Session BP10: Poster Session I: Magnetic Fusion: DIII-D 1, Computational Techniques, Stellarators (9:30am-12:30pm)

DIII-D Program Overview and Long-Range Research Plans

DIII-D is now back into operation following a one-year Long Torus Opening which provided significant upgrades to the facility, including installing a co-counter toroidally steerable off-axis beamline, top-launch ECH system, and realignment of the upper Small Angle Slot divertor, along with significant diagnostic improvements. Experiments will continue up to a short vent in December to install a 1MW helicon antenna for off-axis current drive experiments in FY20, as part of a research campaign aimed at high \textunderscore $_{\mathrm{N}}$ steady-state performance with broad current profiles. Significant run time is allocated to disruption mitigation, including evaluation of shell pellets and a disruption-free protocol. Divertor experiments are evaluating the role of flows and drifts in detachment and a core-edge task force is addressing the physics of the pedestal and its connection to divertor improvements. An isotope mass campaign will address topics related to initial ITER operation in hydrogen. Highlights from recent operation, research plans, and further facility enhancements will be discussed.   

A Performance Upgrade to DIII-D to Close Physics Gaps on Future Fusion Reactors

Future burning plasma facilities will operate in different physics regimes from present devices. A performance upgrade to DIII-D can close gaps on these conditions. By significantly increasing current drive capabilities, a substantial rise (up to x3) in stored energy and density can be achieved in steady state regimes. This increases thermal and bootstrap fractions, with balanced electron and ion heating, significant electron-ion coupling, low rotation and fast ion fraction to explore reactor-relevant fusion cores. The tripling of heat flux and increased density will enable divertor physics exploration with increased opacity, shorter mean free paths, and increased dissipation in regimes where neutrals become more fluid like and Lyman alpha trapped. Pedestal neutral penetration depths will fall and height triple, with low collisionality access expanded to high density to explore optimization of transport-defined pedestals with radiative mantle. Combined with a reactor relevant wall and new 3D and disruption mitigation tools, this will take DIII-D to its full potential to explore and project stable integrated fusion reactor scenarios.   

Reactor-relevant characteristics of DIII-D negative triangularity discharges

A highlight of DIII-D experiments with negative triangularity (NT) shaped discharges was H-mode level confinement at significantly high beta with L-mode edge conditions[1]. Beyond the favorable energy confinement, indications of improved momentum confinement were observed in NT discharges compared to matched positive triangularity (PT) cases. Co-NBI-heated discharges had higher core rotation and rotational shear than predicted from scaling laws while ECH-dominant discharges had toroidal rotation within the expected range. Additionally, a comparison of bootstrap current between equivalent discharges showed somewhat higher bootstrap current that is more broadly distributed and without a peak at the edge in NT over PT Also, NT discharges exhibit 30-60\% higher Shafranov shift than PT for the same plasma pressure. Overall the many positive characteristics of negative triangularity plasmas, with prospects for low consequence ELMs and a low-field side divertor, make it an attractive option for a reactor. \newline [1] Marinoni et al., Phys. Plasmas 26, 042515 (2019).   

Co-evolution of ITB and ELM dynamics in the high poloidal beta scenario

The evolution of edge localized mode (ELM) dynamics in high poloidal beta discharges is found to correlate with changes to the internal transport barrier (ITB) common to this scenario. A large dataset of different types of DIII-D high poloidal beta discharges (spanning a wide range of $q_{95}$, $B_T$, $I_P$, and $\beta_N$ trajectories) shows that weak ITB/strong pedestal equilibria tend to have large compound type-I ELMs with embedded high frequency type-II ELMs and extended ELM-free periods. This is in direct contrast to strong ITB/weak pedestal equilibria that tend to be free of large type-I ELMs and consist almost entirely of high frequency type-II ELMs. This coupling between the pedestal and the ITB supports previous studies [PoP 25, 056113] that describe the interplay between magnetic shear and the Shafranov shift parameter in determining the sizes of the two transport barriers. The evolution of ELM dynamics in these discharges is contrasted between different shot trajectories; both inductive (constant vs. decreasing $q_{95}$) and non-inductive (constant vs. decreasing $B_T$). Trends in ELM frequency and ELM-induced drops in stored plasma energy point to a possible operating point at lower edge collisionality that may correspond to decreased energy exhaust via grassy ELMs.   

New Charge Exchange Recombination Spectroscopy Measurements of DIII-D Poloidal Rotation with PAAR and High Field Side Plasma Density

New sightlines have been installed on the high-field side of the DIII-D tokamak on the charge exchange recombination spectroscopy (CER) diagnostic for the 2019 campaign. Sightlines are toroidal and connected to detectors for simultaneous measurements of impurity (carbon) and main (deuterium) ions. In combination with corresponding measurements on the low-field side, new measurements of impurity density asymmetry and poloidal rotation of impurity and main ions can be made. These new measurements are available in the core from the magnetic axis to normalized minor radius of \textasciitilde 0.6 for typical plasma shapes. The beam neutral density used to determine the impurity density asymmetry is derived from measurements of beam neutral emission on the high- and low-field side. This approach avoids systematic errors that could arise from the use of a beam stopping calculation. The poloidal rotation measurements use the poloidal asymmetry in angular rotation (PAAR) method to avoid complications due to the gyro-orbit cross section effect. This method is particularly useful for the main-ions which resist direct measurement of poloidal rotation because beam neutral emission Doppler shift is low for a vertical view, causing it to overlap the charge exchange emission.   

Testing predictions of electron scale turbulent transport in H-mode pedestals

Electron temperature profiles closely follow the electron-scale ETG instability threshold calculated by CGYRO in the pedestal of two DIII-D ELMy H-mode discharges. The two discharges with different divertor geometry were chosen to analyze the role of transport vs. sources in setting the pedestal density and temperature profiles. Nonlinear simulations predict ETG turbulence can produce significant electron heat flux in the sharp gradient region, comparable to the observed heat flux. Neoclassical transport calculated by NEO predicts a significant contribution to the electron particle flux inferred from SOLPS-ITER analysis. Additional nonlinear simulations are used to predict the sensitivity of ETG transport to variations in input gradients. A pedestal-ETG transport model is derived using an analytic fit to the simulation results, and is used in addition to NEO to predict both ne and Te pedestal profiles. Although ETG and neoclassical transport play important roles in setting these profiles, the modeling suggests an additional transport mechanism may be required to match experimental profiles.   

Main-ion thermal transport and poloidal rotation in the H-mode pedestal

Measurements in DIII-D of the main-ions (D$+)$ show that the ion thermal diffusivity ($\chi $i) is approximately neoclassical (NC) in the H-mode pedestal, whereas the poloidal rotation (V$\theta )$ is significantly larger than predicted by NC theory. D$+$ temperatures (Ti) can be half the value of the standard impurity measurements (Timp) in the steep gradient region of the pedestal on DIII-D. These new measurements greatly improve the accuracy of the electron and ion heat flux (Qi) calculations, resolving historical issues such as negative Qi, which could occur when the ion-electron power exchange was overestimated using Timp. The experimental power balance $\chi $i is approximately at the NC level in an ITER baseline shot and will be presented across a range of collisionalities and compared with modeling using NCLASS, NEO, and XGC0. NC ion thermal transport suggests that an MHD-like mode (i.e KBM), which would be expected to drive transport in all channels including ion thermal, is not the dominant mechanism for transport in the pedestal.   

Electron temperature gradient undulations and transport induced by modulated NBI in DIII-D.

Significant intermittent electron temperature gradient fluctuations, which may be of a size to affect global transport, have been observed in DIII-D hybrid discharges, correlated with modulated neutral beam heating and deeply penetrating ELMs. The beam modulation is controlled by a $\beta _{\mathrm{N}}$ feedback system and hence is not at any constant frequency. When the beam is heavily modulated, ECE and TS diagnostics can show localized changes in T$_{\mathrm{e}}$ gradients, with stationary periods up to 50 ms, with a/L$_{\mathrm{Te}}$ varied around a factor of 4 near the edge of the confinement region. These random gradient undulations are of a sufficient magnitude to affect growth rates of turbulent modes. Linear gyrokinetic simulations from GENE show that during the high gradient phase the growth rate of both electrostatic and electromagnetic modes rise in this region; especially, the growth rate of KBM rises to a similar level of ITG during the high gradient phase and is negligible otherwise. Regimes with intermittent gradient fluctuations have increased transport over regimes without fluctuating gradients, as for example in DIII-D QH-mode discharges. The higher transport is being investigated using non-linear gyrokinetic simulations.   

3D diagnostic mapping for turbulence studies with magnetic islands in DIII-D

The study of turbulence and transport in 3D magnetic topology is difficult but highly relevant for stellarators as well as nominally axisymmetric configurations (including tokamaks and reversed-field pinches) with non-axisymmetric perturbations. Recently gyrokinetic and gyrofluid simulations have been applied to study turbulence in the vicinity of magnetic islands in tokamaks. To facilitate comparisons, we are employing V3FIT with SIESTA to reconstruct a large applied magnetic island in DIII-D. 3D reconstruction enables mapping together diagnostic quantities from multiple spatial locations around the device. V3FIT/SIESTA provides 3D kinetic pressure constrained by Thomson Scattering and Soft X-ray diagnostics, which will enable detailed spatial comparison of pressure gradients versus density fluctuations measured with Beam Emission Spectroscopy. Preliminary analysis indicates that the turbulence intensity is peaked near (but offset from) the X-point, and reduced in the O-point, in qualitative agreement with the results of simulations and simple theoretical arguments relating gradients, fluxes, and fluctuations. The modification of the flow profile and shear by the island could also be contributing to the observed turbulence spatial distribution.   

Experimentally motivated saturation rule for the TGLF turbulent transport model

The TGLF ion and electron heat fluxes have been evaluated for 50,000 points of unique shot/time/radius of DIII-D experiments. The database was compiled without regard to discharge geometry (limited, diverted) or operating mode (L- or H- mode) for normalized rho (toroidal flux) radii=0.1,0.2,\ldots,0.9 and for times=2000,2100,\ldots,2800 ms. There is general agreement with the inferred power balance fluxes for the original (SAT\_RULE=0) saturation rule of TGLF. A newer saturation rule (SAT\_RULE=1) was introduced to better account for multiscale coupling in wavenumber space, but this rule does not compare as favorably to the experimentally inferred database as the original saturation rule. The agreement between experimental and TGLF fluxes can be improved by using a saturation intensity of the form $V=(a+b\log(k))/k^c$, where $a,b,c$ depend on the input parameters for TGLF (electron or ion temperature scale length, etc.) but not explicitly on the growth rates or wavenumbers. This analytic form of intensity was devised by observing the form of the intensity obtained by training a neural network (NN) that would yield intensities such that the TGLF fluxes would match the experimentally inferred fluxes.   

Turbulence, Transport and Energy Confinement Dependence on Plasma Current in DIII-D

The measured characteristics of long-wavelength turbulence vary strongly with q$_{\mathrm{95}}$, including the normalized fluctuation amplitude profile 0.45\textless r/a\textless 0.9 increasing strongly with q$_{\mathrm{95}}$. This is demonstrated by a systematic variation of the plasma current while other global parameters are held nearly fixed. Multichannel transport changes consistently, with both reduced thermal energy and momentum transport at lower q$_{\mathrm{95}}$. This dependence is observed in the core of L-mode and hybrid H-mode regimes. Correlation lengths and decorrelation times of turbulence show weaker variation with q$_{\mathrm{95}}$. Zonal flows decrease in amplitude, while Geodesic Acoustic Modes (GAM) increase in amplitude with q$_{\mathrm{95}}$ in L-mode, qualitatively consistent with theoretical predictions. Empirical scaling relations show that energy confinement time depends approximately linearly on plasma current in regimes with monotonically increasing q-profiles. Given this strong dependence of transport and confinement on plasma current, it is critical to understand the relationship of turbulence on q$_{\mathrm{95}}$, as well as the q-profile shape, to identify regimes of improved performance with optimized q-profiles. Initial results from TGLF modeling will be presented with the experimental data.   

Transport Analysis and Turbulent Ion Fluctuation Measurements with UF-CHERS at T$_{\mathrm{e}}$/T$_{\mathrm{i}}$ \textasciitilde 1 in DIII-D

Radial profiles of multi-field fluctuation measurements (n$_{\mathrm{C}}$, T$_{\mathrm{i}}$, V$_{\mathrm{tor}})$ were obtained with the Ultra Fast Charge Exchange Recombination Spectroscopy (UF-CHERS) diagnostic in a DIII-D experiment studying L-mode turbulent transport at near-unity T$_{\mathrm{e}}$/T$_{\mathrm{i}}$ ratio. For a 10-20{\%} increase in T$_{\mathrm{e}}$/T$_{\mathrm{i}}$ using electron cyclotron heating, analysis of UF-CHERS measurements revealed a radially varying increase in normalized T$_{\mathrm{i}}$ fluctuations of \textasciitilde 1-3{\%} of the equilibrium value, a corresponding decrease in V$_{\mathrm{tor}}$ fluctuations, and little change in n$_{\mathrm{C}}$ fluctuations. The same trend is also observed at increased density/collisionality. ONETWO transport analysis found increased electron and ion energy transport with larger T$_{\mathrm{e}}$/T$_{\mathrm{i}}$, consistent with the measured increase in T$_{\mathrm{e}}$ and T$_{\mathrm{i}}$ fluctuations. TGLF analysis showed increased growth rate for the most dominant modes at higher T$_{\mathrm{e}}$/T$_{\mathrm{i}}$ over the wavenumber range (0.1 $\le $ k$_{\mathrm{\theta }}\rho_{\mathrm{s}} \quad \le $ 10) encompassing UF-CHERS' sensitivity. TGLF also calculated increased T$_{\mathrm{i}}$ fluctuations at higher T$_{\mathrm{e}}$/T$_{\mathrm{i}}$. Further comparisons between experimentally inferred transport, multifield turbulence measurements, and transport models will be presented.   

