but suffer from vertical positional instabilities, leading to Vertical Displacement Event (VDE). Helical magnetic field is thought to provide improved positional stability TOKASTAR-2 is a tokamak-stellarator hybrid device with local helical coils The shape and arrangement of the local helical coils are simple. We found that the existing helical coils were effective on stabilization of the plasma horizontal position but not effective on the vertical position in plasma experiments. Thus, to improve the effects on the vertical positional stability, we plan to install new local helical coils. We designed the new coils using magnetic field line tracing calculation. The effective radial magnetic field generated by the helical coils acts as restoring force, which is expected to stabilize the plasma vertical position. The effective radial field can be obtained by using triangular coils on upper and lower sides of the plasma. The magnitude of the effective field depends on the shape and position of the coils. In the meeting, optimization of the new coils and influence of the installation and manufacturing error of the coils will also be presented.   

Robust analysis of space-, time-, and energy-resolved soft x-ray measurements on MST

A multi-energy soft x-ray diagnostic has recently been installed on the MST reversed-field pinch. Based on a novel calibration of the commercially available ~100,000-pixel PILATUS3 100K detector, this diagnostic can simultaneously sample the SXR spectrum with a unique combination of spatial and spectral resolution. This allows for simultaneous 2D imaging of impurity and $T_e$ structures using SXR emission. Such a capability is valuable in MST due to the presence of bright H- and He-like Al ions with excitation lines ~2 keV, making straightforward measurements of the bremsstrahlung continuum difficult. Data is presented for two distinct MST plasma scenarios: (1) improved confinement, where $T_e$ can reach up to 2 keV, and (2) quasi-single helicity, a 3D state which occurs when the $n=5$ tearing mode grows to dominate the magnetic spectrum. Interpretation of the data is aided by a forward model which considers the underlying atomic physics, geometry, and detector response. Using this model, along with complementary data from the existing diode-based tomography diagnostic, a framework is developed for interpreting ME-SXR data in terms of the underlying temperature and density profiles. The time evolution of these profiles is explored in both plasma scenarios. Supported by US DOE.   

Anisotropic fast ion distribution generated by magnetic reconnection in MST plasmas

While reconnection-driven ion heating is common in laboratory and astrophysical plasmas, the underlying mechanisms for converting magnetic to kinetic energy remains an incompletely solved problem. This work focuses on the particular case of reversed field pinch plasmas, which are often characterized by rapid ion heating during impulsive reconnection that governs the magnetic equilibrium. Comparison of NPA-measured slices of the distribution's tail and global neutron flux with the output of Fokker-Planck modeling confirms several new details. Due to poor confinement of thermal ions, ion heating at magnetic reconnection events typically dissipates within a millisecond. However, successive bursts of reconnection can repeatedly heat thermal ions before they can fully equilibrate, until a small fraction of thermal ions reaches a phase space of good confinement on the order of 20 milliseconds. These well-confined fast ions also experience less friction and are susceptible to runaway from inductive electric fields parallel to the plasma current. Fast ion acceleration reinforced by low diffusivity can create an anisotropic fast ion distribution that produces modest amounts of fusion neutrons without the aid of external heating. Work supported by DOE.   

Measuring fluctuation-driven Poynting flux and dynamo EMF in a reversed-field pinch plasma

In a reversed-field pinch driven by a toroidal electric field, the equilibrium profile is sustained by a net fluctuation-induced ‘dynamo’ EMF. Coherent fluctuations in electric and magnetic fields also result in an outwardly-directed Poynting flux. In the experiments reported on here, insertable edge probes are used to measure the dynamo EMF and Poynting flux associated with these coherent fluctuations. Our results indicate that this outward flux is a significant fraction of the total input power, peaking during discrete magnetic relaxation events (or sawtooth crashes). The flux reaches a maximum near the magnetic reversal surface, suggesting that electromagnetic energy is deposited there. The dynamo EMF measured in the edge balances Ohm’s law. As measurements are made at deeper insertions, the dynamo term changes sign as predicted, though the transition occurs closer than expected to the magnetic reversal surface.   

Turbulent Dissipation and Anomalous Viscosity in MST Reversed Field Pinch Plasma.

During the sawtooth cycle in MST RFP plasmas, tearing mode magnetic fluctuations with $m \quad =$ 1, $n \quad =$ 5-10 are linearly unstable and grow to 2-3{\%} of the mean magnetic field. Through nonlinear coupling this growth culminates in a strong reconnection event and broad spectrum extending to the ion gyroradius scale. An insertable magnetic probe is used to measure the equilibrium magnetic field and the poloidal and toroidal components of magnetic fluctuations. Using two-point correlation techniques the fluctuation power spectrum $S(k_{per})$ is measured in the plasma edge for $r/a$ from 0.75 to 0.96. The magnetic fluctuation spectrum evolves over a sawtooth cycle. Away from the reconnection event, dissipation is limited and the spectrum is nearly a pure power law. At the reconnection event, the spectrum has an exponential component that causes deviations from a power law above a dissipative wavenumber $k_{d}$. For $r/a \quad =$ 0.81 $k_{d}_{\mathrm{\thinspace }}=$ 0.8 cm$^{\mathrm{-1}}$ implying dissipation that is too large to be classical, but is consistent with anomalous viscosity. The corresponding anomalous viscosity is 36 m$^{\mathrm{2}}$/s consistent with a previous measurement of anomalous viscosity from plasma flow damping. The power spectrum, radial profiles of $k_{d}$, and the connection to observed ion heating during reconnection will be presented.   

Measuring Lundquist number scaling in MST RFP plasmas

MHD turbulence appears in both natural and magnetic confinement settings, such as the solar wind, self-organization dynamics in the RFP and spheromak, and current disruptions in tokamak plasmas. Here we describe parameter scaling experiments aimed at understanding the underlying nonlinear MHD dynamics using RFP plasmas. Data have been gathered spanning the accessible parameter space in MST, from Lundquist number,$ S \sim 10^4 –- 10^7$, mainly along three constant ratios of line-averaged electron density to Greenwald density. A programmable power supply allowed data collection at low $S$, which overlaps with parameters available in numerical modeling, and quantitative comparisons will be made with results from the nonlinear MHD codes DEBS and NIMROD. Diagnostics utilized include the magnetic field coil array, Thomson scattering, far-infrared interferometry, charge exchange recombination spectroscopy, and soft x-ray diagnostics. High current data will be used to infer the effective charge state, $Z_{eff}$, on which S depends, via an integrated data analysis technique. $Z_{eff}$ can then be scaled as appropriate at lower currents. This data set is one of the most extensive gathered for an RFP and will be accessible for future studies.   

