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It is well documented that the central electron temperature in the national spherical torus experiment (NSTX) remains largely unchanged as the external heating power, and hence the normalized volume averaged plasma pressure β increases [Stutman, Phys. Rev. Lett. 102, 115002 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.115002]. Here we present a hypothesis that low n, pressure driven ideal magnetohydrodynamic (MHD) instabilities that are nondisruptive, can break magnetic surfaces in the central region and thereby flatten the electron temperature profiles. We demonstrate this mechanism in a 3D resistive MHD simulation of a NSTX discharge. By varying the toroidal magnetic field strength, and/or the heating power, we show that there is a critical value of β, above which the central temperature profile no longer peaks on axis.

Single carbon pellet disruption mitigation simulations using M3D-C1 were conducted in an NSTX-U-like plasma to support the electromagnetic pellet injection concept (EPI). A carbon ablation model has been implemented in M3D-C1 and tested with available data. 2D simulations were conducted in order to estimate the amount of carbon needed to quench the plasma, finding that the content in a $1\,$mm radius vitreous carbon pellet (~ 3.2x10E20 atoms) would be enough if it is entirely ablated. 3D simulations were performed, scanning over pellet velocity and parallel thermal conductivity, as well as different injection directions and pellet concepts (solid pellets and shell pellets). The sensitivity of the thermal quench and other related quantities to these parameters has been evaluated. A 1 mm radius solid pellet only partially ablates at velocities of 300 m/s or higher, thus being unable to fully quench the plasma. To further enhance the ablation, approximations to an array of pellets and the shell pellet concept were also explored. 3D field line stochastization plays an important role in both quenching the center of the plasma and in heat flux losses, thus lowering the amount of carbon needed to mitigate the plasma when compared to the 2D case. This study constitutes an important step forward in `predict-first' simulations for disruption mitigation in NSTX-U and other devices, such as ITER.

A new fluid model for runaway electron simulation based on fluid description is introduced and implemented in the magnetohydrodynamics code M3D-C1, which includes self-consistent interactions between plasma and runaway electrons. The model utilizes the method of characteristics to solve the continuity equation for the runaway electron density with large convection speed, and uses a modified Boris algorithm for pseudo particle pushing. The model was employed to simulate magnetohydrodynamics instabilities happening in a runaway electron final loss event in the DIII-D tokamak. Nonlinear simulation reveals that a large fraction of runaway electrons get lost to the wall when kink instabilities are excited and form stochastic field lines in the outer region of the plasma. Plasma current converts from runaway electron current to Ohmic current, and get pinched at the magnetic axis. Given the good agreement with experiment, the simulation model provides a reliable tool to study macroscopic plasma instabilities in existence of runaway electron current, and can be used to support future studies of runaway electron mitigation strategies in ITER., 26 pages, 16 figures

We explore the impact of realistic plasma resistivity on the linear stability of peeling-ballooning (PB) modes in tokamak discharges with low-aspect ratio. For this study we consider discharges that are subject to edge-localized modes (ELMs) in the National Spherical Torus Experiment (NSTX). Employing the state of the art extended-magnetohydrodynamic (MHD) code M3D-C1 it is demonstrated that non-ideal effects can significantly affect PB stability thresholds in NSTX discharges. In particular, robust resistive PB modes are found to exist well before the ideal PB stability threshold is met. These novel results can explain why ideal-MHD theory often does not accurately describe ELM onset in spherical torus configurations, and also present a valuable basis for the development of a predictive model for ELMs in low-aspect ratio tokamaks.

A class of topological magnetic island bifurcations that has not previously been observed in toroidal plasmas is described. Increasing an externally applied three-dimensional magnetic field in resistive magnetohydrodynamic simulations results in the asymmetric elongation of resonant island flux surfaces followed by a sequence of heteroclinic bifurcations. These bifurcations produce new sets of hyperbolic-elliptic fixed points as predicted by the Poincare-Birkoff fixed point theorem. Field line calculations verify that the new fixed points do not connect to those of the prebifurcated islands as required for heteroclinic bifurcations on a torus with winding numbers composed of common integer factors.