Initial Measurements of Local Electric and Magnetic Field Fluctuations on DIII-D via Beam Emission Spectroscopy

A novel diagnostic for measuring local plasma electric and magnetic field turbulence has been designed and built for DIII-D. It spectrally resolves the Motional Stark Effect (MSE) split neutral beam emission at high frame rates, where fluctuations in the MSE component separation is proportional to local magnetic and electric field fluctuations. Design improvements to the central spatial heterodyne spectrometer (SHS) reduced the leakage of environmental mechanical vibrations and thermal variation into the interferometer. Characterization of the intensified high-speed CMOS detector inform the level of excess noise at the signal gain required for photon noise limited operation. Modeling of the measured photon noise (1{\%} at 500 kHz) and the inherent cross-correlational capabilities of SHS indicate fluctuation detection down to the 0.1{\%} level. Geometric Doppler broadening due to the large plasma collection optic reduces the theoretical fluctuation sensitivity of the diagnostic. Here, a geometric Doppler broadening compensation technique applies an equal but opposite spectral shift via properly offsetting the input aperture of the SHS. Laboratory experiments demonstrate this compensation and agree with theoretical calculations. First measurements and analysis of electric and magnetic fluctuations induced by low and high frequency modes on DIII-D will be presented. Work supported by US DOE under DE-FC02-04ER54698, FG02-89ER53296.   

High spatial resolution density fluctuation measurements of DIII-D pedestal turbulence

Localized 2D measurements of density fluctuations in the H-mode pedestal of DIII-D plasmas reveal a range of broadband modes that vary temporally and spatially during the inter-ELM cycle. These measurements are obtained with Beam Emission Spectroscopy and a new higher radial resolution Charge eXchange Imaging (CXI) prototype diagnostic. Fluctuation characteristics will be presented as a function of q95, electron temperature, triangularity, and collisionality, which have been predicted to impact the growth rate of pedestal instabilities, including microtearing modes (MTM). MTMs are predicted to cause electron thermal transport in the pedestal and other regions of high-beta plasmas. CXI will measure carbon density fluctuations at the pedestals and complement the Beam Emission Spectroscopy (BES) diagnostic, with up to 3x improved spatial resolution. This will enhance sensitivity to fluctuations localized to the narrow pedestal range, enabling the detection of MTMs and the dynamics in between ELMs. Preliminary analysis of prototype CXI data indicates enhanced coherency at higher frequencies when compared to BES along with higher sensitivity to density fluctuations.   

High frequency coherent mode measurement via density profile reflectometry in DIII-D

High temporal ($\ge $25 $\mu $s) and spatial (\textasciitilde 3 mm) density profile reflectometer measurements not only provide routine electron density profile measurements, but also enable the study of fast (\textless 10 kHz) density profile evolution during a variety of plasma conditions. The high frequency bandwidth ($\le $ 30 MHz) of the reflectometer phase data allows high frequency coherent mode activity to be resolved in both space and time. For example, a tearing mode with frequency range of 10-100 kHz is observed to modify a spatially resolved region of the reflectometer phase signals. Using a phase based analysis rather than the analysis of the inverted density profile, the mode spatial distribution may be determined. The location of the induced phase perturbation is found to be consistent with ECE electron temperature measurements. Further analysis and comparisons will be presented to examine the validity of this new technique. Once validated, this analysis will enable improved physics studies of high frequency transient mode structure and time behavior.   

\textbf{Dissimilar }$\beta $\textbf{ effect on electrostatic and electromagnetic turbulence in DIII-D H-mode plasmas}

The anomalous transport in existing tokamaks and stellerators is generally attributed to electrostatic turbulence. The electromagnetic turbulent transport mechanism is predicted to play an important role in future high $\beta $ (ratio of plasma pressure to magnetic pressure) fusion plasmas. It is essential to understand the $\beta $ effect on turbulence to test turbulence theory and simulations. A $\beta_{\mathrm{N}}$ (with $\beta _{\mathrm{N}}=\beta $/(I$_{\mathrm{p}}$/aB$_{\mathrm{T}}))$ ramp experiment was performed in DIII-D H-mode plasmas. It was observed that the internal magnetic turbulence measured by millimeter wave cross-polarization scattering increased with $\beta_{\mathrm{N\thinspace }}$while low-k \~{n} decreased, and intermediate-k \~{n} remained approximately constant. A decrease in electron thermal confinement time was also observed coinciding with the $\beta_{\mathrm{N\thinspace }}$ramp. These results indicate a decoupling of the density and magnetic fluctuations as well as an effect on electron thermal confinement which might be explained by magnetic fluctuations. Comparison with turbulence simulations will be reported.   

Multi-region, multi-timescale plasma burn dynamics modeling for ITER.

A global confinement time (e.g. ITER98) defined to balance global power sources and sinks in steady-state discharges, does not describe the dynamics of tokamaks [1] because the overall plasma dynamics is determined by the interaction of different phenomena with different time constants acting in different spatial regions. In burning plasmas an increase in core fusion rate produces energetic alpha particles that first transfer their energy to heat electrons, producing Electron Cyclotron Radiation [2,3] that distributes this energy to heat electrons over the entire plasma and to heat the wall. The remaining core electron and alpha energy collisionally heats the core ions in $\approx \quad 10^{-2}s$, increasing the core fusion rate $\left\langle {\sigma \upsilon } \right\rangle_{fus} \sim T_{ion}^{2} $. Globally, this additional fusion energy can be compensated by an increase of radiation from edge impurities, but only after that increased core energy has been transported to the edge [4]. Thus we are developing a multi-region burning plasma dynamics model with different time dependences for the different transport, heating, radiation cooling etc. phenomena that occur in the different spatial regions, which can in part be tested in DIII-D. Refs: [1] FS{\&}T 72,162(2017); [2] Nucl. Fus 41,665(2001, [3] Nucl Fus 49,115017 (2009); [4] M.D. Hill, Phd Thesis, GaTech (2018.   

GTEDGE-2: A particle, momentum {\&} energy conserving plasma transport code.

We have reformulated fluid plasma transport theory to rigorously satisfy particle, momentum and energy conservation by: a) retaining long range E{\&}M forces in the momentum balance in the derivation of a ``pinch-diffusion'' theory for the particle density [1]; b) taking into account the loss of plasma ions, momentum and energy by thermalized ions that access orbits that cross the separatrix and are ``ion orbit loss'' from the outflowing ion distribution [2]; c) incorporating these effects into the calculation of radial particle and energy fluxes and a rotation theory for toroidal and poloidal velocities [3]; and c) self-consistently modifying fluid plasma transport theory to incorporate these new effects and demonstrate their importance in the analysis of experiments [4,5]. The extended fluid transport formalism coupled to a 2D GTNEUT neutral particle transport code [6], which will provide a much improved edge pedestal analysis capability, introduces a need to modify the existing numerical iteration strategies. REFS: 1) Contr. Plas. Phys. 48, 94 (2008); 2) Phys. Plasmas 18, 102504 (2011); 3) Phys. Plasmas 20, 092508 (2013); 4) Nuc. Fus.57, 066034 (2017); 5) FS{\&}T 75,251(2019); 6) Phys. Plasmas 13,062509 (2006) and 17, 022507 (2005).   

Investigations of ION Orbit Loss In L-H Transition n DIII-D.

We have recently shown$^{\mathrm{1}}$ that a change in Ion Orbit Loss is involved in the L-H transition in several DIII-D shots, and are now investigating the DIII-D L-H data for evidence of changes in the parameters that determine, via conservation requirements, the minimum ion energy for which an ion can be ion orbit lost. In order to maintain charge neutrality in the presence of ion orbit loss in the edge plasma, it is necessary to have an inward current of either ions or neutrals from the SOL to replace the ions that are ion orbit lost from the edge plasma. It is proposed that the compensating ``return'' currents arising from ion orbit loss in large part determine the radial electric field in the tokamak edge plasma. Setting the current produced by ionization/charge exchange equal to the negative of the IOL ``return'' current plus the viscous current, one can solve for the radial electric field required for charge neutrality in the presence of ion orbit loss.$^{\mathrm{2,3}}$ [1] N. A. Piper {\&} W. M. Stacey, Plasma Phys Control Fusion 61, 055007 (2019). [2] K. C. Lee, Phys. Plasmas 13, 062505 (2006); [3] K. C. Lee, Phys. Plasmas 24, 112505 (2017)   

Interpretation of thermal conductivity in DIII-d, taking into account.

The Georgia Tech GTEDGE edge transport interpretation code, with improved Ion Orbit Loss (IOL) models for neutral beam and thermalized ions in the edge plasma, is being applied to DIII-D shots to facilitate comparisons of various theoretical particle and thermal diffusivity models. The code interprets the thermal diffusivity while correcting for non-diffusive phenomena, including IOL, convection, viscous heating, rotational energy, and work done by the flowing plasma against the pressure tensor. These experimental results are being compared with various theoretical models, including paleoclassical, neoclassical, ITG, drift ballooning mode, TEM, and ETG. We also interpret viscous drag and a pinch velocity using IOL-corrected particle fluxes. Analysis of shot {\#}166606 shows that significant decreases in thermal conductivity are be found in the edge plasma when non-diffusive effects are taken into account.   

Neoclassical toroidal rotation in a tokamak plasma.

Rotation is important in tokamaks because of its effects on confinement and stability. This work evaluates the effectiveness of neoclassical gyroviscous theory in determining the toroidal rotation magnitude and profile in tokamak plasmas, by comparison with DIII-D experiment. We find that when the poloidal dependence, upon which the gyroviscosity depends, is adequately represented, the toroidal rotation is over-predicted to within only a factor of two or less of measured values. In order to make this evaluation, a numerical method for predicting with high accuracy the two-dimensional rotation and density profiles of a multiple species plasma was developed. We developed a conforming spectral Galerkin strategy using a streamline potential decomposition of the velocity. In this method, the velocities and densities are expanded poloidally in a Fourier series and radially in Bessel functions. Our results show promise for this approach and suggest that resulting two-dimensional neoclassical calculations of toroidal rotation may be within a factor of two of experimental values.   

Impact of new heating and current drive sources on the DIII-D high $q_{min}$ scenario

In the DIII-D high-$q_{min}$ scenario, $\beta_N\sim$3.7 and $q_{min}$ have been achieved with almost a fully-noninductive current profile for a few seconds in a still-evolving discharge. Starting from this high-performance discharge, changes to the current and pressure profile will be evaluated with the additional new off-axis beamline and top-launch electron cyclotron current drive (ECCD). The broadening of these profiles is expected to reduce the previously significant fast-ion transport in this scenario, increase $q_{min}$, and improve overall confinement. The original discharge was near its ideal wall limit but DCON modeling has shown that changes to the plasma shape, particularly outer gap and resultant increased triangularity, will increase this limit. During the experiment, shape changes will be implemented to increase its ideal limit and tested with the new heating and current drive sources to achieve higher $\beta_N$. The timing of the neutral beam and ECCD waveforms and their injection location will be varied and changes to the fast-ion activity, confinement, $q_{min}$, profile evolution and inductive fraction will be presented.   

Current density evolution in high qmin scenarios with the new DIII-D beam geometry

Further development of a high-q$_{min}$ ($\sim$2), high-$\beta$ ($\sim$4) scenario is assisted by upgrades to the DIII-D tokamak. Available co-current neutral beam (NB) sources have increased from six to eight, four of which can be injected off-axis. The additional off-axis NB current drive and heating is predicted to broaden the current density and pressure profiles, and increases the ideal stability limit, thus enabling the higher $\beta$ operations. This poster focuses on how the new NB injection capabilities affect the evolution of the current density profile in this high-q$_{min}$ scenario. The increased NB power drives additional current in two ways: direct NB current drive and bootstrap current driven by a change in the temperature and density profiles. TRANSP simulations with experimentally inferred fast ion diffusion predict that the increase in bootstrap current has the larger effect on the broadening of the current density profile. We will report on experiments guided by these simulations, including direct comparisons of predicted and measured current density profiles. This will be used to compare the relative efficacy of on-axis NB, off-axis NB, and electron cyclotron current drive.   

Off-axis Neutral Beam Current Drive on DIII-D

Off-axis Neutral Beam Current Drive (NBCD) physics is being validated by DIII-D experiments using tilted beams. Off-axis NBCD broadens the current and pressure profiles to improve energy confinement and low-n kink-type ideal-MHD stability, enabling access to reactor relevant $\beta_N>4$ at fully non-inductive $f_{NI}=1$ conditions. The off-axis NBCD profiles measured by the magnetic field pitch angles from the motional Stark effect (MSE) diagnostic agree well with modeling using the orbit-following beam-slowing-down Monte Carlo code NUBEAM for H-mode plasmas in a range of discharge conditions without large-scale MHD activities such as Alfvén eigenmodes and sawteeth, showing that the off-axis NBCD efficiency does not decrease with deposition at large minor radius. Projecting to the Compact Advanced Tokamak (CAT) Pilot Plant shows an excellent current drive efficiency with the NBCD peak at $\rho > 0.6$, which aligns well with the high bootstrap current $f_{BS} > 0.8$ operation, maintaining a broad current profile with $q_{min} > 2$. We will report initial results from the NBCD measurement experiment using a newly available 2nd tilted beamline to advance physics understanding of off-axis NBCD for high $\beta_N$ steady-state scenario development.   

Development of High Non-Inductive Fraction High Poloidal Beta Discharges at ITER Q$=$5 Equivalent Performance on DIII-D

Modelling of DIII-D high poloidal beta scenario predicts new off-axis current drive capabilities will enable nearly 100{\%} non-inductive operation at ITER Q$=$5 equivalent performance. Experiments on DIII-D have extended high energy confinement (H98\textgreater 1.5), large radius internal transport barrier (ITB) operation from q95$\ge $10 to lower q95\textasciitilde 7, which is more relevant for the ITER steady-state mission. While large Shafranov shift can stabilize all ion turbulence at betaN\textasciitilde 3 and q95$\ge $10, some drift wave instabilities remain in the lower q95 regime. With betaN$=$3.8, gyrokinetic simulations predict a stronger ITB and better confinement in comparison with experimental data at betaN$=$3.1. Recent DIII-D upgrades, including additional off-axis NBI power, increase off-axis external current drive. This should increase stability and non-inductive fraction at higher betaN. 0D modelling predicts betaN\textasciitilde 4 and H98\textasciitilde 1.5 should enable f\textunderscore NI\textasciitilde 90{\%} with q95\textasciitilde 7. It gives G98$=$betaN*H98/q95\textasciicircum 2\textasciitilde 0.122, matching the normalized performance goal of ITER's Q$=$5, according to the latest ITER simulations using high betap concept (G98\textasciitilde 0.113, J. McClenaghan, NF 2017) Work supported in part by US DOE under DE-SC0010685, DE-FC02-04ER54698, and NNSF of China under Grant No11575248.   