Compressional Fluctuations in Pair-Plasma Microturbulence

Pair plasmas have received renewed interest since their relevance to astrophysical objects has been supplemented by recent as well as planned experiments. One instability driven by pressure gradients in magnetized plasmas that also applies to pair plasmas is the Gradient-driven Drift Coupling (GDC) mode, which relies on the interplay between electrostatic and parallel magnetic fluctuations. By means of electromagnetic full-$f$, fully kinetic simulations, it is shown that, while exact pressure balance of the equilibrium stabilizes this mode, realignment of the background magnetic field occurs on a much slower time scale than that by which the GDC instability is able to excite turbulence and thereby flattens the driving pressure gradient. Thus, systems not initially in balance can exhibit GDC turbulence, and systems in flux but maintaining the pressure gradient may sustain it for longer times, with consequences for an array of physical systems. Laser-generated electron-positron plasmas moving through a magnetic field are likely unable to achieve force balance, and inherent density gradients will cause fluctuations and fluxes to appear and influence plasma dynamics on short time scales.   

Particle Confinement in a Relaxed Taylor State

We present properties of protons confined in a self-organized, helical ``Taylor state'' magnetic field (Beltrami field). Despite the lack of axisymmetry, a significant fraction of the particles are confined and there is evidence of confinement surfaces. Particle confinement has been studied extensively in most magnetized plasma equilibria that can be produced in the laboratory. Very little, however, is known about the confinement properties of the minimum energy force-free equilibrium in an elongated cylinder (Taylor helix or Taylor state). We construct minimum-energy solutions to the force-free equation $\nabla\times\vec{B} = \lambda \vec{B}$ using the PSI-Tet eigenvalue solver and integrate the proton equations of motion using a Boris stepper. Initial results indicate that the fraction of particles confined by the Taylor state magnetic fields is similar to the fraction confined by the well-studied spheromak configuration. Using a large ensemble of initial conditions, we construct statistical characterizations of the particles that remain confined in the Taylor state and those that escape. We also give examples of trajectories that indicate the presence of confinement surfaces and demonstrate progress towards identifying these surfaces.   

Estimating the Taylor Microscale and Magnetic Reynolds Number Through Two-Point Correlations in a Turbulent Laboratory Plasma

The Bryn Mawr Experiment (BMX) is a new experiment at the Bryn Mawr Plasma Laboratory (BMPL) investigating magnetic turbulence using the injection of helicity with a magnetized coaxial gun source into a flux conserving cylindrical wind-tunnel. This presentation represents the first BMX results of MHD turbulence properties. Here, spatial correlation analysis of magnetic fluctuations is used to estimate outer and inner scales of the inertial range of the energy cascade. With these estimates a magnetic Reynolds number is calculated. The spatial correlation scale and the Taylor microscale are used as the outer scale and inner scale respectively.   

A Numerical Study of Turbulence in the Swarthmore Spheromak Experiment

The Swarthmore Spheromak eXperiment (SSX) provides an excellent opportunity to examine the nature of the turbulence that pervades the universe in a controlled, laboratory environment. Plasma in SSX arises during the helicity injection process of a coaxial plasma gun in a process originally developed in the formation of spheromaks and field-reversed configurations. Since the plasma is not confined by a background magnetic field, the internal fields evolve self-consistently and are allowed to be dynamic and turbulent. Global magnetohydrodynamics (MHD) and Hall MHD simulations of SSX have been performed using the HiFi simulation code, providing insights into the global evolution and relaxation of the turbulent plasma. However, SSX, like many plasmas in the universe, is in a moderate to weakly collisional regime, necessitating a kinetic approach to fully characterize the plasma. Therefore, we present a study of the turbulence in SSX using a combination of HiFi global simulations and the fully kinetic Eulerian Vlasov-Maxwell component of the Gkeyll simulation framework. In this study, we leverage the pristine phase space description provided by Gkeyll to characterize some of the kinetic properties of the SSX plasma.   

Projected scaling of sustained spheromak configurations for economical fusion power

Sustained spheromaks are of historical and recent interest for fusion energy applications due to their compactness, engineering simplicity, and projected economic competitiveness with incumbent sources of electrical power generation. Fundamentally, spheromaks are compact plasma configurations with both toroidal and poloidal plasma currents responsible for generating confining poloidal and stabilizing toroidal magnetic fields, respectively. However, due to large field-normalized plasma currents relative to tokamak configurations, some method of energy efficient current drive must be employed to allow for reasonable recirculating power fractions in an eventual spheromak fusion reactor system. A novel method of spheromak plasma current sustainment called Imposed-Dynamo Current Drive (IDCD) originally pioneered by the HIT-SI Research Group at the University of Washington is presented with projected favorable scaling towards high temperature (T \textgreater 1 keV) sustained spheromak plasma conditions. In particular, it is argued that this method of helicity injection current drive will allow for the production of high current gain sustained spheromak configurations with sufficient energy confinement quality required for an eventual spheromak fusion reactor system.   

Model validation and numerical investigation of inductive helicity injection drivers for spheromak formation and sustainment

Numerical investigation of inductive helicity injection drivers, as developed on the HIT-SI family of experiments at the University of Washington, is underway with a focus on developing validated models of relevant driver physics to support exploration and optimization of possible injector configurations for sustainment of spheromak plasmas. Two extended MHD codes are being used: NIMROD [1], where the injectors are approximated through boundary conditions on an axisymmetric domain, and PSI-Tet [2], where the full multiply-connected plasma volume is simulated. Simulations will be benchmarked against experimental data from the HIT-SI (two injectors), HIT-SI3 (three injectors), and the future HIT-SIU (four mouth injector manifold) devices. Validated physical models will then be used to explore possible injector configurations to determine the effect of toroidal/poloidal mode content, frequency, phasing, and other parameters on resulting sustained spheromak equilibria.\\ {[1]} K. Morgan et al. Phys. of Plasmas 24, 122510 (2017)\\ {[2]} C. Hansen et al. Phys. of Plasmas 22, 042505 (2015)   

GPU-based feedback control of kilohertz-scale AC plasma drivers on the HIT-SI3 experiment

The Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI3) experiment studies the formation and sustainment of spheromak plasmas through the use of three fully inductive magnetic helicity injectors. Each injector is a semi-toroid connected to the spheromak volume that drives oscillating RFP-like field structures through the use of both ‘toroidal’ injector flux and loop voltage, which are oscillated in phase to produce constant sign magnetic helicity injection, with operating frequencies are on the scale of 10-70 kHz. These injectors are then driven out of phase from one another to produce non-axisymmetric time-dependent perturbations on the plasma. A Graphics Processing Unit (GPU) based feedback control system has been implemented to control nonlinear plasma interactions between the different injectors during operation and drive the desired temporal waveform of the injector fields. Initial results of the GPU-controller operations are presented, including both demonstration of real-time pre-programmed operation and proportional control algorithms.   