Self-consistent simulations of neoclassical and electrostatic turbulent transport in a DIII-D H-mode edge plasma under resonant magnetic perturbations (RMPs) have been performed using the global total-f gyrokinetic particle-in-cell code x-point gyrokinetic code (XGC), in order to study density pump-out and electron heat confinement. The RMP field is imported from the extended magneto-hydrodynamics code M3D-C1, taking into account the linear two-fluid plasma response. With both neoclassical and turbulence physics considered together, the XGC simulation reproduces two key features of experimentally observed edge transport under RMPs: increased radial particle transport in the pedestal region that is sufficient to account for the experimental pump-out rate and suppression of the electron heat flux in the steepest part of the edge pedestal. In the simulation, the density fluctuation amplitude of modes moving in the electron diamagnetic direction increases due to interaction with RMPs in the pedestal shoulder and outward, while the electron temperature fluctuation amplitude decreases.

In this paper we present initial simulations of pedestal control by Lithium Granule Injection (LGI) in NSTX. A model for small granule ablation has been implemented in the M3D-C1 code [1] , allowing the simulation of realistic Lithium granule injections. 2D simulations in NSTX L-mode and H-mode plasmas are done and the effect of granule size, injection angle and velocity on the pedestal gradient increase are studied. For H-mode cases, the amplitude of the local pressure perturbation caused by the granules is highly dependent on the solid granule size. In our simulations, reducing the granule injection velocity allows one to inject more particles at the pedestal top.

In the future, the U.S. ornamental horticulture industry may be faced with limited water resources and increased requirements to reduce pollution runoff from production areas. The concerns are most evident to outdoor, uncovered container crop production, which relies on daily irrigation. Capture of precipitation and irrigation runoff from ornamental horticulture nurseries to be recycled as irrigation could potentially generate cost savings relative to the cost of alternative water sources. Existing nurseries may incur large investment costs to modify their infrastructure for water capture to recycle. These added costs must be compared with costs of alternative sources such as off-farm municipal or on-farm well water. Using both existing case nurseries and simulated nurseries, this study employed partial budgeting for comparison of annual costs of recapture and recycling to the alternatives of either municipally delivered water or on-farm well extraction. On-site visits were conducted at mid-Atlantic ornamental horticulture operations that recycle water currently to gather data for constructing budgets and to determine factors that enhance or inhibit nursery adoption of recycling. The partial budgeting analysis was followed by breakeven analysis with regard to costs of regrading, pond excavation, and opportunity costs of land to isolate their effects on the nursery adoption decision. Six of eight case nurseries currently obtaining from 20% to 100% of their irrigation needs from recycled water achieve lower production costs as a result of recycling compared with using alternative municipal or well water sources. Recycling would also reduce pollution runoff as water containing nutrients and chemicals would be retained for reuse on the farm rather than being discharged to public water bodies. Two case nurseries and two simulated nurseries that were constructed based on average conditions for nurseries participating in a mail survey see higher production costs as a result of recycling. The cost of land regrading for water recapture, excavating the recapture pond, and the opportunity cost of production area occupied by the recapture pond are critical for determination of the least cost outcome. Public funding incentives for water collection and recycling could motivate increased water conservation and reduced pollution runoff within the horticulture industry.

The ubiquitous sawtooth phenomena in tokamaks are so named because the central temperature rises slowly and falls rapidly, similar to the blades of a saw. First discovered in 1974, it has so far eluded a theoretical explanation that is widely accepted and consistent with experimental observations. We propose here a new theory for the sawtooth phenomena in auxiliary heated tokamaks, which is motivated by our recent understanding of "magnetic flux pumping." In this theory, the role of the (m, n) = (1, 1) mode is to generate a dynamo voltage, which keeps the central safety factor, q(0), just above 1.0 with low central magnetic shear. When central heating is present, the temperature on axis will increase until at some point, and the configuration abruptly becomes unstable to ideal MHD interchange modes with equal poloidal and toroidal mode numbers, m = n > 1. It is these higher order modes and the localized magnetic stochasticity they produce that cause the sudden crash of the temperature profile, not magnetic reconnection. Long time 3D MHD simulations demonstrate these phenomena, which appear to be consistent with many experimental observations.