Theory-based Modeling of ITER Baseline Scenarios on DIII-D with High Power Electron Cyclotron Heating

Theory-based integrated modeling validated against DIII-D experiments predicts that the planned upgrade of high power Electron Cyclotron Heating (ECH) allows access to dominant electron heating regime with low rotation for the ITER baseline scenario (IBS) in a scaled ITER shape on DIII-D. The FASTRAN modeling in the core region with TGLF reproduces reasonably well the experimental profiles of the IBS discharges including electron density, electron and ion temperatures, toroidal rotation, and plasma current (poloidal magnetic flux) self-consistently with EPED1 for edge pedestal, EFIT for MHD equilibrium, NUBEAM and TORAY for external heating and current drives. It is predicted that at least 5 MW ECH is needed to produce an ECH-only IBS to match the normalized ITER value of I$_{\mathrm{p}}$/aB$_{\mathrm{T}}$ and $\beta_{\mathrm{N}}$. It is found that thermal energy confinement H$_{\mathrm{98}}$ depends strongly on the location of ECH deposition and the plasma density, indicating central heating at relatively high density is needed to achieve the target value of H$_{\mathrm{98}}=$1. Preliminary simulations on the effect of heat transport caused by sawteeth will be discussed for cases with ECH inside the radial location of $\rho $(q$=$1)\textasciitilde 0.5.   

Simultaneous Control of Multiple Resistive Wall Modes on the DIII-D Tokamak

Resistive wall modes (RWM) with toroidal mode number n\textgreater 1 have been observed on the DIII-D tokamak following successful stabilization of the n$=$1 mode. This motivates the development of a feedback algorithm for simultaneous multi-n control. In order to determine the optimal control coil configuration, simulations were conducted for various internal and external control coil configurations for both current and voltage control power supplies. The simulations factored in realistic limits on the power supplies as well as studied the effects of various latency values. Both the power supply limits and latency are found to reduce the maximum controllable normalized beta. The simulations also predict significant n$=$1 and n$=$2 plasma response when the plasma pressure is near, but below the marginal points of these modes. This response is a key point of comparison with experimental measurements and indicates the importance of feedback even below the marginal point. The feedback algorithm has been implemented on real-time GPU hardware using parallelized matrix operations to achieve a 5 $\mu $s latency, with the latency increasing logarithmically with matrix size. We will report on the first experimental tests of this new multi-mode control technique and comparisons with simulations.   

How Are NTMs Seeded?

A model for how neoclassical tearing modes (NTMs) are seeded by MHD transients (ELMs and sawteeth) explains experimental observations on DIII-D. This research uses extensive DIII-D diagnostics (comprehensive magnetic perturbation measurements, 1 ms resolution CER vertical and toroidal flows, kinetic profile data analysis tools) to describe NTMs in ISS-type DIII-D discharges in terms of a nonlinear, toroidal-based NTM model that includes for the first time MHD transient effects. The evolution of resonant magnetic perturbations through a sequence of m/n modes that ultimately result in large amplitude 2/1 NTMs is diagnosed. The observed NTMs initially decay or grow slowly after MHD transient events until, in response to a particular MHD event, they can grow robustly and brake plasma rotation into a locked mode that may cause a major disruption. Key conditions for a robustly growing NTM and slowing into a locked mode include sufficient bootstrap current drive and a MHD-induced transient that creates a large enough magnetic island and resultant NTM mode rotation change.   

Plasma Properties of Tearing Stabilized Regime by Rotating External 3d Field in the Presence of Error Field

The edge density profile in a tearing stabilized regime produced by a slowly-rotating 3D field in the presence of a static error field (EF) has the unique property of building up an H-mode edge with a large density gradient. Reduced MHD simulations [S. Inoue (PPCF 2018, IAEA 2018)] have suggested that an external 3D field rotating above a critical velocity can shield out EF as well as the rotating 3D field itself and produce various stabilized tearing structure responses. The tearing structure can be isolated because the EF and rotating external 3D field do not fully penetrate inward radially. In DIII-D experiments, a single-helicity response was found to be produced as predicted, together with a sharp edge electron temperature gradient. Later, a multi-helicity response was formed with a sharp edge density gradient, but the electron temperature profile seems to be dominated by ergodic-magnetic transport, which may not be attractive for reactor application.   

Ramification of error field correction and quasi-axisymmetry in tokamaks

Non-axisymmetric (3D) error field correction (EFC) in tokamaks aims at successful restoration of plasma performance to that expected for axisymmetry, even if the consequence of the ``correction'' is an overall increase of non-axisymmetry. This has been demonstrated in numerous examples, e.g. NSTX(-U), DIII-D, and COMPASS, with EFCs minimizing a dominant resonance. The remnant errors, including non-resonant fields, are typically subdominant with only minor degradation, but can also induce a critical event in particular scenarios that are sensitive to external perturbations. An important example is a disruption during L-H transition as shown in COMPASS, and also in a recent DIII-D study. EFCs against both of these resonant and non-resonant effects are in fact requiring remnant fields to be quasi-axisymmetric (QAS), or practically quasi-isodynamic with minimized parallel currents. Applied 3D fields optimized by the General Perturbed Equilibrium Code (GPEC) to be as QAS as possible within the capabilities of existing coils have been indeed shown to induce nearly no discernable performance degradation in DIII-D. New 3D coil designs using GPEC may be able to further optimize the distinct application or correction of resonant, non-resonant, and QAS 3D fields in tokamaks such as DIII-D, COMPASS-U, KSTAR and ITER.   

Progress towards a new 3D equilibrium reconstruction code

Equilibrium reconstruction is a crucial modeling step for any fusion experiment. In recent years, considerable development efforts have focused on obtaining solutions to the general 3D equilibrium reconstruction problem. While other notable 3D codes typically rely on Fourier decompositions and iterative procedures, the 3D equilibrium code presented in this contribution retains a full geometrical approach and, instead, tackles the equilibrium problem similarly to EFIT, that is, by decoupling the algorithm in a slower precomputation of response function tables, to be run once and stored, and a faster multiplication algorithm to be invoked multiple times. The resulting 3D code, which is under heavy development, is capable of computing the magnetic field and the vector potential at any point in space as produced by a given set of external magnetic coils and a predetermined set of plasma filaments, and therefore predicts the modeled diagnostic signals on any set of magnetic flux loops or probes. The response function matrix is then inverted to obtain the filament positions and currents that best fit the experimentally-obtained magnetic data. The main features of the code are presented here, together with the shortcomings of the filamentary model, and early results and benchmarks.   

\textbf{Argon Expulsion from Runaway Electron Plateau by Massive D}$_{\mathrm{\mathbf{2}}}$\textbf{ Injection in DIII-D}

Massive (500 Torr-L) injection of D2 gas is seen to reduce Ar content of DIII-D runaway electron (RE) plateaus, resulting in greatly reduced RE collisional dissipation but increased excitation of kinetic instabilities. The mechanism for Ar reduction appears to be penetration of the injected neutrals into the RE plateau, which cools the background thermal plasma by elastic and inelastic collisions. This lowers the ionization source term, allowing Ar to recombine. The Ar neutral density is then lowered on-axis due to neutral pressure balance and on-axis heating of the Ar by REs. This sequence results in a rapid (ms) drop in line and bremsstrahlung emission. Comparison between wall heat loads and radiated power indicates that the power loss changes from Ar line radiation to D2 neutral heat transport. Test particle modeling and x-ray data indicate that the RE distribution function itself changes strongly in the keV region but only slightly in the mid-energy MeV region during the Ar expulsion.   

Equilibrium Reconstruction of Post Thermal-Quench DIII-D Disruptions

Equilibrium reconstruction of tokamak plasmas during disruptions is critical to gain physics insight and to develop effective mitigation and control strategies. Reconstructions of such plasmas are challenging due to the development of large attached halo currents flowing in the open magnetic field line region and 3D effects. In this contribution, equilibrium reconstructions of several DIII-D pellet-induced disrupting plasmas are presented. Similar to previous results, the plasma boundaries remain very similar after the thermal quench. During the early current quench phase, the plasmas stay nearly axisymmetric as the halo currents start to flow poloidally. The plasma shapes remain diverted for a short period before hitting the inner vessel wall and become limited. As the current further decays, the plasma continues to shrink and starts drifting vertically until reaching the vessel top or bottom. During this phase, the current profiles continue to peak with a significant increase of the plasma internal inductance. Later in the current quench phase, 3D effects become more important. Details of the 3D and runaway electron effects and use of the new DIII-D 3D magnetic probes to guide reconstructions of 3D perturbed equilibria will be discussed.   

Effect of L-Mode Electric Field Bifurcations and Edge Stochasticity on the L-H Transition Power Threshold with Applied n$=$3 Resonant Magnetic Perturbations*

H-mode access in ITER-similar-shape plasmas in DIII-D ($n_{\mathrm{e}}=$1.5-5x10$^{\mathrm{19}}$m$^{\mathrm{-3}}$, $B_{\mathrm{t}}=$1.9-2T, $I_{\mathrm{p}}=$1.5MA, $q_{\mathrm{95}}=$3.6) with applied n$=$3 Resonant Magnetic Perturbations (RMP) is found to depend on edge collisionality like $P_{\mbox{LH}} /P_{\mbox{LH-08}} \sim (\nu \ast )^{-0.5}$. This is a concern for ECH-heated, low collisionality plasmas on ITER since RMP may be applied before the L-H transition to safely suppress the first ELM. Bifurcations to positive radial electric field, increased toroidal co-rotation, and reduced edge $E\times B$ shear are observed when RMP fields are screened, preventing H-mode access at high applied RMP within the heating power range explored (P$_{\mathrm{loss}}\le $4 MW). Evidence of restored H-mode access with n$=$3 RMP field penetration is presented. An edge stochasticity model accounting for electron loss in the stochastic boundary layer can explain the experimental findings. The observed increase in $P_{\mathrm{LH}}$ at low collisionality is attributed to a reduced ExB shearing rate $\omega _{\mbox{E}\times \mbox{B}} $ and an increased normalized growth rate $\gamma _{\mbox{L}} /\omega_{\mbox{E}\times \mbox{B}} $.   

Role of turbulence mode velocity shear in Triggering the L-H Transition.

Comprehensive 2D edge turbulence and flow measurements across the L-H transition on DIII-D exhibit two poloidally counter-propagating bands of low-k density fluctuations for plasmas that have lower power thresholds in ITER-similar-shape discharges with near zero external torque injection. The velocities of either mode do not individually match the mean Er×B velocity measured with CER, and the mode velocity shear is much larger than the mean Er×B velocity shear. The Reynolds stress inferred from Beam Emission Spectrocopy data consistently increases approaching the L-H transition in the presence of these dual modes. These observations are consistent with previous theoretical gyrokinetic simulations that, in the absence of toroidal ion rotation, the intrinsic diamagnetic drift wave phase velocity shear adds to the ion pressure gradient Er×B velocity shear component and becomes important for turbulence stabilization. These observations are important for developing a predictive capability for the L-H transition power threshold in burning plasmas.   

Database study of fast-ion instabilities

To understand mode stability, over 1000 discharges have been examined for evidence of ellipticity-induced, toroidal, reversed-shear, and beta-induced Alfven eigenmodes (EAE, TAE, RSAE, BAE), for beta-induced Alfven-acoustic eigenmodes (BAAE), and for energetic-particle geodesic acoustic modes (EGAM) instabilities. The database is limited to the initial two seconds of the discharge, where the evolving q profile facilitates identification of RSAEs and provides an effective scan of the dependence of stability upon q. A combination of electron cyclotron emission, magnetics, beam emission spectroscopy, and interferometer data detect the modes. EAEs occur most often when the elongation exceeds 1.8. TAEs and RSAEs are more common than BAEs and BAAEs. RSAEs occur for poloidal betas below 0.8, while BAEs are more likely to be unstable when the poloidal beta exceeds 0.5 and for particular values of q. BAAEs with a characteristic "Christmas light" pattern of brief instability as q evolves occur in plasmas with relatively high electron temperature but low poloidal beta. EGAMs are more common in plasmas in which counter injection and plasma currents between 0.4-0.85 MA cause a significant loss cone.   

Impact of broadened fast ion pressure profile on Alfven eigenmodes in high qmin steady state scenarios in DIII-D

The reverse-shear, qmin\textgreater 2 steady state scenario is of interest for high-beta, fully noninductive long pulse tokamak operation. In previous DIII-D experiments, the high fast-ion fraction (40{\%}) and steep energetic particle (EP) pressure profile strongly drives Alfven Eigenmodes (AEs) that cause redistribution, loss, reduced beam heating and current drive efficiency, and ultimately limit the achievable $\beta_{\mathrm{N}}$. In new experiments, DIII-D's recently upgraded off-axis neutral beams will be used to create EP pressure profiles near the critical gradient, enabling improved control of EP transport. Additional techniques, including reduced beam voltage, q-profile manipulation with electron cyclotron current drive, varied toroidal field, and other plasma parameters will be used to alter AE drive and damping and test limits of whether classical fast-ion behavior can be achieved while preserving heating and current drive performance. The TGLF-EP$+$Alpha critical-gradient model will be compared to experimental EP pressure profile measurements as part of a rigorous validation effort, which is needed to assess accuracy of reduced models for integrated predictive modeling and scenario development in DIII-D and future tokamaks.   

Upgrade and crosscheck of neutron measurements on DIII-D

The neutron diagnostic system on DIIID consists of a set of neutron counters and a set of scintillators which, together provide critical measurements for assessing beam ion confinement. In order to accommodate the large dynamic range encountered in the broad range of DIII-D scenarios, each set contains multiple detectors with different sensitivities. The neutron counter system that formerly used NIM and CAMAC modules has been replaced by modern Field Programmable Gate Array (FPGA) based pulse-counting electronics. The new system features a 12-channel, 16-bit resolution digitizer with maximum sampling rate of 120MSPS. The onboard FPGA is currently used as a pulse height analyzer, and has the potential capability for neutron and gamma discrimination. In addition, the signal of one fission chamber is analyzed with a commercial neutron flux monitor loaned from PPPL, which provides amplification, pulse shaping, discrimination against alpha, gamma and electronics noise in a rackmount drawer. Absolute calibration is obtained using a Cf source on a model train, followed by cross-calibration of less sensitive detectors during plasma shots. Theoretical predictions by the TRANSP code in MHD quiescent plasmas check the calibration. The scintillators provide \textless 0.1ms time resolution, as well as an independent check of the stability of the calibration.   