Overview of power and diagnostic upgrades for HIT-SI3 and planned HIT-SIU experiments

The HIT-SI3 device is being upgraded with new switching power amplifiers (SPAs) and capacitor banks for a 70{\%} increase in nameplate power capacity and a 35{\%} increase in stored energy. The additional power injection will enable optimized j/n and longer duration sustainment of high current (\textgreater 100 kA) and high current amplification (\textgreater 3) spheromaks. A new, multi-chord, two-color interferometer is being constructed to measure plasma density in the toroidal midplane. The new system will be able to operate in HIT-SI3's high density regime (n\textunderscore e \textgreater 5 x 10\textasciicircum 19 m\textasciicircum -3) where the previous far-infrared interferometer could not. Additionally, plans for the new HIT-SI-Upgrade (HIT-SIU) are presented. The three, discrete helicity injectors will be replaced with a manifold which has four connections to the spheromak flux conserver. The new injector manifold will test lower density startup, improved plasma-facing insulating coatings, applied perturbation spectra predicted to improve performance, and a geometry compatible with larger, future devices.   

HIT-SI3 Thomson Scattering Results

The Thomson scattering diagnostic on HIT-SI3 has been modified to enable measurements of electron temperature down to nearly 5 eV, and to allow for up to three simultaneous spatial measurements of $T_{e}$ per discharge. The diagnostic uses a ruby laser (694.3 nm) to induce scattering and three 5-channel polychromators to resolve the Doppler-shifted spectrum. Presented are the first Thomson scattering measurements on the inductively driven HIT-SI3 spheromak, indicating plasma electron temperatures between 5-15 eV. Comparisons of different electron velocity distribution functions used in the fitting routine are shown and the plasma physics consequences are discussed. The possibility of using these results to probe electron drift velocity and density are also explored in the context of simulations and corroborating measurements from other diagnostics.   

Comparison of magnetic activity in MHD simulations of low and high frequency HIT-SI3 discharges

HIT-SI3 (Helicity Injected Torus- Steady Inductive 3) is an experiment that uses AC perturbations from three helicity injectors to drive a DC spheromak. Experimental evidence and extended magnetohydrodynamic (xMHD) MHD simulations of the previous HIT-SI experiment show differences between spheromaks formed at ``low injector frequency'' ($f_{inj}$ $<$ 40 kHz) and those formed at ``high frequency'' ($f_{inj}$ $>$ 40 kHz). Using Biorthogonal Decomposition (BD) to isolate and ``subtract'' injector and equilibrium-related magnetic activity from experimental magnetic probe measurements, plasma-generated periodic fluctuations have been observed in high frequency HIT-SI3 discharges, but not low frequency. The NIMROD xMHD code is used to simulate HIT-SI3 discharges by generating flux and current injector waveforms from experimental data, and applying them as boundary conditions on $\vec{E}$ and $\vec{B}$ in a simulation domain. High frequency and low frequency HIT-SI3 discharges have been simulated in NIMROD using zero-pressure, single temperature, and two-fluid temperature models. BD analysis is performed on these simulations and is compared to experimental data to study the appearance and cause of the periodic activity in high frequency.   

Two temperature effects in the HITSI experiment

We investigate differences between our single temperature and our new two-temperature (ion-electron) extended magnetohydrodynamics (eMHD) simulations of the HITSI device at the University of Washington, using two distinct MHD codes, PSI-Tet and NIMROD. We focus on a number of key issues: illustrating greater agreement with experiment for a number of different measurements than the single temperature code, showing that the approximate linear scaling of beta and current gain with injector frequency persist with two-temperature effects, and investigating ion and electron heat flux to the flux conserver walls. Lastly, density, temperature, and particle diffusion scans are done in PSI-TET in order to better understand the parameter space and indicate possibilities for future work.   

Effects of Boundary Conditions on Helicity-Conserving Systems

The presence of non-axisymmetric features on plasma volumes of Steady Inductive Helicity Injection (SIHI) devices, such as the helicity injectors on HIT-SI and HIT-SI3, is consequential to both the time-dependent performance and the equilibria of the devices, as shown through the use of the 3D MHD code PSI-Tet, which is capable of simulating plasmas in such volumes through the application of FEM mechanics on unstructured tetrahedral grids. The behavior of SIHI devices with different injector geometry, explored through Hall MHD PSI-Tet simulations, will be presented, as will the behavior of (composite) Taylor state equilibria in such volumes, as the presence and nature of nonaxisymmetries appears to qualitatively affect the shape of the minimum-energy-with-conserved-helicity equilibria, through the generation of magnetic islands that appear all the way to the spheromak's magnetic axis according to patterns identified herein.   

\textbf{Recent Achievements in the C-2W Field-Reversed Configuration Experiment}

TAE Technologies, Inc. (TAE) is a privately funded company pursuing an alternative approach to magnetic confinement fusion, which relies on field-reversed configuration (FRC) plasmas composed of mostly energetic and stable particles. TAE's current experimental device, C-2W (also called ``Norman'') [1], is the world's largest compact toroid device which has the following key features: neutral beam injection with high power (up to 20 MW) and intra-discharge variable energy (15--40 keV) functionality; flexible edge-biasing systems in both inner and outer divertors; external magnetic field fast control capabilities, such as ramp-up, and active feedback control of the FRC plasma. In C-2W, record breaking, advanced beam-driven FRC plasmas dominated by fast particles (total $T_{e}+T_{i}$ up to 3 keV, based on a pressure balance) are produced and sustained in steady state (up to 30 ms, limited by the energy storage). Dedicated experimental campaigns have been conducted to further optimize and improve performance and characterize the plasma. This paper will review the highlights of the C-2W experimental program as well as the newly obtained high-performance operating regime. \newline \newline [1] H. Gota \textit{et al}., Nucl. Fusion \textbf{59}, 112009 (2019).   

