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Radiative detached divertor with acceptable separatrix Z eff

The feasibility study is performed for the radiative detached divertor (RDD) concept, which characterizes a variety of detached plasmas with impurity amounts providing the highest levels of divertor radiation without X-point MARFE (XPM), based on a set of restrictive criteria for the leading plasma parameters (LPPs) including, e.g., tolerable peak power loads below 1 MW/m2, low separatrix densities, allowable impurity concentrations, and acceptable Z eff values for a DIII-D like tokamak. For this, extensive simulations with the 2-D edge plasma transport code were done scanning the deuterium and impurity inventories practically for all impurity elements from beryllium to neon and the analysis of LPP variations in these scans is presented. It is shown that, for a given D inventory, the total radiation fraction with an increase in the impurity inventory reaches a flat top level, f rad = 0.85 ± 0.01, whereas the higher f rad corresponds to XPM. This critical fraction is the same for all elements and values of the D inventory. Successful RDD solutions with a flat top radiation meeting all ad hoc LPP criteria are found for some elements. Boron and nitrogen are shown to be the most promising elements for seeding, since they are capable of providing alone the successful RDD at the lowest concentrations. Several important effects on impurity radiation are considered including: cross-field impurity transport in regions with strong temperature gradients, multi-species thermal force, charge-exchange of impurity ions with D atoms originating from recombination, impurity entrainment by parallel flows, flows caused by inner/outer divertor asymmetries, and Mach ∼ 1 flows reached inside radiation-ionization fronts. The impurity radiation profiles of various elements are analyzed suggesting three patterns differing in the radiation front position with respect to the D ionization source. The modeled relocation of D from the pedestal into divertor regions; an enhanced pedestal enrichment for impurities with high first ionization potential; and RDD capability of confining inside the divertors the large D inventories as neutral atoms, are considered as effects of increasing impurity inventory. The responses of a flat-top RDD to the input parameters variation are studied. For example, dependencies of LPPs on the input power increase, which express the sharp and even bifurcation transitions between two distinct branches corresponding to the detached and attached divertors, are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Drift-wave stability in the field-reversed configuration

Gyrokinetic simulations of C-2-like field-reversed configuration (FRC) find that electrostatic drift-waves are locally stable in the core. The stabilization mechanisms include finite Larmor radius effects, magnetic well (negative grad-B), and fast electron short circuit effects. In the scrape-off layer (SOL), collisionless electrostatic drift-waves in the ion-to-electron-scale are destabilized by electron temperature gradients due to the resonance with locally barely trapped electrons. Collisions can suppress this instability, but a collisional drift-wave instability still exists at realistic pressure gradients. Simulation results are in qualitative agreement with C-2 FRC experiments. In particular, the lack of ion-scale instability in the core is not inconsistent with experimental measurements of a fluctuation spectrum showing a depression at ion-scales. Here, the pressure gradient thresholds for the SOL instability from simulations are also consistent with the critical gradient behavior observed in experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A theory of self-organized zonal flow with fine radial structure in tokamak

The (low frequency) zonal flow-ion temperature gradient (ITG) wave system, constructed on Braginskii's fluid model in tokamak, is shown here to be a reaction-diffusion-advection system; it is derived by making use of a multiple spatiotemporal scale technique and two-dimensional (2D) ballooning theory. For real regular group velocities of ITG waves, two distinct temporal processes, sharing a very similar meso-scale radial structure, are identified in the nonlinear self-organized stage. The stationary and quasi-stationary structures reflect a particular feature of the poloidal group velocity. The equation set posed to be an initial value problem is numerically solved for JET low mode parameters; the results are presented in several figures and two movies that show the spatiotemporal evolutions as well as the spectrum analysis—frequency-wave number spectrum, auto power spectrum, and Lissajous diagram. This approach reveals that the zonal flow in tokamak is a local traveling wave. For the quasi-stationary process, the cycle of ITG wave energy is composed of two consecutive phases in distinct spatiotemporal structures: a pair of Cavitons growing and breathing slowly without long range propagation, followed by a sudden decay into many Instantons that carry negative wave energy rapidly into infinity. A spotlight onto the motion of Instantons for a given radial position reproduces a Blob-Hole temporal structure; the occurrence as well as the rapid decay of Caviton into Instantons is triggered by zero-crossing of radial group velocity. A sample of the radial profile of zonal flow contributed from 31 nonlinearly coupled rational surfaces near plasma edge is found to be very similar to that observed in the JET Ohmic phase [J. C. Hillesheim et al., Phys. Rev. Lett. 116, 165002 (2016)]. The theory predicts an interior asymmetric dipole structure associated with the zonal flow that is driven by the gradients of ITG turbulence intensity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Gyrokinetic particle simulations of the effects of compressional magnetic perturbations on drift-Alfvenic instabilities in tokamaks