Measurements to characterize Alfven eigenmode induced critical gradient conditions using a new FIDA diagnostic on DIII-D

A new high resolution fast ion D-alpha (FIDA) diagnostic with reduced channel-to-channel uncertainty for detailed energetic particle (EP) transport model validation has been installed on DIII-D. The system measures co-passing EPs profiles with outstanding spatial resolution and it is composed of simultaneous 2D imaging FIDA (I-FIDA) and a full spectrum (650-662 nm) system (S-FIDA). The I-FIDA sub-system generates a 2D image of the blue-shifted FIDA signal, integrated in the spectral region 650-652 nm (E$\simeq$40-80 keV), with spatial resolution $\leq$2 mm for precision in EP gradient computation, asymmetry assessment, and detection of EP interactions with MHD modes. The S-FIDA sub-system shares the I-FIDA input optics to allow for the same viewing geometry, with 15 chords between R=1.55-2.0 m at 3 cm resolution. Previous experiments show that Alfven eigenmodes cause critical gradient EP transport, resulting in stiff profiles for EP distribution functions above the critical gradient threshold. New measurements of the time evolution of EP gradient will be used to build an empirical database of the critical gradient in a variety of conditions of magnetic shear, fast-ion fraction, and fast-ion profiles using DIII-D’s recently upgraded off-axis neutral beam.   

A Novel Stacked Scintillator Detector for Bremsstrahlung Measurements of the Runaway Electron Distribution Function

A novel stacked scintillator detector (SSD) has been developed at DIII-D to measure bremsstrahlung radiation produced by runaway electrons. Designed to be interchangeable with the existing Bismuth-Germanate (BGO) scintillating crystal detectors in DIII-D's Gamma Ray Imager's (GRI), the SSD have several improved characteristics compared to the BGO detectors. When running in pulse-height counting mode the BGO detectors provide excellent energy resolution; however, when the incoming flux becomes large, pulse pile makes it difficult to distinguish individual pulses. Additionally, due to the presence of pre-amplifying circuits, the BGO signal can saturate. These problems can be resolved at the cost of energy resolution by running the BGO detectors in current mode. The new SSD recovers a coarse energy resolution while running in current mode by stacking multiple scintillating crystals separated by attenuating material. In this work, we will discuss the design of the SSD and characterize their instrumental response. Additionally, the sensitivity of the detectors to different points in the runaway electron orbit-space (orbit weight functions) will be shown.   

Observation on Phase Space Route of Fast Ion Transport during Alfvén Eigenmodes Activities in Toroidal Plasma

The imaging neutral particle analyzer (INPA) in DIII-D tokamak for the first time observes the fast ion transport route in the velocity space during the intense activities of multiple Alfvén eigenmodes (AE). The experiment investigates the maximum achievable signal at each local phase space by scanning the power of relevant neutral beams. It is found that the signals from certain phase space are easily saturated with only single neutral beamline. In other words, any additional power of neutral beam steered into those phase space does not produce any signal expected in neoclassical theory, exhibiting the nature of anomalous transport. The phase space with such character is referred to ‘deficit region’. A velocity-space map of the deficit region is obtained and following features are observed: (1) The outermost boundary of the deficit region is correlated to the radial extension of the relevant AE mode. (2) The deficit region connects different resonances of three major types of AE instabilities in velocity space. (3) The deficit region bridges the phase space of 80keV in the core to 65keV in the edge, following a pattern of particle streamline that particle energy is exchanged with toroidal angular momentum with a constant magnetic moment.   

\textbf{Neoclassical toroidal viscosity due to energetic particles}

The strength of neoclassical toroidal viscosity (NTV) induced by energetic particles (EPs) is investigated in DIII-D experiments. The NTV torque, which can greatly affect the plasma momentum confinement, is a result of drift kinetic non-ambipolar transport in the presence of 3D fields, where both thermal particles (most current research) and EPs can play a contributing role theoretically. A sophisticated DIII-D experiment is designed to validate the NTV torque due to trapped EPs by varying neutral beam injection angle and beam energy in the presence of the n$=$2 magnetic perturbations, and measuring the induced NTV from these EPs. The plasma response and NTV torque are compared between the experimental measurements and MARS-K kinetic simulation, to verify the existence and parametric dependence of EP induced NTV. This theory validation is the first step towards predicting the EP NTV for future devices such as ITER, where the NTV is expected to play an important role in the momentum balance.   

Dependence of compressional Alfv\'{e}n eigenmode instability on fast-ion density and phase space distribution on DIII-D

Instability of compressional Alfv\'{e}n eigenmodes (CAEs), driven through Doppler-shifted cyclotron resonance with beam ions, is studied in an experiment on DIII-D that varies beam current at constant beam voltage. A mode excited by an off-axis co-I$_{\mathrm{P}}$ injected beam is observed with a pair of toroidally separated magnetic field sensing loops to be propagating counter to the beam direction with n$=$-5 and f \textasciitilde 0.57f$_{\mathrm{c}}$. The mode is unstable at high beam current and observed to stabilize as the current drops below a threshold. This would seem consistent with a simple theoretical expectation for CAEs to be unstable at beam densities above a dissipation-based threshold [Belova 2017]. However, TRANSP modeling shows that the fast-ion phase space distribution changes in a complex way over the lifetime of the mode. The initial destabilization of the mode is observed to be delayed \textasciitilde 10ms after beam turn-on. The complicated evolution of mode stability during the beam current scan motivates an in-depth analysis of the changing fast-ion distribution to determine the exact features controlling the instability. Analysis is underway to compare mode stability with expectations from the orbit-averaged resonance equation evaluated for particles in the fast-ion population.   

\textbf{Measurements of CAE }\textit{\~{n}}\textbf{ in DIII-D and identification of intermediate frequency AEs}

New analysis is reported of recent measurements of fast-ion driven compressional Alfv\'{e}n eigenmodes (CAE, $\omega $\textless $\sim \omega_{ci})$ and intermediate frequency AEs ($v_{A}/R \ll \omega \ll \omega_{ci})$. These modes are of interest because they can potentially cause electron energy transport; additionally, these measurements advance the development of AE spectroscopy as a tool for non-invasive diagnosis of fast-ions in DIII-D and burning plasmas. Measurements of CAE radial structure obtained with an array of eight fixed frequency reflectometers are analyzed to determine absolute \textit{\~{n}}. Intermediate frequency modes preliminarily identified as Alfv\'{e}n eigenmodes (AE) were observed in beam-heated ELMing H-mode plasmas. However, the observed frequencies---$f \sim $1 -- 2 MHz $\sim $ 2 -- 5 $v_{A}$/2$\pi R$ (where $v_{A}$/$R$~$\sim $~0.03 $\omega_{ci})$---are too low for CAEs and too high for toroidicity-induced or reverse shear AEs. The observed frequencies and two-point toroidal mode number measurements (\textbar $n$\textbar $=$ 3 -- 6) will be compared with the spectrum of AEs predicted by the ideal MHD eigenmode code NOVA in order to potentially identify the type of mode observed.   

Uniqueness of Stellarators and Their Design

Stellarators are unique among all fusion concepts--inertial and magnetic--in not relying on the plasma as a part of the confinement concept. HSX and W7-X demonstrated that radically new stellarator designs actually work. One can computationally determine the best conceptual design and then build a validating experiment rather than driving development by a decades-long experiment based on an extrapolation. Even the design of reactor-scale stellarators seems credible; no known physics issues must be overcome, such as disruption avoidance in tokamaks. Much remains to be computationally explored to make stellarators more attractive and to assure the achievement of fusion. An optimal reactor has rapid transport in the central part of the plasma with the confinement provided by a wide annulus. An unexplored option, \url{http://arxiv.org/abs/1906.06807}, is to focus on that annulus by finding a magnetic surface $\vec{x}_s(\theta,\varphi)$ in Boozer coordinates that gives the desired form for the field strength, such as $B_s(\theta-N\varphi)$. This requires two of the three free functions in $R,\zeta,Z$ cylindrical coordinates. A single function of $\theta,\varphi$ specifies the external field. Coil designs could be simpler and allow open access to the plasma chamber.   

Optimizing Stellarator Surfaces Using Magnetic Island Width Sensitivity

To improve confinement, stellarator vacuum magnetic flux surfaces must be optimized to eliminate magnetic islands. Small perturbations to the intended magnetic field configuration may nonetheless cause the appearance of small magnetic islands at rational flux surfaces. For the construction of a fusion device, a large sensitivity of the width of any magnetic island on small perturbations implies that tighter tolerances on the position of coils producing the vacuum magnetic field are necessary. A quantity called shape gradient, which can be readily related to the local tolerance of the coils, appropriately quantifies the island width sensitivity from a practical point of view. Optimizing stellarator surfaces to have low island width sensitivity is achieved by minimizing this shape gradient. We present progress made in the development of a tool that aims to efficiently compute the shape gradient of the characteristic magnetic island width of stellarator vacuum magnetic fields. J. D. Hanson and J. R. Cary, Physics of Fluids B: Plasma Physics \textbf{3}, 1006 (1991). M. Landreman, E. J. Paul, Nuclear Fusion \textbf{58 }(7), 076023 (2008).   

A proposed simple stellarator - SAS

A new concept for making 3D fields using permanent magnets has led to a proposal for a new experiment, called SAS, to be located at the Princeton Plasma Physics Laboratory. The idea, born from the observation that stellarator shaping fields are nearly magneto-static, is to use permanent magnets in concert with a simple toroidal solenoid with planar coils to create an optimized stellarator. The proposed device will use components of the cancelled NCSX experiment, including the toroidal field coils and the vacuum vessel, along with and array of neodymium magnets which are mounted to a structure near the plasma boundary. Neodymium magnets have surface residual magnetic fields of 1.4T, but careful arrangement of the geometry can amplify this value using Halbach arrays. The toroidal field anticipated for this device will be in the neighborhood of 0.5T. Initial calculations indicate that the total mas of magnetic material required for the planned machine at the target TF field is \textasciitilde 2m$^{\mathrm{3}}$. Concept designs will be presented including methods for holding the magnets and support structures for the various components. Additionally, we present results from new optimization methods that have led to improvements in several physics attributes of the planned equilibrium.   

Simple-coil optimized stellarator designs for pilot plants.

Permanent magnets provide a method to produce optimized stellarator configurations using very simple coils. Simple coils should reduce the cost and engineering risk of stellarator experiments and enable large-aperture sector maintenance for fusion systems, resolving a long-standing research need. Commercially available permanent magnets can produce local magnetic fields of \textasciitilde 1.7T in a background field up to 7.7 T when cooled. Permanent magnets impose different constraint on plasma shape optimization than coils. Analysis of NCSX alternative designs shows that permanent magnets can produce plasma shapes not accessible with physical coils. This flexibility has been used to re-examine stellarator optimization for quasi-axisymmetric plasma confinement. Parametric variation is used to identify promising design approaches and parameters for physics experiments and compact fusion pilot plants, building on earlier studies.   

Novel methods to design permanent magnets for stellarators

Excessively complex coil is one of the main challenges for stellarators. In recent years, tremendous efforts have been devoted to simplifying stellarator coils. These studies are all concentrating on current-carrying electromagnet, which is the only type that has been used on stellarators to date. As the most common way to generate magnetic field, permanent magnet (PM) has the potential to extremely simplify stellarator coils. Here, we introduce two novel methods to design PM for stellarators. The first method takes a surface current potential solved by conventional coil design codes and discretizes magnetic dipoles to exactly recover the target magnetic field. By incrementally stacking multiple layers, the maximum magnetization could be constructed below the existing material limit. The second method nonlinearly optimizes the position, orientation and moment of each dipole to simultaneously minimize the magnetic field error and PM volume. It has the capability to find the most efficient arrangement for permanent magnets. By employing the two methods, we are able to design permanent magnets for stellarators. Numerical results of quasi-axisymmetric stellarators are shown.   

Advancement towards a free boundary SIESTA

Advanced stellarators purposely break the nested topology of equilibrium fields to form islands for divertors. Bootstrap currents can change the size and location of scrape off layer islands potentially damaging plasma facing components. Protection of these components critical for achieving high performance operation requires understanding the underlying equilibrium. From an initial VMEC equilibrium, SIESTA allows for a radial component of the magnetic field and breaking the nested surfaces opening island and stochastic regions. Previously, SIESTA equilibria were limited to the bounds of the VMEC equilibrium. A new free boundary implementation extends the computational domain beyond the VMEC last closed flux surface allowing the modeling of islands in the scrape off layer.   

Stellarator Equilibrium Construction based on a Poincar\'e Sections Approach

Computing ideal magnetohydrodynamic equilibria of non-axisymmetric devices is not trivial, and this presents a significant challenge for the continued advancement of stellarator research. A more efficient equilibria construction code could expand the search space during stellarator optimization and enable real-time control systems to deal with bootstrap currents. In contrast to the energy principle method used by traditional codes like VMEC, a new technique is proposed that casts the search for an equilibrium into solving a system of ordinary differential equations. The advantage of this approach is twofold: First, the equilibrium equations are used as constraints to reduce the system to minimum dimensionality, with the plasma modeled by variables that lie on Poincar\'e sections. Second, root-finding techniques such as Newton's method can be used to solve the system of equations, which is generally faster than optimization techniques to find a minimum energy state. An overview of the new method is presented along with numerical results to validate that it converges to the same equilibria solutions as VMEC for tokamaks and stellarators with finite pressure. Continued work is being done to quantify the speed and radius of convergence of this algorithm.   

Influence of Plasma Profiles on Particle Disposition in Wendelstein 7-X like Simulation

An investigation of Beam Emission Spectroscopy (BES) signals subject to different plasma profiles is simulated for a Wendelstein 7-X (W7X) like configuration with the BEAMS3D code. BEAMS3D is a guiding center particle code that follows user defined particles and models neutral beam injection. A study is performed of the influence of plasma profiles on the particle deposition model. A goal of this study is to assess whether BES data can be used to constrain plasma density profiles. Simulation with different numbers of injected particles is being explored to assess incorporation of the BES forward model into STELLOPT for equilibrium reconstruction. As BEAMS3D is a Monte-Carlo code, the number of particles can play an important role in interpretation of results. Should a smaller number of starting particles produce comparable results, we can greatly reduce the runtimes and space needed when running the simulations.   