Overview of the C-2W Experimental Diagnostic Systems

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 (15 – 40 keV, total power up to 20 MW), advanced divertors, end bias 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 represents the world’s premier venue for studying fast ion-dominated FRC plasmas. The C-2W diagnostic suite has been fully leveraged to quantify and explore a newly emerged high-performance plasma regime. The suite consists of 20 separate categories of diagnostics with 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.   

Transport Scaling from C-2 to C-2W Field-Reversed Configuration Experiments

In TAE Technologies’ current experimental device, C-2W (also called “Norman”)\footnote{H. Gota et al., \textbf{Nucl. Fusion 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 (15-40 keV, total power up to 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. New data on the plasma confinement from the C-2W experiment will be presented and interpreted by an improved fidelity model, focusing on confinement variation as a function of both machine and plasma parameters. Experimental confinement times have been collected from TAE Technologies’ C-2, C-2U and C-2W FRC experiments. Previous work has identified collisionality ($1 / {\nu *}$) as a strong predictor of electron heat confinement. The emerging electron energy confinement time appears to be proportional to a positive power of the electron temperature\footnote{M.W. Binderbauer et al., \textbf{AIP Conf. Proc. 1721}, 030003 (2016)}, which may ultimately enable advanced fuel fusion concepts.   

0D Power Flow Analysis on the C-2W Device

In TAE Technologies’ current experimental device, C-2W (also called “Norman”) [1], 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 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. It is important to measure and account for various power flows at the 0D level for experiments in the C-2W device and a data processing routine has been developed to calculate such power flows. In this poster, we will describe the architecture of this data processing routine, the diagnostic inputs to the routine, and the inherent modeling assumptions required. In addition, the results of power flow analysis will be presented for typical experiments in the newly-obtained high-performance operating regime. [1] H. Gota et al., Nucl. Fusion 59, 112009 (2019).   

The C-2W plasma control system : Overview and experimental results

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. In C-2W, the Keeping the FRC plasma well centered inside the confinement vessel to minimize stochastic fast ion losses is one of the key ingredients of the high-performance operating regime. This is achieved by a combination of end electrode biasing and magnetic control. The C-2W plasma control system (PCS) provides high bandwidth (2.5 MHz) data acquisition and low latency (10 us) magnetic control of plasma shape and position, as well as kinetic control of electrode biasing current and Neutral Beam Injection grid acceleration voltage. PCS is a distributed digital control system based on Speedgoat modules for fast data acquisition and plasma control, which use multi-gigabit transceivers with Xilinx Aurora protocol to communicate among data acquisition systems, control modules and actuators. The core functionality, system setup, observers, and control algorithms are implemented using Matlab scripts and Simulink and HDL coder workflow. This enables a quick and easy transition from model-based designs to FPGA hardware implementations. Recent results with boundary flux and plasma radius control will be presented and discussed. [1] H. Gota et al., Nucl. Fusion 59, 112009 (2019)   

High-fidelity Bayesian inference of transient FRC plasma perturbations in C-2W

A holistic, high-fidelity plasma reconstruction based on Bayesian inference is applied to study the advanced beam-driven Field Reversed Configuration (FRC) in the C-2W machine[1] at TAE Technologies, Inc. The method employs a statistical distribution of possible plasma states, including variables that persist across time points to enhance resolution of plasma dynamics. This implementation of “time-linked” Bayesian inference is used to evaluate electron density fluctuations at the C-2W midplane. Likely values and statistical confidence intervals are generated for density perturbation mode amplitudes, frequencies, and radial profiles. Synthesis of multiple high-frequency diagnostics provides significantly increased reconstruction fidelity compared to single instrument analysis. These include FIR interferometry, Mirnov magnetic field probes, and neutral beam induced secondary electron emission detection. This analysis is performed at 2 us resolution for the entire 10 - 30 ms plasma lifetime via distributed computing. Results include evaluation of the midplane density profile evolution, and observation of low-level intermittent azimuthal modes that rotate about the machine axis with frequencies in the range of 10-100 kHz. \\ \\ $[1]$ H. Gota et al., Nucl. Fusion 59, 112009 (2019).   

Electron Temperature and Density Profiles in the New High-Performance Regime of C-2W Plasmas

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 bias electrodes, and an active plasma control system. Study of the electron temperature and density profiles under various experimental settings is critical for understanding the physics of the high-performance operating regime and for planning of future experimental campaigns. The C-2W Thomson scattering system [2] was designed to provide full spatial and temporal coverage of the plasma size and lifespan. In this poster, we will present the results of the Thomson scattering measurements in C-2W, including the electron temperature and density profiles and their temporal evolution under different experimental configurations. In addition, we will present the recent improvement of the calibration procedure of the C-2W Thomson scattering system using the Raman scattering method to avoid the stray light issue inherent with calibration using Rayleigh scattering. [1] H. Gota et al., Nucl. Fusion 59, 112009 (2019). [2] K. Zhai et al., Rev. Sci. Instrum. 89, 10C118 (2018).   

Density profiles of C-2W High Performance FRC

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 bias electrodes, and an active plasma control system. The performance of the fast ion-dominated FRC and the effects on it from beam injection and end biasing are examined using a 14-chord interferometer array in the 432.5 um far-infrared (FIR) range. Equilibrium density profiles from the array, together with other diagnostic measurements, are presented to compare early C-2W discharges and new high-performance regime plasmas. [1] H. Gota et al., Nucl. Fusion 59, 112009 (2019).   

Radiative Losses from C-2W's High-Performance FRC

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], record breaking, advanced beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams, expander divertors, end bias electrodes, and an active plasma control system. As energy confinement times and temperatures continue to improve, radiation and ionization losses due to impurities could lead to significant power loss. To monitor these losses, an array of over 600 channels of XUV and soft x-ray sensing diodes has been implemented. The diagnostic achieves both good spatial resolution and wide-angle collection of plasma emission. Additionally, the diagnostic is fitted with differing thin, metallic, optical filters for coarse spectral resolution. Multi-dimensional reconstruction of plasma emission is performed to infer the total power losses. In the C-2W's high performance regime, which relies on extensive titanium gettering of the confinement vessel walls, the total impurity radiation power loss is estimated to be less than 200 kW. [1] H. Gota~\textit{et al,} ~Nucl. Fusion~\textbf{59,}~112009 (2019).   