The capability to model the nonlinear magnetohydrodynamic (MHD) evolution of stellarator plasmas is developed by extending the M3D-$C^1$ code to allow non-axisymmetric domain geometry. We introduce a set of logical coordinates, in which the computational domain is axisymmetric, to utilize the existing finite-element framework of M3D-$C^1$. A $C^1$ coordinate mapping connects the logical domain to the non-axisymmetric physical domain, where we use the M3D-$C^1$ extended MHD models essentially without modifications. We present several numerical verifications on the implementation of this approach, including simulations of the heating, destabilization, and equilibration of stellarator plasmas with strongly anisotropic thermal conductivity, and of the relaxation of stellarator equilibria to integrable and non-integrable magnetic field configurations in realistic geometries., Comment: 8 pages, 6 figures

Equilibria with extended regions of weak magnetic shear, including some tokamak scenarios and stellarators, can be susceptible to pressure-driven internal MHD instabilities even though there is no mode rational surface in the plasma. Nonresonant modes, in particular, can have properties that are unattractive for confinement, including displacing substantial volumes of the plasma and leading to more efficient pressure gradient flattening in the nonlinear regime. The onset and linear properties of the low shear stability regime are examined using the initial-value, extended-MHD code M3D-C1. For monotonic q-profiles, we demonstrate a clear correlation between the convergents associated with the continued fraction representation of q0 and the spectrum of unstable modes. Nonresonant modes are observed to be destabilized preferentially to any other resonant instability with the same toroidal mode number when n > 1. Using the observed connection between the spectrum associated with q0 and the overall equilibrium stability properties, we suggest a technique for reducing the uncertainty on both q0 and magnetic shear in the core region, obtained either via measurement or through the analysis and reconstruction of experimental results.

Over the last decade, a variational principle based on a generalisation of Taylor’s relaxation, referred to as multi-region relaxed magnetohydrodynamics (MRxMHDs) has been developed. The numerical solutions of the MRxMHD equilibria have been constructed using the Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502). In principle, SPEC could also be established to describe the MRxMHD stability of an equilibrium. In this work, a theoretical framework is developed to relate the second variation of the energy functional to the so-called Hessian matrix, enabling the prediction of MHD linear instabilities of cylindrical plasmas, and is implemented in SPEC. The negative and positive eigenvalues of the Hessian matrix predict the stability of an equilibrium. Verification studies of SPEC stability results with the M3D-C 1 code and the tearing mode Δ ′ criterion have been conducted for ideal and resistive MHD instabilities, respectively, in a pressureless cylindrical tokamak, and have shown good agreement. Our stability analysis is a critical step towards understanding the MHD stability of three-dimensional MHDs where nested flux surfaces, magnetic islands and stochastic regions co-exist.

Nonresonant internal modes can be difficult to anticipate as there is no resonant surface in the plasma. However, equilibria that are unstable to multiple nonresonant magnetohydrodynamic (MHD) modes may be more prone to global loss of confinement since these instabilities generate spatially extended linear displacements, potentially enhancing magnetic field line chaos via nonlinear interactions. Here, we successfully predict the unstable nonresonant pressure-driven modes for equilibria with zero shear in the plasma core, irrational q on axis, and a central pressure gradient, which is consistent with pre-crash profiles in sawtoothing tokamak plasmas in the large-aspect-ratio limit. A criterion for identifying nonresonant modes most likely to be unstable is developed from the convergents of the continued fraction representation of q0. A higher-order analysis of the standard Energy Principle reveals the conditions under which these modes are expected to dominate. Linear growth rate spectra, as a function of toroidal mode number (up to n = 30), calculated using the initial-value extended-MHD code, M3D-C1, recover the characteristic dependence observed for ideal infernal modes. Nonresonant modes have also been invoked in some ideal sawtooth crash models. This work provides a mechanism to predict the mode numbers of infernal modes and, potentially, the width of some post-sawtooth-crash profiles.