Modifications for Efficient NIMROD Stellarator Dynamics Computations

When pushed to high-beta conditions that are expected to excite MHD activity, stellarator and heliotron experiments show remarkable robustness and avoid disruptive behavior [1]. Time-dependent studies of the nonlinear evolution have been accomplished [for example, 2-3], but accurately representing the dynamics presents computational challenges. To meet these challenges, a variant of the NIMROD code is being developed to allow: expanding metric information and equilibrium fields in toroidal Fourier harmonics, performing all spatial integration at nodes over the toroidal angle, and incorporating 1D solves over the toroidal angle to complement existing preconditioner strategies. Besides these changes to the physics kernel, pre-processing is being modified for the setup of stellarator computations. Computational choices with respect to the new geometric representation are presented, together with results from verification tests. Progress on preconditioning the 3D algebraic systems is also presented. [1] A. Weller, et al., NF 49, 065016 (2009). [2] K. Ichiguchi, et al., PPCF 55, 014009 (2013). [3] T. A. Bechtel, C. C. Hegna, and C. R. Sovinec, this meeting.   

Stochastic Transport in Collisional High-beta Stellarator Equilibrium

The nonlinear, extended MHD code NIMROD is employed to simulate self-consistent high beta stellarator physics in the collisional limit. Heat is transported both along and across magnetic fields by finite diffusion operators that are highly anisotropic. This work concentrates on interpreting the transport features of the resulting MHD equilibria through comparison with Rechester and Rosenbluth style transport models. The configuration under investigation is an l=2, M=10 torsatron with vacuum rotational transform near unity. Finite-beta plasmas are created using a volumetric heating source and temperature dependent resistivity. Nonlinear, extended MHD simulations are performed to generate steady state solutions. These 3D self-consistent equilibria show that the magnitude of finite parallel heat conduction has a dominant effect on the temperature profile in regions with stochastic magnetic fields. This conclusion is corroborated by the effective cross-field thermal conduction which is computed a posteriori. Preliminary analysis of this effective transport shows impressive agreement with non-self-consistent analytic models of stochastic field transport. Comparison with the linear MHD equilibrium code, HINT2, as well as more sophisticated transport models is ongoing.   

Turbulent transport optimization in stellarators: trapped electron modes

Using three-dimensional shaping to reduce turbulent transport is an emerging theme in stellarator optimization. Recent work focused on understanding turbulent saturation physics as a means to affect ion temperature gradient instability induced transport [C. C. Hegna, et al, Phys. Plasmas 25, 022511 (2018)]. In this work, the dominant nonlinear energy transfer channel is determined by a three-wave interaction involving instabilities coupling to damped modes at comparable wavelength. The theory identifies metrics for turbulent suppression that are strong functions of 3D shaping. We are expanding this model to include the effects of trapped electron mode turbulence. This is accomplished through the introduction of bounce-averaged trapped electron modifications to a fluid model.   

Global simulations of ion temperature gradient driven modes in stellarator geometry with the gyrokinetic code XGC-S

Neoclassical optimisation has enabled stellarators where anomalous transport dominates, as in tokamaks. This is seen in Wendelstein 7-X's OP1.2. Simulations are needed to improve our understanding of turbulent transport in stellarators. Optimisation is also possible with the help of high performance computing. So far core global linear delta-f and nonlinear flux tube ensemble simulations have been performed. XGC is now being extended with a new version, XGC-S, ultimately including the code family's main features: total-f gyrokinetics to the first wall, for stellarators. XGC-S has recently been verified for fast particle orbit tracing, geodesic acoustic modes, and linear delta-f ion temperature gradient-driven (ITG) modes. Here, we will show the results of verification studies for linear and nonlinear delta-f ITG modes, which are believed to cause anomalous transport. They demonstrate that the tool can be used with confidence to simulate such physics globally in general stellarator geometry. Linear and nonlinear simulations of ITG modes in NCSX and W7-X geometries will be presented. Comparison between the global behaviour of the two stellarator types can be made. Ongoing implementation of new techniques for EM gyrokinetic simulation, also for stellarators, will be described.   

Global gyrokinetic simulations of the W7-X stellarator using the GTC code

Ion temperature gradient (ITG) turbulence in the Wendelstein 7-X (W7-X) is simulated using the gyrokinetic particle simulation code GTC. Using an electrostatic model with adiabatic electrons in a 3D geometry with magnetic coordinates, linear and non linear simulations are carried out in a partial torus. Numerical results are compared with other codes. Mode structure and coupling in W7-X stellarator is analyzed. Suppression of ITG turbulence due to zone flows is observed. Initial comparisons between neoclassical transport and turbulence transport are reported.   

Temperature screening of impurities in stellarators and tokamaks deviating from symmetry

Quasisymmetric stellarator configurations aim to combine the stability of stellarators with the confinement of tokamaks, making them particularly interesting for optimization efforts. However, perfect quasisymmetry can only be achieved on a single flux surface at best, making it useful to study configurations with small deviations from perfect quasisymmetry, a regime in which devices will have to operate. A particular neoclassical phenomenon that occurs in tokamaks, which are naturally quasisymmetric, is a favorable outward radial flux of highly charged impurity ions, commonly referred to as impurity temperature screening. Conversely, stellarators generally display an~\textit{inward}~impurity flux, causing an impurity accumulation in the core that can be detrimental to performance. In this work, we use the SFINCS drift-kinetic solver to explore how the impurity particle flux is influenced as the degree of symmetry-breaking is varied between realistic levels and perfect quasisymmetry, over various reactor-relevant parameter regimes and configurations. We aim to answer the question of exactly how much symmetry-breaking a particular configuration can tolerate before impurity temperature screening is lost.   

Upgrade of the Helically Symmetric eXperiment (HSX) with a new 70 GHz gyrotron

HSX is a neoclassically optimized stellarator with major and minor radii of 1.2 and 0.12 m, respectively. It has been operated successfully since 2001 and demonstrated improved neo-classical confinement and strong turbulent heat transport in the electron channel. However, studies of the neoclassical and turbulent ion-heat transport have been challenging since the available 28 GHz ECRH system can only be applied during low-density plasmas to avoid cut-off. Thus, an additional 70 GHz, 500 kW gyrotron, previously used at W7-AS, is being installed which will be operated in the X2 polarization scheme, requiring a 25{\%} increase of the magnetic field strength of HSX. With the new heating system, plasma experiments with 3x higher densities and about 5x more absorbed heating power will become possible. 1D modelling results of the expected performance will be presented that predict increased coupling between electrons and ions and a reduced level of charge-exchange losses due to the increased density. In combination with the application of new wall-cleaning techniques and strike-line protection, this might provide ion-temperatures on the order of 300 eV such that the ion confinement can be addressed for the first time in a quasi-symmetric stellarator experiment featuring low collisionality.   

Deuterium Beam Injection For Fast Ion Confinement Studies On The Helically Symmetric Experiment (HSX)

Fast ion confinement is of critical importance in advancing the stellarator concept. In order to study fast ions in quasi-helically symmetric fields, a neutral beam injector (1.2ms, 20keV, 40A) and neutron detector have been acquired for use on HSX from the MST group. Initial diagnostic results including beam-on-target D-D neutronics are presented. Computational analyses from GNET and BEAMS3D show that within present experimental constraints, sufficient ionization and confinement of injected neutrals can be observed. The background neutral density in HSX will substantially lower the confinement time of a fast ion population via charge exchange, so efforts to curtail this effect using advanced wall conditioning and strike line protection are discussed. There is an ongoing upgrade to the heating system in HSX which will facilitate lower background neutral density and higher ionization fraction by allowing a factor of three higher plasma density. Changes in the injection geometry will also be investigated as part of this upgrade to improve experimental conditions.   

Finite Plasma Flow Close to the Magnetic Axis in HSX

Profiles of the impurity ion mean parallel flow and radial electric field in HSX are measured using charge exchange recombination spectroscopy (CHERS). The technique involves measurement of the ion parallel flow at two locations on a flux surface. The parallel flow close to the plasma core is measured to be approximately 10 km/s for the Quasihelically Symmetric (QHS) configuration and up to 20 km/s in a magnetic geometry in which the quasihelical symmetry is intentionally degraded. In this same region, the pressure gradients are small, making it difficult to understand how the flow remains finite. One proposed explanation for the finite flow is that there is a torque on the plasma due to an ECH driven suprathermal electron flux. The flux is calculated using the GNET code and the fluid equation approach is used to model the evolution of the plasma flow and ambipolar radial electric field in HSX. The magnetic field spectrum in Hamada coordinates is used to calculate the plasma viscosity. Included in the model is momentum damping due to neutrals, which is significant for the low density, ECRH heated plasmas. Initial results indicate that the calculated parallel flow due to the ECH-driven torque is on the order of the measured flow.   

Hydrogen Isotope Effect on Particle Transport and Density Fluctuations in the HSX Stellarator

Plasma particle transport is studied using modulated gas puffing on the HSX stellarator. Isotope effects are investigated in hydrogen and deuterium dominant plasmas. In addition to density perturbation evolution, density fluctuations are simultaneously measured along 7 interferometer chords. Transport coefficients D and V are extracted by comparing measured amplitude and phase of the density modulations using a 1-D cylindrical model. For the model calculations, the particle source rates are estimated using the EMC3-EIRENE code. Results for magnetic configurations with and without quasi-symmetry are investigated. During these studies, the electron density was scanned in range of (1.5 - 5)x10$^{\mathrm{12}}$cm$^{\mathrm{-3}}$. Deuterium and hydrogen contents in plasmas are inferred from measured ratio of D$_{\mathrm{\beta }}$ and H$_{\mathrm{\beta }}$ emissions.   

Impurity Transport Experiments at the HSX Stellarator with Laser Blow-Off Injections

The laser blow-off technique is used to inject aluminum atoms into the confined region of HSX. To study the radial propagation and confinement properties of the injected impurities, signals from several arrays of AXUV diodes are evaluated and compared with modeling results from the impurity transport code STRAHL. Initial results from hydrogen plasmas featuring electron densities in the range of $3\times10^{12}\ \text{cm}^{-3}$ and temperatures of up to 1.2 keV demonstrate centrally peaked emissivity profiles. The rapid appearance of core localized emissions after injections agrees with STRAHL modeling when assuming values of anomalous diffusion well above the neoclassical level. A sensitivity study shows that the uncertainties in the background neutral density and the scrape-off layer loss time make detailed studies of anomalous diffusion profiles challenging. However, studies of the dependence of the impurity confinement ($\tau$) on the absorbed ECH power (P) exhibit a $\tau \sim \text{P}^{-1}$ scaling, similar to the ISS04 scaling, suggesting a substantial impact of turbulence on the impurity confinement in HSX.   

Experimental measurements of heat flux and density fluctuations compared to gyrokinetic simulation in the HSX stellarator

The Helically Symmetric eXperiment (HSX) has demonstrated reduced neoclassical transport in the plasma core with quasisymmetry, but strong anomalous transport outside this region. Previous work\footnote{W. A. Guttenfelder, Thesis, UW–Madison, 2008.}\footnote{G. M. Weir, et al., PoP 22, 2015.}\footnote{B. J. Faber, et al., PoP 22, 2015.} suggests this transport is due to the Trapped Electron Mode (TEM). This study compares linear and nonlinear gyrokinetic simulations to experimental heat flux and density fluctuation measurements for two configurations: Quasi-Helical Symmetry (QHS) and broken symmetry (Mirror). Linear growth rates are smaller in Mirror, while the nonlinear heat flux is actually larger. Experimental thermal diffusivity measurements agree with the difference between configurations from nonlinear simulation. Reflectometer measurements provide a direct connection to turbulence amplitudes, localized to the peak driving gradient. Fluctuations of the reflectometer phase are predicted to be linearly related to density fluctuations, and measurements are interpreted via a 2D model. We present the scaling of reflectometer fluctuations with respect to driving gradients, and compare to the scaling of density fluctuations from simulation.   

Modeling Ferritic Inserts with ANSYS-MAXWELL to Reduce Coil Ripple in Stellarators

Confinement of energetic particles is a critical issue for a fusion reactor. Ferritic inserts are used in ITER to reduce losses of energetic particles. This poster shows an initial implementation of ferritic inserts in a stellarator to reduce ``coil ripple'' and reduce losses. In order to produce a desired equilibrium with coils, it is advantageous to have the coils close to the plasma. However, this introduces a coil ripple term in the magnetic spectrum with toroidal number equal to the number of coils. This mode can reduce the confinement of energetic particles due to their trapping in coil ripple wells. Ferritic inserts can reduce coil ripple by decreasing magnetic flux density at the coil and increasing magnetic flux between the coils. We present ANSYS-MAXWELL simulations of shaped tokamaks and HSX as an example of a stellarator with and without ferritic inserts. We present the magnetic spectra showing the effects of the ferritic inserts on the amplitudes of all the modes.   

A Crossed-Beam Correlation Interferometer for Spatially Resolved Density Fluctuation Measurements in HSX

Turbulent transport has been shown to be important in HSX. At present, a primary physics goal is to study how spectral content and density scale lengths can affect turbulence. Recent gyrokinetic (GENE) simulations also show TEM associated fluctuation intensity varies as a function of poloidal angle on a given flux surface. Previous line-integrated measurements using interferometry indicated a flux surface asymmetry in the density fluctuation amplitude. Spatially resolved density fluctuation measurements are needed for comparing the measurements with GENE results. The existing multichannel interferometer in HSX is being modified to include a single probe beam perpendicular to the existing beams and apply crossed-beam correlation techniques (Fisher, 1967) to these measurements. This modification enables measurements of density fluctuation as a function of poloidal angle along the flux surface where the density gradient peaks. Measured fluctuation intensity and spectral data can then be compared to GENE simulations for the quasihelically symmetric configuration (QHS) and configurations where quasisymmetry is degraded. Results from GENE simulations and crossed-beam interferometry correlation bench testing are presented.   