Initial Results From The Polarimetry Upgrade To The Far-Infrared Interferometer-Polarimeter On C-2W

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 bias electrodes, and an active plasma control system. Measurements of the equilibrium profiles and fluctuations of the plasma density and magnetic field are critical for understanding FRC behavior and improving performance. The far-infrared interferometer-polarimeter diagnostic on C-2W has reliably operated as a two-wave interferometer for density measurements along 14 chords with high time resolution. The system upgrade to a three-wave diagnostic for simultaneous interferometer-polarimeter operation is underway, with the planned capability to resolve predicted Faraday rotation angles less than 0.5 degrees while maintaining high bandwidth for fluctuation measurements. We evaluate the impact of vibrations on the phase measurement and present efforts to mitigate them. We will present the design and status of the upgrade, with initial measurements of equilibrium magnetic profiles in FRC plasmas. [1] H. Gota et al., Nucl. Fusion 59, 112009 (2019)   

Interpretation of the charge exchange neutral energy spectrum of C-2W

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 20 MW), 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 current drive and plasma heating, is critical for understanding the FRC behavior. Neutral Particle Analyzers (NPAs) are used to measure the energy spectrum of fast ions that charge exchange on background or beam neutrals and are lost from the plasma. The fast ion energy spectrum can be reconstructed by modeling the spatial distribution of fast ions and neutral particles. We present measurements made with both an electromagnetic and electrostatic NPA---the electromagnetic NPA provides isotopic separation of beam and bulk plasma species, while the lighter electrostatic NPA can be steered with a 2-axis gimbal to access a wide range of pitch angles. Forward modeling of the spectra with a hybrid MHD-Monte Carlo code is used to examine the collisional processes of fast ion slowing down on electrons and charge exchange loss. Non-collisional ion acceleration by a beam-driven wave, similar to that observed on C-2U [2], is also observed in C-2W and modeled with a particle-in-cell code. [1] H. Gota~\textit{et al,} ~Nucl. Fusion~\textbf{59,}~112009 (2019) [2] R. M. Magee \textit{et al}, Nature Physics \textbf{15} (2019)   

First Measurements of Multi-scale Density Fluctuations and $E$x$B$ Velocity via Doppler Backscattering in the C-2W Field-Reversed Configuration

An advanced multi-channel combined Doppler Backscattering (DBS) diagnostic has been installed at the C-2W Field-Reversed Configuration (FRC) device. First measurements of intermediate wavenumber density fluctuations 2$\le k_{\mathrm{tor}}\rho_{\mathrm{s}}\le $10 in the FRC core plasma (outside the null field region) and in the scrape-off layer are presented. The DBS diagnostics also allows measurements of the ExB velocity, extracted from toroidal turbulence advection. Plans and preparations for the first tests of Cross Polarization Scattering [1] (CPS, for the measurement of perpendicular magnetic field fluctuations from the DBS scattering volume) are also discussed. GENRAY ray tracing predicts that magnetic fluctuations with 2$\le k_{\mathrm{tor}}\rho_{\mathrm{s}}\le $ 30 can be accessed in the FRC core and scrape-off layer (SOL). DBS data from the previous C-2U FRC experiment [2] already show the absence of ion-scale density turbulence in the FRC core. Global gyrokinetic simulations attribute core stability to Finite Larmor radius effects, short fieldline connection length, and favorable magnetic field gradient. In contrast, multi-scale turbulence including short-scale electron modes has been observed in C-2U via DBS in the mirror-confined SOL plasma, also in agreement with global gyrokinetic simulations which predict unstable drift-interchange modes for $k_{\mathrm{tor}}\rho_{\mathrm{s}}\ge $1.5. [1] X.L. Zou et al., Phys. Rev. Lett. 75 1090-93 (1991). [2] L. Schmitz et al., Nature Comm. 7 13860 (2016).   

Measurements of fusion products in the beam-driven field-reversed configuration

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. Measurements of fusion products in the C-2W FRC reveal the dynamics of the highest energy fusile ions in the plasma$_{\mathrm{.}}$ In the case of deuterium neutral beam injection (NBI) into deuterium plasmas, fast ions born from charge exchange of injected beam neutrals are studied. Measurements of 3 MeV DD protons and 2.45 MeV DD neutrons are used to discern their confinement, accumulation, and spatial distribution in the plasma. In the case of pure hydrogen NBI into deuterium plasma, measurements of fusion products reveal plasma ion acceleration by a beam-driven wave. A fast tail in the bulk ion population is drawn out on sub-collisional timescales. This wave has been identified as an Ion Bernstein Wave though particle-in-cell simulation.$^{\mathrm{2}}$ [1]$^{\mathrm{\thinspace }}$H. Gota~\textit{et al,} ~Nucl. Fusion~\textbf{59,}~112009 (2019) [2] R. Magee \textit{et al}, Nature Physics \textbf{15}, 281-286 (2019)   

Direct Measurement of Injected Neutral Beam Power in C-2W

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. Heating, current drive, and refueling from neutral beam injection are essential to FRC sustainment. Previously, evaluating injected neutral power relied on the modeling of neutralization and duct losses. A new tungsten wire calorimeter has been designed, built, calibrated on a test stand, and implemented in the confinement vessel to make the first direct measurements of the injected beam power into C-2W. An array of 8 wires are arranged along the beam injection port so that the beam power deposition profile can be reconstructed to find the total injected power. We will report on the calorimeter design, calibration methods, and early experimental results from C-2W, including the optimization effort to increase the input power by improving beam aiming and neutralization. [1] H. Gota~\textit{et al,} ~Nucl. Fusion~\textbf{59,}~112009 (2019)   

Correlation of global instabilities with high-frequency fluctuations in the scrape-off layer of C-2W