The compressional component of magnetic perturbation δB- || to can play an important role in drift-Alfvenic instabilities in tokamaks, especially as the plasma β increases (β is the ratio of kinetic pressure to magnetic pressure). In this work, we have formulated a gyrokinetic particle simulation model incorporating δB- || , and verified the model in kinetic Alfven wave simulations using the Gyrokinetic Toroidal Code in slab geometry. Simulations of drift-Alfvenic instabilities in tokamak geometry shows that the kinetic ballooning mode (KBM) growth rate decreases more than 20% when δB- || is neglected for β e = 0.02, and that δB- || to has stabilizing effects on the ion temperature gradient instability, but negligible effects on the collisionless trapped electron mode. Lastly, the KBM growth rate decreases about 15% when equilibrium current is neglected.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Turbulence, transport, and zonal flows in the Madison symmetric torus reversed-field pinch

The robustness and the effect of zonal flows in trapped electron mode (TEM) turbulence and Ion Temperature Gradient (ITG) turbulence in the reversed-field pinch (RFP) are investigated here from numerical solutions of the gyrokinetic equations with and without magnetic external perturbations introduced to model tearing modes. For simulations without external magnetic field perturbations, zonal flows produce a much larger reduction of transport for the density-gradient-driven TEM turbulence than they do for the ITG turbulence. Zonal flows are studied in detail to understand the nature of their strong excitation in the RFP and to gain insight into the key differences between the TEM- and ITG-driven regimes. The zonal flow residuals are significantly larger in the RFP than in tokamak geometry due to the low safety factor. Collisionality is seen to play a significant role in the TEM zonal flow regulation through the different responses of the linear growth rate and the size of the Dimits shift to collisionality, while affecting the ITG only minimally. A secondary instability analysis reveals that the TEM turbulence drives zonal flows at a rate that is twice that of the ITG turbulence. In addition to interfering with zonal flows, the magnetic perturbations are found to obviate an energy scaling relation for fast particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electron parallel transport for arbitrary collisionality

Integral (nonlocal) closures [J.-Y. Ji and E. D. Held, Phys. Plasmas 21, 122116 (2014)] are combined with the momentum balance equation to derive electron parallel transport relations. For a single harmonic fluctuation, the relations take the same form as the classical Spitzer theory (with possible additional terms): The electric current and heat flux densities are connected to the modified electric field and temperature gradient by transport coefficients. In contrast to the classical theory, the dimensionless coefficients depend on the collisionality quantified by a Knudsen number, the ratio of the collision length to the angular wavelength. The key difference comes from the proper treatment of the viscosity and friction terms in the momentum balance equation, accurately reflecting the free streaming and collision terms in the kinetic equation. For an arbitrary fluctuation, the transport relations may be expressed by a Fourier series or transform. Finally, for low collisionality, the electric resistivity can be significantly larger than that of classical theory and may predict the correct timescale for fast magnetic reconnection.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Study of the parametric dependence of linear and nonlinear microtearing modes in conventional tokamak discharges

We see that a reduced transport model for microtearing modes is developed for use in integrated predictive modeling studies, employing a unified fluid/kinetic approach to derive the nonlinear dispersion relation. This approach advances the kinetic description and allows the inclusion of nonlinear effects due to magnetic fluctuations. In this numerical study, the dependence of the microtearing mode real frequency and growth rate on plasma parameters and on DIII-D like L-mode and H-mode plasma profiles is examined. The magnetic fluctuation strength as well as electron thermal diffusivity due to microtearing modes is computed. The saturated amplitude of the magnetic fluctuations is calculated utilizing numerically determined microtearing mode eigenvalues in the nonlinear microtearing modes envelope equation. It is found that the electron temperature gradient in the presence of moderate collision frequency is required for the microtearing mode to become unstable. The effects of small and large collisionality and small and large wavenumbers on microtearing modes are found to be stabilizing, while the effects of density gradient, plasma beta, low current density, and large magnetic shear are found to be destabilizing. The microtearing mode growth rate, magnetic fluctuation strength, as well as electron thermal diffusivity is found to be larger in the H-mode plasma than in the L-mode plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Extending the validation of multi-mode model for anomalous transport to high beta poloidal tokamak scenario in DIII-D