The Enhanced Pedestal (EP) H-mode regime is an attractive wide-pedestal high-βp scenario for the National Spherical Torus Experiment Upgrade (NSTX-U) and next-step devices as it achieves enhanced energy confinement (H98y,2 > 1.5), large normalized pressure (βN > 5), and significant bootstrap fraction (fBS > 0.6) at Ip/BT = 2 MA/T. This regime is realized when the edge ion collisionality becomes sufficiently small that a positive feedback interaction occurs between a reduction in the ion neoclassical energy transport and an increase in the particle transport from pressure-driven edge instabilities. The EP H-mode was most often observed as a transition following a large edge-localized mode in conditions with low edge neutral recycling. It is hypothesized that the onset of pressure-driven instabilities prior to the full recovery of the neutral density leads to a temporary period with an elevated ion temperature gradient that triggers the transition to EP H-mode. Linear CGYRO and M3D-C1 calculations are compared to beam emission spectroscopy and magnetic spectroscopy in order to describe the evolution of the edge particle transport mechanisms during the ELM recovery and the saturated EP H-mode state. The observations are consistent with the hypothesis that the onset of pressure-driven edge instabilities, such as the kinetic ballooning mode and kink-peeling mode, can be responsible for the increased particle transport in EP H-mode.

A benchmark exercise for the modeling of vertical displacement events (VDEs) is presented and applied to the 3D nonlinear magneto-hydrodynamic codes M3D-C$^1$, JOREK and NIMROD. The simulations are based on a vertically unstable NSTX equilibrium enclosed by an axisymmetric resistive wall with rectangular cross section. A linear dependence of the linear VDE growth rates on the resistivity of the wall is recovered for sufficiently large wall conductivity and small temperatures in the open field line region. The benchmark results show good agreement between the VDE growth rates obtained from linear NIMROD and M3D-C$^1$ simulations as well as from the linear phase of axisymmetric nonlinear JOREK, NIMROD and M3D-C$^1$ simulations. Axisymmetric nonlinear simulations of a full VDE performed with the three codes are compared and excellent agreement is found regarding plasma location and plasma currents as well as eddy and halo currents in the wall., Comment: The following article will be submitted to Physics of Plasmas

XGC1 and M3D-C1 are two fusion plasma simulation codes being developed at Princeton Plasma Physics Laboratory. XGC1 uses the particle-in-cell method to simulate gyrokinetic neoclassical physics and turbulence (Chang et al. Phys Plasmas 16(5):056108, 2009; Ku et al. Nucl Fusion 49:115021, 2009; Admas et al. J Phys 180(1):012036, 2009). M3D-$$C^1$$C1 solves the two-fluid resistive magnetohydrodynamic equations with the $$C^1$$C1 finite elements (Jardin J comput phys 200(1):133---152, 2004; Jardin et al. J comput Phys 226(2):2146---2174, 2007; Ferraro and Jardin J comput Phys 228(20):7742---7770, 2009; Jardin J comput Phys 231(3):832---838, 2012; Jardin et al. Comput Sci Discov 5(1):014002, 2012; Ferraro et al. Sci Discov Adv Comput, 2012; Ferraro et al. International sherwood fusion theory conference, 2014). This paper presents the software tools and libraries that were combined to form the geometry and automatic meshing procedures for these codes. Specific consideration has been given to satisfy the mesh configuration and element shape quality constraints of XGC1 and M3D-$$C^1$$C1.

A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at $q\approx 1$, thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C$^1$ code. In these simulations, the most important mechanism responsible for the flux pumping is that a saturated $(m=1,n=1)$ quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect. It is shown that sawtoothing is prevented in the simulations if $\beta$ is sufficiently high to provide the necessary drive for the $(m=1,n=1)$ instability that generates the dynamo loop voltage. The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile., Comment: submitted to Physics of Plasmas (23 pages, 15 Figures)

In this paper, we present simulations of pedestal control by lithium granule injection (LGI) in NSTX. A model for small granule ablation has been implemented in the M3D-C1 code (Jardin et al 2012 Comput. Sci. Discovery 5 014002), allowing the simulation of realistic lithium granule injections. 2D and 3D simulations of Li injections in NSTX H-mode plasmas are performed and the effect of granule size, injection angle and velocity on the pedestal gradient increase is studied. The amplitude of the local pressure perturbation caused by the granules is found to be highly dependent on the solid granule size. Adjusting the granule injection velocity allows one to inject more particles at the pedestal top. 3D simulations show the destabilization of high order MHD modes whose amplitude is directly linked to the localized pressure perturbation, which is found to depend on the toroidal localization of the granule density source.