Effects of Electron Cyclotron Heating on the Toroidal Flow in HSX Plasmas

Spontaneous toroidal flows have been observed in electron cyclotron heating (ECH) plasmas in HSX. HSX has two typical magnetic configurations: The Quasi-Helically Symmetric (QHS) configuration and the Mirror configuration, where a set of auxiliary coils breaks the helical symmetry. The QHS configuration has a neoclassical viscosity that is smaller than that of the Mirror configuration, so we expected that the toroidal flow velocity in the QHS configuration would be larger than that of the Mirror configuration. However smaller toroidal flow was observed in the QHS configuration. It has not been understood well yet. In previous studies, we have found that ECH can drive the $j_r\times B$ and collisional force, and the $j_r\times B$ force overcomes the collisional force. In this study, we evaluate the forces by ECH, and compare them to the experimental results. To evaluate these forces, we apply the GNET code, which can solve a linearized drift kinetic equation for supra-thermal electrons by ECH in 5-D phase space. Solving the momentum balance equations and Amp\`ere's law, we evaluate the toroidal flow velocity. Experimentally we will measure the plasma flow velocity in HSX as a function of plasma parameters (density and temperature), and compare them with simulations.   

\textbf{Overview of Compact Toroidal Hybrid Experimental Plans}

The Compact Toroidal Hybrid (CTH) is a torsatron/tokamak hybrid with the ability to vary the confining magnetic field configuration and generate rotational transform profiles that are tokamak-like with ohmically driven plasma current for disruption and MHD studies. The main goals of the CTH experiment are to study disruptive behavior as a function of applied 3D magnetic shaping, and to test and advance the V3FIT reconstruction code and NIMROD modeling of CTH. Past and recent disruption studies will be overviewed and their relevance to tokamaks and quasi-axisymmetric stellarators discussed. Ongoing diagnostic development for the experiment includes an upgrade to the interferometer, new spectroscopic studies, and coherence imaging of plasma flows. CTH also serves as a test bed for diagnostic development for our collaborations on the larger facilities like DIII-D and W7-X. These facility collaborations will be briefly summarized along with a new research direction to explore low temperature plasmas on magnetic surfaces.   

Density Limit Disruption Studies in the Compact Toroidal Hybrid Experiment

The Compact Toroidal Hybrid (CTH) is a torsatron/tokamak hybrid capable of substantially varying the magnetic configuration by having rotational transform supplied predominantly by either currents in external helical coils or internal plasma currents. The addition of plasma current increases the rotational transform of the system causing it to have a tokamak-like profile. Observed density limit disruptions are investigated as a function of the vacuum and fractional transform applied to an ensemble of discharges. Experimentally increasing the vacuum transform allows for plasma densities to surpass an estimate of Greenwald density limit without using core fueling methods. Results of a study of disruption phenomenology utilizing a recently upgraded interferometer diagnostic to measure profile peaking and SXR and bolometry arrays to characterize the radiative properties of the plasmas. * Work supported by USDOE grant DE-FG02-00ER54610   

Design and Operation of a 28GHz Gyrotron System for the Compact Toroidal Hybrid Experiment

The Compact Toroidal Hybrid (CTH) is an $\ell=2, m=5$ torsatron/tokamak hybrid ($R_0=0.75$\,m, $a_p\sim 0.2$\,m, and $|B|\leq 0.7$\,T). It can generate its highly configurable confining magnetic fields solely with external coils, but typically operates with up to 80\,kA of of plasma current for ohmic heating. A gyrotron system has been installed that features a Varian VGA-8050M tube operating at 28\,GHz and capable of up to 200\,kW of power. The system is used for 2nd harmonic ECRH to supplement the existing 10\,kW klystron system operating at the fundamental frequency; the latter generating target plasmas. Ray-tracing calculations that guided the selection of launching position, antenna focal length, and beam-steering characteristics of the ECRH were performed with the TRAVIS code$[1]$. The calculated absorption is up to 95.7\% for vertically propagating rays; however, the absorption is more sensitive to magnetic field variations than for a side launch where the field gradient is tokamak-like. The design of the waveguide path and components for the top-launch scenario will be presented, as well as ECRH results showing the efficacy of the gyrotron system.\\ $[1]$N.B. Marushchenko, Y. Turkin, H. Maassberg, Comp. Phys. Comm. 185 165 (2014)\\   

Coherence Imaging Spectroscopy Characterization on the CTH and W7-X Experiments

Two-dimensional profiles of line-integrated impurity emissivity and velocity in the Compact Toroidal Hybrid (CTH) experiment are obtained with Coherence Imaging Spectroscopy (CIS), a polarization interferometry technique with fixed delays. To characterize the optical setup, CIS observations are benchmarked against Doppler-shifted spectroscopy measurements. Spectroscopy confirmed toroidal He$^{\mathrm{+}}$flows of 10-15 km/s while also identifying contaminating lines within the CIS spectral filter and associated errors.Additionally, two CIS instruments investigating the 3D physics of the W7-X island divertor provide ion flow measurements in orthogonal directions.A continuously tunable laser and wavemeter supply an absolute reference during W7-X plasma operations to simplify analysis and allow for measurements of multiple ion species. He$^{\mathrm{+}}$flow profiles and their comparison to C$^{\mathrm{+\thinspace }}$flow structures in the W7-X divertor will be presented.   

STRAHL modeling of impurity transport experiments with on- and off-axis heating during the first divertor campaign on Wendelstein 7-X

In the first divertor campaign (OP 1.2a{\&}b) of Wendelstein 7-X, impurity transport experiments were performed with iron via laser blow-off injection. The iron line radiation was collected at various off-axis ECRH heating levels by the x-ray imaging spectrometer systems, HR-XIS and XICS, and the high efficiency XUV overview spectrometer, HEXOS. These measured spatial and temporal iron emissivities are used to infer the radial diffusion and convective velocity profiles by means of the 1D transport code STRAHL. To accomplish this inference the temporal evolution of the iron line radiation is modeled with neo-classical diffusion and convection profiles provided by the drift kinetic equation solver, DKES, in addition to assumed stationary anomalous diffusion and convective velocity profiles. To match both the observed line-integrated iron emissivity and a corresponding spatially resolved emissivity profile for the He-like state, a chi-squared minimization is done on the experimental data by varying the input spatial values of the anomalous diffusion and convective velocity parameters in STRAHL.   

Parametric Equilibrium Reconstructions for Wendelstein 7-X with V3FIT

Plasma equilibrium reconstruction is important for interpreting diagnostic signals and understanding the plasma performance for toroidal fusion experiments. The process is iterative and involves solving the MHD equilibrium, computing synthetic diagnostic signals based on that equilibrium, and comparing these signals to measured ones. Parameters that describe the equilibrium are adjusted between iterations to find a best fit of the measured and synthetic signals. The shape of the plasma, the location of the plasma edge, and profile information regarding the plasma pressure, current, and individual plasma species (e.g. Te, Ne, Ti, Ni) are the output of the reconstruction. These profiles are used to interpret diagnostic information and for further physics analysis. The constraints for the reconstructions of plasmas at Wendelstein 7-X (W7-X), which include diagnostics and conditions on the plasma last closed flux surface, and the importance of the coil model are discussed. Equilibrium reconstructions for various magnetic configurations and the extension of the equilibrium model beyond the last closed flux surface are also shown. Future plans for the application of V3FIT reconstructions to W7-X plasmas are discussed.   

Neutral density measurements in a microwave generated plasma with varying fractional ionization

Understanding the transition region between fully ionized and neutrally dominated plasmas is important to the study of the magnetosphere of the earth, the corona/chromosphere transition regions of the sun, and detached divertors in stellarators. Precisely characterizing the fractional ionization of the plasma requires accurately measuring neutral density. We explore the use of an absolutely calibrated spectrometer, a triple probe, and an interferometer to measure the neutral density, electron density, and electron temperature of argon plasmas in a Compact Toroidal Hybrid heated by ECRH with up to 2 kW of input power. The electron temperatures range from 5 eV to 10 eV and the electron densities from 1 x 10$^{\mathrm{17}}$ m$^{\mathrm{-3}}$ to 10 x 10$^{\mathrm{17}}$ m$^{\mathrm{-3}}$. The radial profiles of the electron temperature and density are relatively flat over the minor cross section of the plasma. Results will be presented from a study of the fractional ionization within the plasma volume and an analysis of the argon metastable and ion populations.   

Enabling access to high performance scenarios using scraper elements in Wendelstein 7-X

The W7-X stellarator has recently completed the first campaign with an island diverted configuration, successfully demonstrating 30 second plasmas with stable power detachment and record triple products for a stellarator. High performance discharges are envisioned for the next campaign, for which simulations predict a net toroidal current of 40kA which evolves over \textasciitilde 100 seconds and shifts the island chain radially inwards. This evolution results in a predicted transient overload along the edges of the divertor. One solution to this overload problem is the installation of ``scraper elements'', which intercept flux to the overloaded components during the toroidal current evolution. To test this concept, two scraper elements were installed during the last campaign. A set of magnetic configurations were developed to mimic the topology of specific points in the current evolution using the W7-X coil set. Experiments showed measured heat flux patterns that agreed well with predictive simulations from field line diffusion and EMC3-EIRENE. The scraper elements reduced the flux to the divertor edges as expected, with a corresponding reduction in the subdivertor pressure. These results demonstrate that scraper elements can enable access to high performance scenarios with significant current.   

Design and Initial Tests of a Gas-Puff Imaging Diagnostic for W7-X.

A Gas-Puff-Imaging (GPI) diagnostic is being designed for use on the W7-X stellarator. It will allow for detailed study of boundary and scrape-off-layer physics during the long-pulse W7-X operation period OP2. The main components of the diagnostic are 1) a system for puffing controlled amounts of H$_{\mathrm{2}}$ or He gas into the outboard edge of the W7-X plasma, and 2) a system that images, with high time-resolution(\textasciitilde 1 $\mu $s) and good 2d spatial resolution (\textasciitilde 5 mm), the emission resulting from the interaction of the puff with the local edge plasma. The nozzles used for the gas puff are novel in that they are ``converging-diverging'' cones inducing supersonic flow at and beyond the nozzle ``throat'', thereby providing a more collimated beam. Good collimation is critical because the nozzle is \textasciitilde 120 mm outside the LCFS. Gas flow rates and expansion angles for the puffed beam are measured and will be presented. The design of the imaging system includes a water-cooled re-entrant tube with a metal turning-mirror that is deployed as part of the tube shutter. The turning-mirror allows observation of the emission along sightlines that are within 15$^{\mathrm{o}}$ of the field-lines local to the emission region. The collected light is relayed up the tube and imaged directly onto an 8x16 array of APD detectors.   

Parameter Dependencies of the Configuration-Dependent 1-2 kHz Fluctuation in W7-X

A 1-2 kHz electromagnetic fluctuation is present in a large fraction of W7-X discharges that are produced in the magnetic field configuration with iota 0.97 at the last closed flux surface and 5/5 island structure. This fluctuation, first observed as a quasi-coherent modulation in visible light from the divertor, was found to be present in signals from a number of diagnostics including line-integrated density, diamagnetic energy, edge electron temperature, floating potential, and divertor tile temperature. It occurs during steady-state operation and is not present in other magnetic configurations, some of which have signature fluctuations below 1 kHz. In this study, a survey of extensive Mirnov coil data sheds light on the plasma parameters related to the occurrence and attributes of the 1-2 kHz fluctuation. Toroidal current is positively correlated with the fluctuation's frequency and power, and the fluctuation power increases with ECRH power and decreases with plasma density. Finally, the mode structure and radial extent are studied using data from Mirnov coils and Langmuir probes.   

Investigation of Turbulence and Transport by Phase Contrast Imaging on the Wendelstein 7-X stellarator

While the Wendelstein 7-X stellarator is optimized to minimize the neoclassical transport, \sout{and} the role of anomalous transport driven by turbulence remains largely unknown. A phase contrast imaging diagnostic (PCI) has been implemented on W7-X for turbulence measurement in the form of density fluctuations. Ion-scale turbulence is generally observed in W7-X and predicted to be driven unstable either by the ion temperature gradient (ITG modes) or by trapped electrons (TEM modes). Reduced anomalous impurity diffusion, and therefore longer impurity confinement times, were observed accompanied with reduced turbulence. Clear correlation between turbulence reduction and increase in the diamagnetic energy was observed in several scenarios where the density and ion temperature gradients were modified by external perturbations so that the gradient ratio $\eta_{\mathrm{i}}$ is about 1, where gyrokinetic simulations by GENE predicted reduced ITG and TEM activities. These observations suggest that turbulence plays an important role in the particle and energy transport in W7-X.   

The He/Ne beam diagnostic for line ratio spectroscopy in the Island Divertor of Wendelstein 7-X

A line-ratio spectroscopy system based on thermal helium (He) and neon (Ne) collisional-radiative models (CRM) enables measurement of n$_{\mathrm{e}}$ and T$_{\mathrm{e}}$ in front of the horizontal divertor target of the Wendelstein 7-X optimized stellarator. Spectral line emission from locally-injected helium and neon is channeled to multiple 20cm and 32cm Czerny-Turner spectrometers, allowing high spectral resolution observation of diagnostic helium and neon lines, as well as various visible impurity lines and Balmer series lines. In this work, T$_{\mathrm{e}}$ and n$_{\mathrm{e}}$ profiles across the divertor island are shown for a variety of experimental conditions, including impurity-seeded and detached plasmas. Profiles inferred from neon and helium are presented and compared. Also presented are first-time measurements of plasma parameters over changing island sizes. Systematic variations of the island size in front of the diagnostic have a marked impact on the profile shape and gradients. These first- time measurements provide evidence of for a local confinement in the islands of the divertor at W7-X.   

Optimizing the Spatial Resolution and Fluctuation Wavenumber Sensitivity during Design of the Wendelstein 7-X Heavy Ion Beam Probe

A heavy ion beam probe diagnostic is being designed for the Wendelstein 7-X (W7-X) stellarator. The diagnostic will measure equilibrium electric potential, fluctuations of electric potential and density, fluctuation wavenumbers, the cross-phase between fluctuations of density and potential, and electrostatic fluctuation induced particle flux. As part of the design process, we have developed computational techniques that optimize the spatial resolution of the electric potential measurement and maximize sensitivity to high wavenumber fluctuations. A small number of beam ion trajectories are used to numerically determine an ion optics matrix which describes how the W7-X magnetic field will focus the injected and detected ions. The ion optics matrix is used to determine the optimum initial focal length of the injected beam, and correspondingly, the properties of a quadrupole lens that provides the required focus. Computational results show that this tailored beam focus produces significantly smaller sample volumes than an initially parallel beam. The new techniques also allow us to simulate a finite phase-space volume beam and obtain more realistic estimates of the sample volume characteristics than with our traditional approach. This work is supported by US DoE Award DE-SC0013918.   