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 bias electrodes, and an active plasma control system. Global MHD modes are largely stabilized by sheared plasma rotation just outside the separatrix. Magnetic [2] and electrostatic probes have been installed in the open field line region to investigate the FRC stability and fluctuations outside the separatrix. Each probe has a wide bandwidth; therefore, we can observe and compare not only MHD modes but also high frequency fluctuations. Additionally, the FRC density profile at the mid-plane as well as plasma's global motion can be observed with far infrared interferometry (FIR). By combining these diagnostics, we investigate the correlation between the motion of the core plasma and fluctuations outside the separatrix. The correlation between global instabilities and high-frequency fluctuations outside the separatrix will be presented and discussed. [1] H. Gota et al., Nucl Fusion, 59 , 11 (2019) [2] T. Roche et al., Rev. Sci. Instrum. 89, 10J107 (2018)   

\textbf{Behavior of a tracer-containing compact toroid in a transverse magnetic field}

Fusion reactor plasma cooling can be caused by impurity contamination, which worsens plasma confinement. Therefore, studying the behavior of impurities in a magnetically confined plasma is of interest. A tracer-containing compact toroid (TCCT) injection technique that utilizes a magnetized coaxial plasma gun (MCPG) has been proposed as a new tracer injection method for impurity transport study [1]. The MCPG with a tracer source has been developed as a TCCT injector. The tracer source consists of a rod electrode made of tracer elements and a cylindrical electrode. The plasma containing tracer ions are generated by an independently controlled pulsed discharge in the tracer source. Then, the plasma is accelerated up to several hundreds of km/s by an MCPG discharge and ejected as a TCCT. The main purpose of this study is to observe impurity behavior in a field-reversed configuration (FRC) using the TCCT technique. Experiments on TCCT injection into a transverse magnetic field emulating the confinement magnetic field of an FRC have been conducted to understand whether tracer ions can be injected into FRCs without separation from a TCCT. [1] D. Kobayashi \textit{et al}., Rev. Sci. Instrum. \textbf{89}, 10I111 (2018).   

Development of a Low Frequency Magnetic Field Sensor Array for the C-2W Experiment

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], record breaking, advanced beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams, expander divertors, end bias electrodes, and an active plasma control system. Fast magnetic fields in C-2W are thoroughly diagnosed using B-dot probes and Rogowski coils. However, these sensors have limited low-frequency response and may introduce long-timescale errors in integrators and ancillary electronics. It is beneficial to have an independent and absolute validation of these fields, which are quasi-DC on the plasma timescales. As such, an array of high-precision Hall sensor-based low frequency probes, has been developed. Details of the diagnostic, as well as preliminary data will be presented. [1] H. Gota et al., Nucl. Fusion 59, 112009 (2019)   

Measurement of Axial Plasma Losses in the C-2W High-Performance Regime

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 (15 -- 40 keV, total power up to 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. In C-2W, the FRC core plasma is surrounded by a mirror-confined scrape-off layer on open field lines. An array of energy analyzers and bolometers mounted in the divertors of C-2W \footnote{M. E. Griswold et. al., Rev. Sci. Instrum. \textbf{89}, 10J110 (2018) } measure axial power losses as well as the electron temperature and ion energy distribution of the plasma at the termination point of the open field lines. Measurements taken in the C-2W high-performance regime show bulk ion temperatures greater than 500 eV that are sustained throughout the shot. They also indicate that a strong ambipolar potential ($\sim$4.5 $T_{e}$) develops along the open field lines to control electron losses, and that the energy lost per ion, $\eta_{e}$, is close to the theoretical minimum.   

Electrode biasing system in C-2W

In TAE Technologies’ current experimental device, C-2W (also called “Norman”) [1], record breaking, advanced beam-driven field reversed configuration (FRC) plasmas [2] are produced and sustained in steady state utilizing variable energy neutral beams (15 –- 40 keV, total power up to 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. The end bias electrode system provides stabilization and heating of the high-beta axisymmetric plasmas by inducing azimuthal plasma rotation via the application of radial electric fields [3]. The bias electrodes and limiters are designed for high voltage operation and were tested for up to 15 kV in vacuum. The bias voltage of -2 kV (on the device axis) with the total current through the electrodes of 5-7 kA were proven sufficient for stabilization of the C-2W plasmas. The details of the electrode-biasing system, protection and measurement circuits, as well as experimental results will be presented. \newline [1] H. Gota \textit{et al}., Nucl. Fusion \textbf{59}, 112009 (2019).\newline [2] M.W. Binderbauer \textit{et al}., AIP Conf. Proc. \textbf{1721}, 030003 (2016).\newline [3] A.D. Beklemishev \textit{et al}., Fusion Sci.Technol. \textbf{57}, N4, 351 (2010).   

Effect of electrode biasing on C-2W electron temperature

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], record-breaking, advanced beam-driven field reversed configuration (FRC) plasmas are produced. FRCs are sustained in the central confinement vessel (CV) in the steady state utilizing variable energy neutral beams, advanced divertors, end bias electrodes, and an active plasma control system. In this presentation, we study the effect of end electrode bias both under steady-state and transient conditions on the e$^{\mathrm{-}}$ temperature (T$_{\mathrm{e}})$ measured using a Thomson scattering diagnostic in the mid-plane of CV. The steady-state analysis allows distinguishing between the effects of bias voltage versus current. Dynamic bias allows measuring T$_{\mathrm{e}}$ rise/decay rates and thus makes it possible to analyze the effect of bias on e$^{\mathrm{-}}$ confinement. The effectiveness of biasing -- fraction of current and voltage delivered to CV -- is analyzed using a single-sided bias where electrodes on the opposite end act as floating electrostatic probes. A strong correlation of T$_{\mathrm{e}}$ with the bias is observed, which might be an indication of e$^{\mathrm{-}}$ heating by the applied bias. [1] H. Gota et al., Nucl. Fusion 59, 112009 (2019).   

Fast-ion charge-exchange losses in C-2W

In TAE Technologies' current experimental device, C-2W (also called ``Norman'')\footnote{H. Gota, et al. Nuclear Fusion 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 (15--40 keV, total power up to 20 MW), advanced divertors, end bias electrodes, and an active plasma control system. Beam injection produces large-orbit fast ions that sample both the core FRC and the surrounding axisymmetric mirror plasma, where they can be lost via charge-exchange with neutrals. Since collisional energy transfer from fast ions is a primary heating source for the bulk plasma, their spatial and velocity distribution affects the overall power balance and understanding fast ion loss is critical. Balmer-$\alpha$ emission measured with filtered high-speed cameras is used with DEGAS2 neutral particle modeling to reconstruct the neutral distribution consisting of a cold population from wall recycling and a non-axisymmetric warm population generated from beam capture (via charge-exchange with the bulk plasma). Monte Carlo modeling is then used to estimate the rate and distribution of fast ions lost by charge-exchange, which is compared to bolometer measurements.   