The presence of error fields in a tokamak device is inevitable, so it is of fundamental importance to understand their impact on the operation of the device and up to what level they can be tolerated. In this paper a prediction of the impact on the magnetic footprints on the divertor plates due to the misalignment of NSTX-U equilibrium coils is presented. Resistive MHD simulations are used to predict the magnetic field perturbations experienced by the field lines due to the presence of error fields. A linear relation between the magnitude of the misalignment and the area of the magnetic footprints is found, as well as an inverse proportionality between the size of a magnetic footprint and the plasma penetration of the field lines composing the footprint. This study is intended as a starting point in the process of investigating divertor footprints associated with the plasma response to intrinsic error fields with resistive MHD codes. A basic interpretation of the results suggests that large footprints resulting from equilibrium coils misalignment may be desirable, to some extent, to decrease the peak heat load on the divertor components. A more complete interpretation of the results presented here will involve a number of complex physics issues, for example pedestal transport and stability, along with the role of various scrape-off layer and divertor processes, as well as experimental data to confirm the predictions.

An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor$q$at the 95 % poloidal flux surface,$q_{95}$, is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections (Shafranov,Sov. Phys. Tech. Phys., vol. 15, 1970, p. 175) when$q_{edge}$, the safety factor at the outermost closed flux surface, lies just below a rational value$m/n$. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and$q_{edge}$decreases through successive rational surfaces. For$q_{edge}, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which$q_{edge}$is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when$q_{95}$, reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when$q_{95}, but$q_{edge}\gg 2$. The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the$q=2$surface. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.

New evidence indicates that there is significant 3D variation in density fluctuations near the boundary of weakly 3D tokamak plasmas when resonant magnetic perturbations are applied to suppress transient edge instabilities. The increase in fluctuations is concomitant with an increase in the measured density gradient, suggesting that this toroidally localized gradient increase could be a mechanism for turbulence destabilization in localized flux tubes. Two-fluid magnetohydrodynamic simulations find that, although changes to the magnetic field topology are small, there is a significant 3D variation of the density gradient within the flux surfaces that is extended along field lines. This modeling agrees qualitatively with the measurements. The observed gradient and fluctuation asymmetries are proposed as a mechanism by which global profile gradients in the pedestal could be relaxed due to a local change in the 3D equilibrium. These processes may play an important role in pedestal and scrape-off layer transport in ITER and other future tokamak devices with small applied 3D fields.

An integrated model for the ionization, radiation, and advection of impurities in the extended-magnetohydrodynamic code M3D-C1 is described. This implementation makes use of the KPRAD model, which calculates bremsstrahlung radiation and impurity ionization, recombination, and radiation rates using a model in which the density of each charge state is advanced separately. The integrated model presented here allows the independent evolution of electron and ion temperatures, which is necessary to accurately model cases where the electron temperature drops more quickly than the electron–ion thermal equilibration time. This model is used to simulate the disruption of a model NSTX discharge caused by the introduction of argon impurities, using physically realistic resistivity. Despite well-mixed impurities, contraction of the current channel is found to lead to magnetohydrodynamic instabilities that result in stochastization of the magnetic field, a fast thermal quench, and localized parallel electric fields that can exceed the axisymmetric values by a factor of five for brief periods.

This work is an extension of the previous semi-analytical work (Teng et al 2016 Nucl. Fusion 56 106001), explaining the density limit with a thermo-resistive tearing mode model. The thermo-resistive island growth is calculated with a 3D MHD code M3D-C 1 (Jardin et al 2012 Comput. Sci. Discovery 5 014002). It is shown with nonlinear 3D MHD simulations that impurity radiation stimulates large magnetic islands at the density limit. The impact of thermal perturbations inside and outside of the island is explored. Inside the island, net cooling enhances the island growth and net heating suppresses its growth. Outside the island, thermal perturbations have a much smaller impact on the island growth. When the plasma density is increased towards the density limit, the island changes from being heated to being cooled and grows to a much larger island width. The convergence test of the simulations over the temporal and spatial grid is performed. The numerical model and the semi-analytical model are compared by calculating the terms, which are defined in the modified Rutherford equation, and good agreement is observed.