Quantifying and Improving Performance of the XGC code to Prepare for the Exascale

The Exascale Computing Project "WDMApp" develops high-fidelity whole device modeling software for magnetically confined plasmas, relevant to the performance of future fusion reactors such as ITER by coupling core and edge gyrokinetic codes. We will focus primarily on the performance of the XGC code itself, as well as the performance implications of using various methods coupling methos provided by ADIOS2. For XGC, it is expected that the main computational bottlenecks are going to be the electron push kernel as well as the collision operator. For the electron push, we are going to analyze the performance of various implementations: regular Fortran, CUDA-Fortran, Fortran driven by Kokkos/Cabana as well as C++ with Kokkos/Cabana. We will quantify how the performance-portable Kokkos/Cabana approach compares to hand-coded kernels. XGC implements a fully nonlinear Landau collision operator based on continuum representations. For ITER, it is expected that many charge states of Tungsten to be tracked, which increases the computational cost significantly, as it scales with the square of the number of species. We will investigate both computational approaches to reduce the cost (e.g., optimized GPU implementation, pre-calculated matrices), as well as possible algorithmic changes.   

A Fully Implicit Particle-in-Cell Method for Gyrokinetic Electromagnetic Modes in XGC

Electromagnetic gyrokinetic particle-in-cell methods are known to suffer from numerical difficulties, limiting their applicability to low-$\beta$ or short wavelength regimes. The $v_{\parallel}$ formulation with explicit time discretization suffers from a severe time step constraint, and the $p_{\parallel}$ formulation suffers from an inexact cancellation of two large, non-physical terms appearing in Ampère’s law that emerge from the choice of coordinates. Here, we describe our implementation of a fully-implicit time integration scheme based on the work of Chen and Chacón [1-2] for a gyrokinetic ion, drift kinetic electron electromagnetic model employing the $v_{\parallel}$ formulation in the full volume fusion plasma code XGC1. By using an implicit discretization scheme, we overcome the previous time stepping difficulties associated with the $v_{\parallel}$ formulation and avoid introducing non-physical terms in Ampère’s law. The resulting system of nonlinear equations is solved iteratively using a preconditioner derived from an electron fluid model. We consider kinetic ballooning and micro-tearing modes to verify the scheme. [1] G. Chen, L. Chacón, and D.C. Barnes, J. Comput. Phys. 230 (2011) 7018. [2] G. Chen, L. Chacón, Comput. Phy. Comm. 197, (2015) 73-87.   

Structure preserving six-dimensional particle simulation model in the XGC code

We plan to implement a structure-preserving geometric Particle-In-Cell (PIC) algorithm [1] in the XGC code [2] to simulate drift wave range instabilities and turbulence. We plan to take a step-by-step approach. In the algorithm to be presented at this meeting, as the first step, electrostatic instabilities and turbulence with ions treated as 6D kinetic particles and electrons as adiabatic. An explicit non-canonical symplectic integrator [3] will be implemented in an unstructured triangular toroidal XGC mesh. The charge density and electric potential will be calculated on the unstructured mesh via Whitney interpolation. The algorithm and code will be benchmarked against analytic theories and the previous Gyrokinetic simulation results. Plans for extension to electromagnetic drift-kinetic and gyrokinetic electrons on exascale and post-exscale HPCs will also be discussed. [1] J. Xiao and H. Qin, arXiv:1902.03898 (2019). [2] S. Ku et al., Phys. Plasmas 25, 056107 (2018). [3] Y. He et al., Physics of Plasmas 22,124503 (2015).   

Electromagnetic full-$f$ continuum gyrokinetics in the tokamak scrape-off layer

We present the first electromagnetic continuum gyrokinetic simulations of turbulence on open field lines in the tokamak SOL. Gkeyll, a full-$f$ continuum gyrokinetic code, is being developed to study turbulence in the edge region of fusion devices. The edge region involves large-amplitude fluctuations, electromagnetic effects, and plasma interactions with material walls, making it more computationally challenging than the core region. Gkeyll models the turbulence by solving the 5D full-$f$ gyrokinetic system in Hamiltonian form using an energy-conserving high-order discontinuous Galerkin scheme. The Gkeyll code has been extended to include self-consistent electromagnetic perturbations using a symplectic ($v_\parallel$) formulation. We present linear benchmarks of kinetic Alfv\'en waves and kinetic ballooning mode instability calculations that illustrate the success of the electromagnetic scheme and the avoidance of the Amp\`ere cancellation problem. We then present nonlinear electromagnetic turbulence simulations in a model helical SOL geometry with sheath boundary conditions on open field lines. These simulations use parameters from NSTX SOL measurements. We make comparisons between the electromagnetic simulations and electrostatic simulations with the same setup.   

Validating gyrokinetic simulations of plasma turbulence in the Texas Helimak

Using the computational plasma framework Gkeyll, we present the first continuum gyrokinetic simulations of plasma turbulence in the Texas Helimak, a simple magnetized torus experiment [1,2]. The device has features similar to the scrape-off layer region of tokamaks, such as bad-curvature-driven instabilities and sheath boundary conditions, which we include in our model. A bias voltage can be applied across conducting plates to drive $E \times B$ flow and study the effect of velocity shear on turbulence suppression. We performed simulations of grounded and limiter-biased scenarios, which produced equilibrium profiles and fluctuation amplitudes that approach experimental values. Comparison with experimental data also illustrated some important quantitative differences, and we discuss how including additional physical and geometric effects in our model improves agreement with experiment. [1] Bernard et al., PoP 26(4), 042301 (2019) [2] Bernard, UT Austin PhD thesis (2019)   

Nonlinear full-$f$ simplified Fokker-Planck multi-species collisions in (gyro)kinetics

We present a simplified, nonlinear collision model of like-particle and multi-species collisions for full-$f$ kinetic plasma studies. This Fokker-Planck-like model is a generalization of the popular Dougherty operator, formulated to more rigorously support arbitrary mass ratios, non-quasineutral pairs, and flexible collision frequencies. In particular, this approach can be extended to support velocity-dependent collisionalities. The proposed operator preserves the conservative properties of the Fokker-Planck operator and, in the case of velocity-independent collisionality, can be shown to obey the H-theorem. Non-decreasing entropy can be proved as long as the cross-species temperature remains positive, even in the non-equilibrium case of unequal temperatures. Benchmarks, like Landau damping of Langmuir waves, show the effect of this simplified model to be comparable to that of the full Fokker-Planck operator. These features make it an attractive approach for direct numerical simulation of plasmas where using the full Fokker-Planck operator may be prohibitively expensive. We will present the formulation, discontinuous Galerkin implementation within Gkeyll, and various tests carried out for testing and validation.   

Conservative Recovery Discontinuous Galerkin Scheme for the Fokker-Planck Collision Operator

Continuum kinetic plasma models are used to study plasmas by directly evolving ion and electron distribution functions using the Vlasov equation along with Maxwell's equations. In this work, a novel implementation of the Fokker-Planck operator for collisions is presented. It is based on the Rosenbluth formulation where the increments $\langle\Delta v_{\mu}\rangle$ and $\langle\Delta v_{\mu} \Delta v_{\nu}\rangle$ are calculated as the derivatives of the Rosenbluth potentials. Recovery of higher-order representation and computer algebra systems are highly utilized to calculate the derivatives and integrals in the discontinuous Galerkin algorithm. These two key elements allow for a high-order, efficient, and conserving scheme.   

A quadrature- and matrix-free discretization of the multi-species, non-relativistic, Vlasov-Maxwell system of equations

We present a novel algorithm for the numerical solution of the multi-species, non-relativistic, Vlasov-Maxwell system of equations which uses high order discontinuous Galerkin finite elements to discretize the system on a phase space grid. The resulting numerical method is robust and retains a number of important properties of the continuous system, such as conservation of mass and energy. In addition, we will discuss a number of discoveries concerning the computational implementation of the algorithm which bring the cost of directly discretizing the Vlasov-Maxwell system down tremendously. We devote a portion of the presentation to the central motivation of developing a continuum discretization of the Vlasov-Maxwell system: a clean, noise-free representation of the distribution function and electromagnetic fields. We discuss a set of recent results (Skoutnev et al. ApJ Letters 2019) which disagree with particle-in-cell simulations with the same parameters and initial conditions, and demonstrate the role particle noise plays in the disagreement. We thus argue for the utility of the continuum approach, which despite its challenges and expense compared to the particle-in-cell method, nonetheless provides a complementary tool for addressing kinetic problems in plasma physics.   

Continuum Gyrokinetic Simulations of Turbulence in a Model Tokamak Scrape-Off Layer for NSTX-like Parameters

We review the first continuum gyrokinetic simulations of turbulence in a model of the tokamak scrape-off layer (SOL) region, using the Gkeyll code [1, 2]. These initial simulations were done with a simple helical magnetic model of the SOL, which includes key effects such as bad curvature drive and model sheath boundary conditions. (General geometry extensions are under way.) NSTX-like parameters were used. Gkeyll is a full-F code using a version of discontinuous Galerkin algorithms that conserve energy exactly for Hamiltonian problems (in the continuous time limit). It also has a full Vlasov-Maxwell solver. The present model for the sheath interactions is discussed in the simple case of magnetic fields with normal incidence on end plates. It uses the long-wavelength gyrokinetic Poisson Eq.\ to include polarization effects in the plasma and allows for currents flowing through the sheath and walls. Dependence of the turbulence and resulting divertor heat-flux width on connection length is investigated. [1] E.L. Shi, Princeton Ph.D. Dissertation 2017, https://arxiv.org/abs/1708.07283 [2] E.L. Shi, et al. Phys. Plasmas 2019 https://doi.org/10.1063/1.5074179   

An Unstructured Mesh Based Infrastructure for Exascale PIC Simulations

Particle-in-cell (PIC) methods are effective for modeling fusion plasmas. In a number of important cases the simulation domain is complex and the fields have large spatial variations. In such cases it is desirable to take advantage of unstructured mesh technologies. This poster will overview PUMIpic, a distributed unstructured mesh infrastructure for PIC calculations and indicate the status of its use in two fusion plasma modeling applications. A key feature of PUMIpic is using a partitioned mesh as the core data structure with particles accessed via the mesh. Both the mesh and associated particle data structures, and the mesh/particle interaction operations are designed for effective execution on accelerator based exascale computers. PUMIpic is being used in the development of versions of two fusion plasma physics PIC codes; XCG for edge plasma simulations and GITR wall impurity transport simulations.   

Gyrokinetic equation for tokamak plasmas with sonic level equilibrium toroidal flow

We present the electromagnetic gyrokinetic equations in the presence of a sonic level equilibrium toroidal flow, suitable for implementation in the delta-f Particle-in-Cell code GEM. A unique feature of the GEM algorithm is the appearance of the vorticity equation, which is the time derivative of the quasi-neutrality condition. Without the large toroidal flow, all terms in the vorticity equation are of the second order in the gyrokinetic ordering parameter. When the sonic level flow is present, terms proportional to the flow appear, and such terms are first order. These first order terms must cancel physically, but might not be properly cancelled numerically. We derive a form of the vorticity equation that makes the cancellation of the first order terms explicit. The derivation of the gyrokinetic equation follows the procedure of Artun et. al. [M.~Artun and W.~M.~Tang, Physics of Plasmas 1, 2682 (1994)]. The gyrokinetic equation appears to contain additional terms that are not contained in the equation of Sugama and Hortan [Physics of Plasmas 5, 2560 (19980)]. Implementation details will be discussed.   

Coupling core delta-f and edge total-f gyrokinetic codes with kinetic electron dynamics

The Exascale High-fidelity Whole Device Modeling project is about coupling an edge total-f gyrokinetic simulation to a core delta-f simulation so that a high fidelity gyrokinetic solution can be economically obtained in the whole ITER volume with the prediction for pedestal height and width. A strongly coupled simulation across a surface interface is a difficult problem. We have succeeded in the gyrokinetic ion coupling with adiabatic electrons [Dominski et al., Phys. Plasmas 25, 072308 (2018)] exchanging only the 3D charge-density. To enable the kinetic electron coupling, we upgrade this coupling scheme in which the particle distribution function information is exchanged between core and edge simulations on a 5D grid. Using an intermediate grid enables to couple different numerical schemes, i.e., coupling Eulerian with PIC or delta-f with total-f. The scheme is first developed between two XGC code versions: core delta-f and edge total-f versions. The transfer of information between marker particles and the grid employs a re-sampling technique~[D. Faghihi et al, submitted to JCP]. The successfully coupled codes in the ECP-WDM framework will provide a base for further code coupling to incorporate other important physics, such as rf-heating, MHD, NBI, energetic particles, PMI.   

A new preconditioning strategy for fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

Large transport anisotropy ($\chi_\parallel/\chi_\perp \sim 10^{10}$), chaotic magnetic fields, and non-local heat closures make solving the electron transport equation in magnetized plasmas extremely challenging. A recently developed asymptotic-preserving semi-Lagrangian method\footnote{Chac\'on, et al., {\em JCP}, {\bf 272}, 719, 2014} overcomes this complexity by an analytical treatment of the direction parallel to the magnetic field. Further, a fully implicit, second order extension of the method has been recently proposed.\footnote{Koshkarov, et al., {\em JCP}, submitted} In principle, the method is able to deal with arbitrary anisotropy ratios, different parallel heat-flux closures, and non-trivial magnetic topologies accurately and efficiently. However, in order to achieve competitive performance, implicit time integration requires fast and scalable preconditioning. Here, we propose and analyze a new preconditioning strategy that builds on the Lagrangian character of the algorithm, and ensures optimal scaling for different temporal and spatial resolutions, as well as for different anisotropy ratios. We demonstrate the merits of the method with a two dimensional boundary layer problem, which admits an exact analytical solution.   

Accurate numerical, integral method for computing drift-kinetic Rosenbluth potentials

The Rosenbluth potentials are defined by a pair of Poisson equations in velocity space written in differential or integral forms. The integral forms handle infinite domains with an appropriate quadrature scheme, require no boundary conditions, and require no extra computer memory to store the Rosenbluth potentials since the integral forms can be applied directly. Although solvers that use the differential forms avoid integrable singularities, they require extra storage incurred in larger preconditioning matrices needed when treating the collision operator in a time-implicit fashion. Inspired by numerical solutions of the axi-symmetric Poisson equation in astrophysics [J. M. Huré, A&A, 434, 1 (2005).], we develop an analogous technique for accurately computing the drift-kinetic Rosenbluth potentials that regularize the integrand via analytic integration of the singularity. The result is higher accuracy and improved efficiency. This method is implemented in the NIMROD code and utilized in continuum kinetic closure calculations. Results are presented for applications involving equilibration along magnetic field lines which leads to temperature flattening across magnetic islands in slab, cylindrical and toroidal geometry.   