The Multi-Mode Model (MMM7.1) for anomalous transport is tested in predictive modeling of temperature profiles of a high beta poloidal DIII-D discharge. This new H-mode plasma regime, with high beta poloidal and high bootstrap currents, has been studied in DIII-D tokamak discharges. The role of instabilities that can drive the anomalous transport described by MMM7.1 is investigated. The temperature profiles for a high beta poloidal DIII-D discharge are computed using the NCLASS model for the neoclassical transport and the Weiland and Electron Temperature Gradient (ETG) components of the MMM7.1 model for the anomalous transport. Here, the neoclassical transport is found to be the main contributor to the ion thermal transport in the plasma core.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. In conclusion, this work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport

A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3D geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.

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Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

Here, verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for k y ρ s ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers.

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Zonal structure effect on the nonlinear saturation of reverse shear Alfven eigenmodes

A gyrokinetic ion/fluid electron hybrid model is used to study the nonlinear evolution of reverse shear Alfven eigenmodes (RSAE) driven by energetic particles. When only the energetic particle nonlinear effects are included, the saturation amplitude of a single-n RSAE follows the trapping scaling, δB/B~(γ/ω) 2 . When the nonlinear effects of thermal ions and electrons are included, zonal structures are force generated but do not affect the saturation amplitude for γ/ω≤0.03. No spontaneous generation of zonal structures is observed, in contrast to ion-temperature-gradient-driven modes. At larger energetic particle drive, the effects of zonal structures cause a significant reduction in the RSAE saturation amplitude. The reduction is not caused by the zonal flow shearing of the RSAE, but by the force-generated n = 0 component in the thermal ion distribution function and the electron density. Finally, these n = 0 perturbations lead to nonlinear evolution of the RSAE mode structure and enhance damping.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Uncertainty analysis of axial temperature and Seebeck coefficient measurements

Experimental investigations of solid materials at elevated temperatures rely on the optimized thermal design of the measurement system, as radiation becomes a predominant source of heat loss which can lead to large uncertainty in measured temperature and related physical properties of a test sample. Advancements in surface temperature measurements have reduced thermal losses arising from the cold-finger effect using axially inserted thermocouples and from radiation using shields or other thermal guards. The leading technology for temperature sensing at temperatures up to ~900 °C makes use of these design features for measuring thermopower, yet uncertainty analysis estimation of this technique is not known. This study makes use of finite element modeling to determine spatial temperature distributions to obtain the upper limit of confidence expected for the axially inserted thermocouple approach when a heated radiation shield is incorporated into the design. Using an axially inserted thermocouple to measure the sample surface temperature, the temperature variations across the sample hot and cold surfaces at 900 °C for a temperature drop of 0, 5, and 10 °C are calculated to be as low as 0.02, 0.21, and 0.41 °C, respectively, when a heated radiation shield is employed. Uniform temperature distribution on the thermocouple cross-wire geometry indicates that the axial thermocouple measurement design is indeed effective for suppressing the cold-finger effect. Using a heated radiation shield is found to significantly reduce the temperature gradient across the thermocouples.

30 DIRECT ENERGY CONVERSION↗

A combined phase contrast imaging and heterodyne interferometer system for multiscale fluctuation measurements (invited)

In this work, a novel combined diagnostic capable of measuring multiscale density fluctuations that extend from magnetohydrodynamic (MHD) to the lower range of electron temperature gradient turbulence has been designed, installed, and operated at DIII-D. The combined diagnostic was constructed by adding a heterodyne interferometer to the pre-existing phase contrast imaging (PCI) system, both of which measure line-integrated electron density fluctuations. The port-space footprint is minimized via use of a single 10.6 μm probe beam. With temporal bandwidths in excess of 1 MHz, the PCI measures high-k (1.5 cm -1 < |k R | ≤ 25 cm -1 ) fluctuations with sensitivity 3×10 13 m -2 /$\sqrt{kHz}$, while the interferometer simultaneously measures low-k (|k R | < 5 cm -1 ) fluctuations with sensitivity 3×10 14 m -2 /$\sqrt{kHz}$. The intentional mid-k overlap has been empirically verified with sound-wave calibrations and allows quantitative investigation of multiscale effects that are predicted to be significant in the reactor-relevant T e ~ T i regime. Lastly, via correlation with the primary DIII-D interferometer, the toroidal mode numbers of core-localized MHD can be measured.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Variable location channels to improve efficiency and precision for direct ∇ T e measurements and high spatial resolution T e -profile measurements using electron cyclotron emission