Electric field profile measurements in C-2W from impurity ion radial momentum balance

In the C-2W experiment [1], edge biasing is used to drive rotation, stabilize, and heat an advanced beam-driven field-reversed configuration (FRC) plasma embedded in a magnetic mirror. Highly charged oxygen impurity ions that exist in the plasma are sensitive to biasing effects and their azimuthal rotational velocity magnitude and direction are dependent on the applied electrode bias voltage and polarity, respectively. The radial momentum balance equation for impurity ions is utilized to extract the local electric field near the mid-plane of the confinement vessel. A multi-chord passive Doppler spectroscopy diagnostic targeting the O$^{\mathrm{4+}}$ triplet lines near 278 nm is used to measure impurity ion temperature, density, and azimuthal velocity profiles. Results show that for biased plasmas the diamagnetic term inside the separatrix is small relative to the $E\times B$ force term which drives the O$^{\mathrm{4+}}$ rotation. These findings are consistent with other experimental observations and computational equilibrium reconstruction of C-2W plasma. [1]~H. Gota et al., Nucl. Fusion~\textbf{59}, 112009 (2019).   

Two-dimensional density profiles of rotating mode structures using the Radon transform on the C-2W experiment

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], record breaking, advanced beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams [NBI], expander divertors, end bias electrodes and an active plasma control system. Although global MHD modes are largely stabilized, coherent density fluctuations can be occasionally seen in the time traces of the mid-plane 14 chord far-infrared (FIR) interferometer. These benign fluctuations are due to rigid non axisymmetric density structures rotating about the plasma's axis. Of particular interest are the common FRC n$=$2 rotating mode and micro-burst mode activity associated with fast ions from NBI. Both are manifested as symmetric line integrated density [LID] radial profiles at any time in a modal period. A new so-called Seesaw mode has been observed that produces lopsided LID profiles that seesaw in the cycle. The high spatial and temporal resolution of the interferometer allows reconstruction of rigidly rotating 2-d density distributions including the Seesaw mode. Inverse Radon transform generated 2-d modal density structures will be presented and discussed along with correlated observations from magnetic Mirnov arrays and electrostatic probes. [1] H. Gota et al., Nucl. Fusion \textbf{59}, 112009 (2019).   

Impurity Transport in the C-2W Experiment

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 bias electrodes, and an active plasma control system. Reduction of impurity influx from material surfaces is essential to achieve high temperatures in fusion experiments. In the C-2W device, the quartz tube of the formation section and the metal surfaces in the inner divertor may both act as sources of oxygen impurities. Here we investigate the transport of oxygen with spectroscopic and fast imaging measurements. Density profiles of oxygen for different charge states in the confinement vessel and inner divertor are presented. In addition, a method for determining the particle confinement time from impurity spectral line ratios is proposed and evaluated. 1 H. Gota~et al, ~Nucl. Fusion~59,~112009 (2019).   

Integrated Modeling of Stability and Transport of FRC Plasmas

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], record breaking, advanced beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams, expander divertors, end bias electrodes, and an active plasma control system. We give an overview of our ``Numerical FRC'' integrated modeling effort, which includes interpretive and predictive work on the equilibrium, stability, and transport of C-2W FRC plasmas. Fast particles from neutral beam injection (NBI) are modelled using a full orbit Monte Carlo code. This is used to calculate fast ion contributions to hybrid kinetic$+$thermal equilibria, to compute source terms in experimental plasmas which have been reconstructed with Bayesian Inference, and to augment a 2D extended MHD code to create a global transport model which includes NBI, electrode biasing, expander divertors, and neutral gas. FRC states computed from these 2D models are analyzed for 3D effects using the ANC code which models electrostatic turbulence, and the FPIC code which models global stability under the influences of NBI, electrode biasing, and magnetic field shaping. [1] H. Gota et al., Nucl. Fusion \textbf{59}, 112009 (2019).   

Simulation of Fast Ion Effects on Global Stability of C-2W Equilibria

The stability of field-reversed configuration (FRC) plasmas has been investigated both experimentally and theoretically by other authors mainly in terms of the thermal plasma components. The kinetic effects due to a fast particle population are a topic of active debate and the corresponding changes in the plasma dynamics still need to be clarified. TAE Technologies’ most advanced and recent FRC machine, C-2W, can take advantage of up to eight particle beams to build high pressure of energetic ions and produce fast ion-dominated FRCs. In order to investigate the fast ion effects on FRCs, both TAE’s equilibrium and hybrid codes, LReqMI and FPIC respectively, have been modified to include fast ion components. We present FPIC results of the evolution of this new kind of equilibria and address the stabilizing and destabilizing effects for both the rotational and longitudinal modes, which have been studied and presented in the past. The results of a parametric study of fast ion effects will be presented.   

1-Dimensional Equilibrium of C-2W plasma

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], 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 bias electrodes, and an active plasma control system. We present an interpretative tool to calculate the internal magnetic field, electric field, and fast ion population using experimentally measured quantities such as magnetic field and poloidal flux (measured near the wall), electron density and temperature, ion temperature, and neutral density. The internal plasma state is found through equilibrium reconstruction. Using Ampere's law, a 1-D radial profile of the magnetic field is calculated by evolving fast ions using a Kinetic Monte Carlo Simulation with measured thermal plasma profiles. An alternative model applies multi-ion species fluid equations to determine flux and ion surface equilibrium functions for the equilibrium reconstruction. Sustained by neutral beam injection, the growing fast ion population drives current and modifies the magnetic field. The steady state solution provides a plasma equilibrium with a significant fast ion population. The steady state equilibrium can be used further to estimate the electric field, neutrons production, and power balance in the new high-confinement operating regime. [1] H. Gota et al., Nucl. Fusion \textbf{59}, 112009 (2019).   