Continuum kinetic poloidal flow damping verification with NIMROD

Close agreement between numerics and analytics has been obtained in delta-F drift kinetic, poloidal flow damping calculations with NIMROD. In these calculations, an initial kinetic distortion is imposed on an axisymmetric equilibrium, which provides an initial poloidal flow which damps in time. Steady state poloidal flows differ from analytical results [1] by only a few percent, and time-dependent poloidal flow damping rates also agree with analytics. Similar calculations using a Chapman-Enskog-like (CEL) approach [2] have also been undertaken, and results for sound wave damping are presented. The Chapman-Enskog-like approach differs from delta-F since the lowest-order Maxwellian evolves with the n, T, and \textbf{V} velocity moments handled using NIMROD’s fluid model. This approach has an added benefit that the electric field, which appears in the momentum equation, can be specified using Ohm’s law. Future work will include using the CEL implementation in NIMROD to study the effects of resonant magnetic perturbations (RMPs) in Tokamaks. [1] S.P. Hirshman and D.J. Sigmar 1981 Nucl. Fusion \textbf{21} 1079. [2] J. J. Ramos, Phys. Plasmas \textbf{18}, 102506 (2011).   

Capturing Collisional Effects in Drift Kinetics Using Nonclassical Quadrature Weights

Implementing closures in hybrid fluid/kinetic codes requires accurate evaluation of the collision operator and its moments. Efficient evaluation of the needed TR potentials should address the different resolution requirements for like species, electron-ion, and ion-electron collisions. A method based on nonclassical quadrature weights tailored to these individual responses has been implemented in NIMROD's continuum kinetic coding. Two speed domains are used to capture the large electron Maxwellian/ion background response at low electron speeds, $v\sim v_{Ti}$. In order to highlight the efficiency of this approach, results are presented for the Spitzer conduction and thermalization problems.   

Formulation and verification of simulation model near the ion cyclotron frequency.

A simulation model using fully kinetic ions and drift kinetic electrons in toroidal geometry (such as tokamaks), has been formulated and verified for simulations of waves with frequencies comparable or higher than ion cyclotron frequency, such as ion cyclotron emission (ICE) and global Alfven eigenmode (GAE). Quasi-neutrality condition is used to remove the undesired higher frequency electron plasma waves. The kinetic electron model can be reduced to the massless fluid electron, which recover the modified shear Alfven wave (SAW) and generalized ion Bernstein waves (IBW). The model further reduces to shear Alfven wave (SAW) and compressional Alfven waves (CAW) when ion kinetic effects are removed. Implementation and verification in the gyrokinetic toroidal code (GTC) will be reported.   

Volterra Integral Equation Method for Linearized Electron Plasma Wave Dynamics Including Temporal Echoes.

We solve the Volterra/Penrose integral equation formulation of the linear kinetic plasma wave response problem using a spectrally accurate and efficient Chebyshev collocation method. The solution is represented by Fourier modes in space and either Hermite polynomial expansions in velocity space or by evaluating a reconstruction formula that can be computed rapidly at any desired set of velocity points, once the plasma density's evolution in time is known by solving the Volterra/Penrose equation. The resulting integral equation is solved to very high accuracy but efficiently. We show the interplay between ballistic modes, the Landau solution and temporal plasma wave echoes both with stable (single hump) and unstable (double hump) initial electron velocity distribution functions. The advantage of the numerical method used is that it can handle very large contrast or large dynamic range in the solution while maintaining arbitrarily high accuracy.   

Integration of Full-Orbit and Gyro-Center Methods for Multi-Scale Modeling of Edge Plasmas Including Sheath Effects

Simulation of the edge region of a magnetically-confined plasma and its interaction with surface materials is a multi-scale physics problem which is essential to the development of a viable commercial fusion reactor. Correct modeling of this system requires the integration of a gyrokinetic approach capable of modeling the larger-scale regions of the edge plasma with a full-orbit description of the magnetic presheath and plasma sheath at the boundary of the plasma region. In order to accomplish this goal, we have coupled two plasma edge simulation codes with extensive use on DOE Leadership Class computers: hPIC and XGC. hPIC is a full-orbit electrostatic particle-in-cell code specifically targeting plasma presheath and sheath, plasma--surface interaction problems including surface erosion and material composition changes. XGC is a gyrokinetic particle-in-cell code exploring the remainder of the edge region. Code coupling is achieved using the ADIOS-2 input/output framework for in-memory communication on HPC systems. Material impurities released by plasma-facing components are characterized and their effects on the XGC edge plasma are analyzed using this novel approach.   

A numerical study of plasma-neutral interaction effects on gas penetration into a tokamak plasma

The plasma edge dynamics has become an area of extreme importance in plasma physics investigations. Many experimental studies has indicated that the overall performance characteristics of confined plasmas are determined by phenomena happening in this thin region. Atomic reactions between plasma and neutral species involving recycling and fueling are important in the dynamic behavior of magnetically confined plasma devices particularly in edge region. Also, injecting massive high pressure gas, liquid jets, and killer pellets are a few of the possible approaches to mitigate disruptions and control damage to vessel structures. In this research, a reacting plasma-neutral model [Meier \& Shumlak, POP 19 (2012)] is incorporated into the NIMROD plasma simulation code allowing for the study of electron-impact ionization, radiative recombination, and resonant charge-exchange in plasma-neutral systems. The penetration of neutral gas into a tokamak plasma during a massive gas injection is modeled for both 1D and 2D configurations. It is expected that atomic reactions strongly block the gas penetration and a shock wave starts to propagate backwards into the incoming gas.   

Electron density fluctuation reconstruction for 2D beam emission spectroscopy plasma edge and SOL measurements

SOL and edge plasma turbulence contributes significantly to the radial particle losses of the plasma, thus, tampering the confinement. Furthermore, the radially moving density filaments could cause high erosion on the wall. These rise great interest to analyze the scrape-off layer turbulence in detail. It has been demonstrated, that beam emission spectroscopy is a capable diagnostic for measuring turbulence in both SOL and edge plasmas. However, due to the finite lifetime of the excitation states during the beam - plasma interaction, and the optics, spatial smearing is introduced to the measurement. This unwanted feature hinders the detailed analysis of SOL turbulence, which would quantify the size of the intermittent events ultimately leading to analysis of the expected particle flux of the SOL turbulence. A numerical method was developed to overcome this unwanted effect, which can deconvolute the spatial smearing by minimizing the undulation of the fluctuations calculated from realistic fluctuation - response transfer functions. By applying the numerical reconstruction on Deuterium BES data, it is demonstrated, that this method can successfully retrieve the local electron density fluctuations.   

Automating kinetic equilibrium reconstruction for tokamak stability analysis

An automatic tool for producing consistent kinetic equilibrium reconstructions has been developed to facilitate large scale studies of plasma stability. Kinetically constrained MHD equilibrium reconstructions provide useful information about pressure and current density distributions within the plasma which can be used for further calculations essential for stability analysis. Properly transforming experimental data into the constraint profiles needed to form a kinetic equilibrium reconstruction used to be a time intensive, manual process and lacked a consistent standard. Through OMFIT, capabilities for user-created kinetic equilibria and best practices emerged on the path towards full automation, while retaining user interaction and best judgement, but challenges for complete automation remained. The Consistent Automatic Kinetic Equilibria generator tool (CAKE) has been developed to overcome these challenges and produce kinetic equilibrium through a r obust and automatic routine. Techniques are developed to account for varying data quality and availability, as well as for tuning parameters affecting fit quality.   

A discontinuous-Galerkin sparse-grid Fokker-Planck solver for runaway electrons

The understanding and control of runaway electrons (RE) is a top priority of the fusion program because, if not avoided or mitigated, RE can severely damage the plasma facing components of ITER and future machines. There is thus a pressing need to develop accurate models of RE dynamics as well as efficient computational algorithms. The full kinetic description of RE requires the solution of high-dimensional (up to 6-D) partial differential equations. To address this challenging problem, Discontinuous Galerkin (DG) methods and Spare Grid (SG) techniques might offer a viable alternative to standard methods known to face shortcomings due to lack of good conservation properties and the ``curse of dimensionality'' To explore this alternative in a tractable setting we present a DG-SG solver for a 2-D Fokker-Planck model describing RE dynamics in energy and pitch angle phase space including electric field acceleration, collisions, and synchrotron radiation damping. The accuracy and conservation properties, as well as the numerical efficiency of the proposed method, are discussed in detail. Simulations illustrating RE physics are also presented along with preliminary ideas on extending the solver to higher dimensions.   

Modeling the HIDRA Plasma in the Presence of the LiMIT and FLiLi PFCs

HIDRA is a hybrid stellarator/tokamak device operated at the Center for Plasma-Material Interactions (CPMI). Its ability to run at steady-state in its classical stellarator configuration allows it to efficiently be used to develop and test innovative plasma facing components (PFCs). Special interest at CPMI involves the study of the plasma interaction with liquid lithium with two PFC concepts, the Liquid Metal Infused Trenches (LiMIT) and the Flowing Liquid Lithium (FLiLi), planned to be installed and tested on HIDRA in various configurations. To this end, it is essential to have a complete knowledge of the HIDRA plasma and magnetic structure. Magnetic flux surface mapping was conducted on HIDRA, from which a complete magnetic grid was generated, incorporating the inherent $n=1$ error field existing on HIDRA. The grid was used to perform EMC3 simulations of the energy and particle fluxes expected during experimental runs on HIDRA. From the simulations' results, upgrading the heating capability of the machine is being considered to achieve conditions closer to fusion environments. The experimental measurements during the LiMIT/FLiLi campaigns will help benchmark the EMC3 simulations and the EIRENE code will also be used to further study and model the plasma-lithium interaction.   

BARS: Bidirectional Adaptive Refinement Scheme for Advanced, Learned PIC Simulations of Nonlinear Kinetic Plasma Physics

BARS, or the Bidirectional Adaptive Refinement Scheme promises to optimize PIC code performance in modeling plasma kinetic phenomena. It is a learning algorithm meant to facilitate the simulation of a large number of interrelated nearby problems by using optimum phase space tiling and grid choices learned from previous simulations. We show its power and functionality by simulating nonlinear kinetic electron plasma waves, NL-EPW, and kinetic electrostatic electron nonlinear or KEEN waves. Under-resolving or over-resolving the particle density in various partitions of phase space will be compared and contrasted.   

Fast and Accurate Transport Coefficients for Dense Plasma Applications

Mixing of high-$Z$ ablator materials into thermonuclear fuel can spoil burn conditions. Understanding the impact, and controlling the mixing process requires a detailed knowledge of transport coefficients across wide plasma regimes; the ability to rapidly compute these properties in dense plasma mixtures remains a challenge. Existing microscopic models such as Kohn-Sham density functional theory molecular dynamics (KS-DFT-MD) and pair-potential molecular dynamics (PP-MD) can determine these transport properties; however, relatively speaking, the former requires many CPU hours while the latter typically does not. We use the Vienna Ab-initio Simulation Package (VASP) to generate KS-DFT-MD data for force matching with the Yukawa and EGS [1] pair-potentials; we see a preliminary speedup of $10^{5}$ times. We plan to use the inexpensive PP-MD to aid in the design and interpretation of Z Machine experiments at Sandia National Laboratories. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525 SAND Number: SAND2019-7663 A   

Numerical Simulations of Electron Transport across a Plasma-Water Interface using Zapdos-CRANE

Plasma-liquid systems are experiencing growing interest due to their wide range of applications in low temperature plasmas (medicine, chemical production, chemical processing). Even so, the transport of electrons, ions, neutrals, and their distribution moments, such as heat and energy fluxes, in the interface layer between the plasma and the surface remain poorly understood. In this work, we perform our simulations using the new open-source software package Zapdos-CRANE, built on top of the MOOSE framework, which can be utilized to model general problems involving plasma-liquid interfaces. Zapdos is a multi-species electrostatic plasma transport model, previously used to study plasma-liquid interactions, while CRANE (https://github.com/lcpp-org/crane) is a plasma chemistry software written to solve reaction networks of arbitrary size and complexity. The package is here utilized to model the transport of electrons and heavy species from the plasma into liquid water, and the chemical reactions that occur in the interface layer is examined.   

Multi-scale modeling of relativistic shear flow interface

Recent large scale 2D and 3D Particle-in-Cell (PIC) simulations have demonstrated that in unmagnetized relativistic electron-ion shear flows, strong transverse d.c. magnetic fields are created by self-generated currents on opposite sides of the shear interface due to the electron counter-current instability. Instead of dissipating the shear flow energy via turbulence and mixing as in MHD simulations, the kinetic results show that a relativistic shear flow stabilizes itself via the formation of a robust ion vacuum gap supported by the self-generated magnetic field, which effectively separates the opposing ion flows with no mixing. This strongly magnetized shear interface appears stable and lasts many tens of light crossing times of the simulation box, while the electrons are energized to reach the ion kinetic energy, with approximately 10 percent of the total energy in electromagnetic fields. Here we report our recent attempts to recreate the essential features of the PIC simulation results using a 2-fluid non-ideal MHD approximation. The goal is to perform fluid-scale global simulations of shear interfaces and apply them to macroscopic astrophysical systems such as relativistic jets passing through ambient matter.   

Modeling and Scalability Analysis for Single Pancake Charging Solenoid using both Direct and Iterative Solvers

We present a mathematical model for the charging simulation of a single pancake solenoid and propose its fully discrete backward-Euler scheme. The parallel implementation of the scheme is done in Petra-M, which is a physics layer built on the top of PyMFEM, a python wrapper for Modular FEM (MFEM) library. For the iterative solver, flexible inner-outer Krylov subspace approach is considered with FGMRES as the outer solver and GMRES as the inner solver. As a direct solver, we use Multifrontal Massively Parallel Sparse (MUMPS) direct solver. The scalability analysis is performed with the iterative and direct solvers for both single turn solenoid and T-1 (twenty turns magnet) models. We observe the iterative solver together with the Auxiliary Space Maxwell Solver (AMS) preconditioner outperforms over the direct solver in both cases.