Electron cyclotron emission (ECE) diagnostics that use variable location channels based on yttrium iron garnet (YIG) bandpass filters improve the precision and the efficiency of measurements of electron temperature (T e ) profiles and fluctuations (δT e ). These variable frequency filters were substituted for fixed frequency filters in the intermediate frequency section to achieve the required higher resolution over a target radial range, just before the experiment. In this paper, we present the proof-of-principle for high temporal resolution measurement of the electron temperature gradient, via real-time slewing of a YIG filter for relocation of an ECE channel during a long pulse. The key component is the application of YIG tunable filters with their narrow bandwidth and capability for a high slew rate of their center frequency. This application permits fast relocation of the ECE channels for direct measurement of the gradient and close spacing of channels to investigate the magnetic island’s dynamic behavior.

47 OTHER INSTRUMENTATION↗

Upgrade of the ECE diagnostic on EAST

The electron cyclotron emission (ECE) diagnostic on the experimental advanced superconducting tokamak (EAST) was upgraded recently to provide electron temperature profile measurement with wider radial coverage and better precision. Here, the lower limit of the ECE detection frequency band was extended from 104 GHz to 97 GHz by adding a new 8-channel heterodyne radiometer, which ensures capability for the measurement of the second harmonic ECE with toroidal magnetic field down to 1.75 T. Also, the existing 32-channel heterodyne radiometer has been upgraded, with the frequency interval for the lower frequency range up to 120 GHz reduced from 2 GHz to 1 GHz by introducing eight channels in the intermediate frequency part. In addition, a plan is presented to incorporate tunable yttrium iron garnet filters into the existing heterodyne radiometer to obtain detailed measurements of the electron temperature gradient scale length as well as finer spatial pinpointing of magnetohydrodynamic modes. Examples from DIII-D are provided where similar ECE diagnostic allowed precise measurement of the center and width of neoclassical tearing modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Cross-verification of the global gyrokinetic codes GENE and XGC

A detailed cross-verification between two global gyrokinetic codes, the core continuum code GENE and the edge particle-in-cell code XGC, for the linear and nonlinear simulations of ion-temperature-gradient modes is carried out. With the recent developments in the edge gyrokinetics, it may be feasible someday to describe the whole tokamak plasma on turbulence timescales using a coupled gyrokinetic simulation model. Before pursuing this, the core code (GENE) and the edge code (XGC) must be carefully benchmarked with each other. The present verification provides a solid basis for future code coupling research. Also included in the benchmarking is the global particle-in-cell code ORB5, to raise the confidence in the quality of the obtained results. An excellent agreement between all three codes is obtained. Lastly, in order to facilitate a benchmark framework for other codes, we make a specific effort to provide all the relevant input parameters and precise details for each code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The two-dimensional kinetic ballooning theory for trapped electron mode in tokamak

The two-dimensional (2D) kinetic theory for a collisionless trapped electron mode is developed based on the Fourier-ballooning transform in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The system consists of two equations: the ballooning (integral) equation with a parameterized Floquet phase and a second order differential equation for the distribution of the Floquet phase. The coupled equations are, then, numerically solved as an eigenvalue problem yielding the 2D mode structure (in real space) as well as the global (phase-independent) eigenvalue for an L-mode parameter set. The 2D mode structure exhibits apparent radial-poloidal asymmetry; due to the poloidal coupling, the radial correlation length is found to be, at least, twice as large as the poloidal one. The global (phase-independent) eigenvalue of the mode differs considerably from the conventional local (phase-dependent) estimate. Finally, this paper shares many technical aspects with a published paper that works out the 2D kinetic theory for the ion temperature gradient mode [Xie et al., Phys. Plasmas 24, 102506 (2017)]

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