Resonant magnetic perturbations (n = 3 RMPs) are used to suppress large amplitude ELMs and mitigate naturally occurring 'grassy'-ELMs in DIII-D plasmas relevant to the ITER steady-state mission. Fully non-inductive discharges in the ITER shape and pedestal collisionality (nu(e)* approximate to 0.05-0.15) are routinely achieved in DIII-D with RMP suppression of the Type-I ELMs. The residual grassy-ELMs deliver a low peak heat flux to the divertor as low as 1.2 x the inter-ELM heat flux in plasmas with sustained high H-factor (H-98y2 approximate to 1.2). The operating window for the RMP grassy-ELM regime is q(95) = 5.3-7.1 and external torque in the range 9-0.7 Nm in the co-Ip direction, which is in the range required for a steady-state tokamak reactor. The RMP grassy-ELM regime is associated with a two-step pedestal, with strong flattening of the density around the zero crossing in the E x B shear. The edge magnetic response of the plasma to the n = 3 RMP is found to be approximate to 2-3x larger than for comparable ITER baseline plasmas (beta(N) approximate to 1.8, q(95) approximate to 3.1). The amplification of the RMP is consistent with the weak magnetic perturbation level (delta B/B approximate to 1. x 10(-4)) required for effective Type-I ELM suppression. Cyclic variations in the pedestal pressure, width, and toroidal rotation are observed in these plasmas, correlated with cyclic variations in the strength and frequency of the grassy-ELMs. Extended MHD analysis and magnetic measurements indicate that these pedestal pulsations are driven by cyclic variations in the resonant field strength at the top of the pedestal. These pedestal pulsations reveal that the grassy-ELMs is correlated with the proximity of the pedestal to the low-n peeling-ballooning mode stability boundary. The use of low amplitude magnetic fields to access grassy-ELM conditions free of Type-I ELMs in high beta poloidal plasmas (beta(p) approximate to 1.5-2.0) opens the possibility for the further optimization of the steady-state tokamak by use of edge resonant magnetic perturbations.

Small 3D perturbations to the magnetic field in DIII-D ( δB/B∼2×10−4) result in large modulations of density fluctuation amplitudes in the pedestal, which are shown using Doppler backscattering measurements to vary by a factor of 2. Helical perturbations of equilibrium density within flux surfaces have previously been observed in the pedestal of DIII-D plasmas when 3D fields are applied and were correlated with density fluctuation asymmetries in the pedestal. These intra-surface density and pressure variations are shown through two fluid MHD modeling studies using the M3D-C1 code to be due to the misalignment of the density and temperature equilibrium iso-surfaces in the pedestal region. This modeling demonstrates that the phase shift between the two iso-surfaces corresponds to the diamagnetic direction of the two species, with the mass density surfaces shifted in the ion diamagnetic direction relative to the temperature and magnetic flux iso-surfaces. The resulting pedestal density, potential, and turbulence asymmetries within flux surfaces near the separatrix may be at least partially responsible for several poorly understood phenomena that occur with the application of 3D fields in tokamaks, including density pump out and the increase in power required to transition from L- to H-mode.Small 3D perturbations to the magnetic field in DIII-D ( δB/B∼2×10−4) result in large modulations of density fluctuation amplitudes in the pedestal, which are shown using Doppler backscattering measurements to vary by a factor of 2. Helical perturbations of equilibrium density within flux surfaces have previously been observed in the pedestal of DIII-D plasmas when 3D fields are applied and were correlated with density fluctuation asymmetries in the pedestal. These intra-surface density and pressure variations are shown through two fluid MHD modeling studies using the M3D-C1 code to be due to the misalignment of the density and temperature equilibrium iso-surfaces in the pedestal region. This modeling demonstrates that the phase shift between the two iso-surfaces corresponds to the diamagnetic direction of the two species, with the mass density surfaces shifted in the ion diamagnetic direction relative to the temperature and magnetic flux iso-surfaces. The resulting pedestal density, potential, and turbul...

The main results of an intense vertical displacement event (VDE) modelling activity using the implicit 3D extended MHD code M3D-C1 are presented. A pair of nonlinear 3D simulations are performed using realistic transport coefficients based on the reconstruction of a so-called NSTX frozen VDE where the feedback control was purposely switched off to trigger a vertical instability. The vertical drift phase is solved assuming axisymmetry until the plasma contacts the first wall, at which point the intricate evolution of the plasma, decaying to large extent in force-balance with induced halo/wall currents, is carefully resolved via 3D nonlinear simulations. The faster 2D nonlinear runs allow to assess the sensitivity of the simulations to parameter changes. In the limit of perfectly conducting wall, the expected linear relation between vertical growth rate and wall resistivity is recovered. For intermediate wall resistivities, the halo region contributes to slowing the plasma down, and the characteristic VDE t...