Anatomy of an FRC

Advanced beam-driven operation in C-2W produces a steady-state FRC. The baseline diagnostics are external magnetic probe arrays and multi-chord interferometry. The former yields no internal data while the latter only scans the symmetry plane. These measurements are the ``tangibles.'' Of key interest are ``intangibles'' not directly measureable, which call for a reconstruction tool that inputs only tangibles. ``Grushenka,'' developed for this purpose, builds on a modified Grad-Shafranov equation roughly equivalent to a ``split-rigid-rotor'' distribution of the ion species. Importantly, it accounts for end-loss effects, reducing the density outside the separatrix. Beside the 2D field structure, key intangibles include the trapped flux, currents flowing in core and periphery, inventories in core and periphery, and common stability indices (tilt, interchange, tearing). Grushenka results may answer several critical questions. Does the plasma contain an imbedded FRC at its heart or is it a high-beta mirror with no core of closed field lines? Another question is the link between ``positive field index'' control and the steady sustainment observed on the C-2W facility.   

Numerical Model Developments for Turbulent Transport in C-2W

In TAE Technologies' current experimental device, 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, advanced divertors, end bias electrodes, and an active plasma control system. In a prior experiment, C-2U, Doppler Backscattering (DBS) measurements of the advanced beam-driven FRC plasmas exhibited distinct qualities in the density fluctuations when comparing the core and scrape-off layer (SOL) regions: core fluctuations are consistently low in amplitude while SOL fluctuations have large amplitude at ion-scales and decrease towards electron-scales. Gyrokinetic simulations using the cross-separatrix particle-in-cell ANC code show that such fluctuation spectra arise from the interaction of the quiescent core and less stable SOL: unstable modes grow in the SOL; these fluctuations can then spread across the separatrix into the core. Two important features, present in C-2W, were neglected by previous simulations: low magnetic field regions, where particles with large orbits may cross, and electrode biasing at axial ends, which can introduce shear. Recently, a fully kinetic ``drift-Lorentz'' particle mover, valid throughout the FRC, has been implemented. A Dirichlet boundary has also been added for end biasing. The numerical developments will be discussed, and preliminary results of microturbulence simulations will be presented.   

A Current-Vorticity Model for FRC plasma control

A current-vorticity MHD model and code have been developed for FRC plasma control applications in the C-2W device [1]. The model uses a flexible filtering technique to restrict the frequency bandwidth of the simulations to the control bandwidth of interest. For dynamic systems written in the state space form \textit{dx/dt}$=f(t,x)$, we propose an algorithm based on a frequency domain eingenvalue analysis to remove frequency components above a certain desired frequency threshold of interest, typically determined by the desired control bandwidth. For small systems of a few states this filtering technique works effectively. For systems with a large number of states, a direct calculation of the Jacobian and its eigenvalues becomes impracticable, so we have developed a modified method which reduces the number of states (shrinking to a small system), filters and reconstructs the original high order system using a Gaussian Process inversion technique. The main purpose of the plasma model is to be applied to control system design, whose function is to maintain macroscopic plasma parameters such as shape, position, elongation, etc. at prescribed values. Details of the model and simulations will be presented. [1] H. Gota et al., Nucl. Fusion 59, 112009 (2019).   

Q2D simulations of the neutral gas in the divertors of C-2W

In TAE Technologies' current experimental device, C-2W (also called ``Norman'') [1], record breaking, advanced beam-driven field reversed configuration (FRC) plasmas are produced and sustained in steady state utilizing variable energy neutral beams, expander divertors, end bias electrodes, and an active plasma control system. The neutral gas, which is produced in divertors by neutralization of the plasma flow at the divertor target plates, may negatively affect the plasma by reducing the ion and electron temperatures through ionization and charge exchange. To minimize these effects, the divertors have a large volume and a powerful pumping system to reduce the neutral gas density to an acceptable level. The neutral gas in the divertor and its effect on the plasma flow have been studied numerically using the Q2D code. Q2D is a 2D MHD code with distinct ion and electron temperatures, and neutral gas treated as a fluid. The simulations show that the gas distribution in the divertor is substantially nonuniform, which improves the effectiveness of the pumping system and reduces the interaction of the neutrals with the plasma flow. The plasma flow compresses the neutrals near the target plates and reduces the neutral density in the rest of the plasma jet coming from the FRC. Under such conditions, the interaction of neutrals with the plasma is reduced, which allows the divertors to operate normally at higher plasma outflows than were estimated earlier. [1] H. Gota et al., Nucl. Fusion 59, 112009 (2019).   

Beam-Driven Ion-Cyclotron Modes in FRC

The population of high-energy ions created by neutral beam injection in a high-beta field-reversed configuration (FRC) plasma drives a class of ion-cyclotron modes that gives rise to coherent, large-amplitude ion waves at ion-cyclotron harmonics. These waves exhibit the physics of wakefields saturated at the Tajima-Dawson field while generating energetic tails of fast ions observed in C-2U experiments [1] and sufficient to yield fusion enhancement in future devices. The underlying mechanism behind this effect is the fast phase velocity of the wave relative to the ion thermal velocity, which prevents bulk disruptions of the plasma such as turbulence or anomalous transport despite a robust field amplitude. Using particle-in-cell (PIC) simulations, the nonlinear physics of this mode is explored, particularly with regard to the generation of fast ions, and a scheme of targeted excitation of this mode is considered. [1] R. M. Magee, A. Necas, R. Clary, S. Korepanov, S. Nicks, T. Roche, M. C. Thompson, M. W. Binderbauer, T. Tajima, Nature Physics \textbf{15}, 281-286 (2019)   

Non-Perturbative Measurements of Low and Null Magnetic Field in High Temperature Plasmas Using the Hanle Effect

Magnetic fields are typically used to confine high-temperature fusion plasmas. However, the plasma itself can generate magnetic fields that compete with those externally imposed to modify the confinement strategies. In a Field Reversed Configuration (FRC) or similar confinement configurations, in-situ non-perturbative measurement of magnetic fields is particularly difficult due to its low and near-zero magnitude. While the insertion of probes can measure the low field, they severely degrade the plasma, and the probe devices themselves can be damaged owing to high temperature. We explore the use of the Hanle effect as non-perturbative probe of magnetism in the confined plasma. The effect is regularly used in solar plasmas for the field measurements. The Hanle effect refers to how resonance scattering polarization is modified in the presence of "weak" fields (i.e., Zeeman broadening is comparable to natural broadening). We report on a pilot study using He-Ne lasers for proof of concept.