An integrated-modeling workflow has been developed for the purpose of performing predict-first analysis of transient-stability experiments. Starting from an existing equilibrium reconstruction from a past experiment, the workflow couples together the EFIT Grad-Shafranov solver [L. Lao et al., Fusion Sci. Technol. 48, 968 (2005)], the EPED model for the pedestal structure [P. B. Snyder et al., Phys. Plasmas 16, 056118 (2009)], and the NEO drift-kinetic-equation solver [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)] (for bootstrap current calculations) in order to generate equilibria with self-consistent pedestal structures as the plasma shape and various scalar parameters (e.g., normalized β, pedestal density, and edge safety factor [q95]) are changed. These equilibria are then analyzed using automated M3D-C1 extended-magnetohydrodynamic modeling [S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)] to compute the plasma response to three-dimensional magnetic perturbations. This workflow was created in conjunction with a DIII-D experiment examining the effect of triangularity on the 3D plasma response. Several versions of the workflow were developed, and the initial ones were used to help guide experimental planning (e.g., determining the plasma current necessary to maintain the constant edge safety factor in various shapes). Subsequent validation with the experimental results was then used to revise the workflow, ultimately resulting in the complete model presented here. We show that quantitative agreement was achieved between the M3D-C1 plasma response calculated for equilibria generated by the final workflow and equilibria reconstructed from experimental data. A comparison of results from earlier workflows is used to show the importance of properly matching certain experimental parameters in the generated equilibria, including the normalized β, pedestal density, and q95. On the other hand, the details of the pedestal current did not significantly impact the plasma response in these equilibria. A comparison to the experimentally measured plasma response shows mixed agreement, indicating that while the equilibria are predicted well, additional analysis tools may be needed. Finally, we note the implications that these results have for the success of future predict-first studies, particularly the need for scans of uncertain parameters and for close collaboration between experimentalists and theorists.

M3D-C^1 is an implicit, high-order finite element code for the solution of the time-dependent nonlinear two-fluid magnetohydrodynamic equations [S.C. Jardin, J. Breslau, N. Ferraro, A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions, J. Comp. Phys. 226 (2) (2007) 2146-2174]. This code has now been extended to allow computations in toroidal geometry. Improvements to the spatial integration and time-stepping algorithms are discussed. Steady-states of a resistive two-fluid model, self-consistently including flows, anisotropic viscosity (including gyroviscosity) and heat flux, are calculated for diverted plasmas in geometries typical of the National Spherical Torus Experiment (NSTX) [M. Ono et al., Exploration of spherical torus physics in the NSTX device, Nucl. Fusion 40 (3Y) (2000) 557-561]. These states are found by time-integrating the dynamical equations until the steady-state is reached, and are therefore stationary or statistically steady on both magnetohydrodynamic and transport time-scales. Resistively driven cross-surface flows are found to be in close agreement with Pfirsch-Schluter theory. Poloidally varying toroidal flows are in agreement with comparable calculations [A.Y. Aydemir, Shear flows at the tokamak edge and their interaction with edge-localized modes, Phys. Plasmas 14]. New effects on core toroidal rotation due to gyroviscosity and a local particle source are observed.

We describe a new method for solving the time-dependent two-fluid magnetohydrodynamic (2F-MHD) equations in two dimensions that has significant advantages over other methods. The stream-function/potential representation of the velocity and magnetic field vectors, while fully general, allows accurate description of nearly incompressible fluid motions and manifestly satisfies the divergence condition on the magnetic field. Through analytic manipulation, the split semi-implicit method breaks the full matrix time advance into four sequential time advances, each involving smaller matrices. The use of a high-order triangular element with continuous first derivatives (C1 continuity) allows the Galerkin method to be applied without introduction of new auxiliary variables (such as the vorticity or the current density). These features, along with the manifestly compact nature of the fully node-based C1 finite elements, lead to minimum size matrices for an unconditionally stable method with order of accuracy h4. The resulting matrices are compatible with direct factorization using SuperLU_dist. We demonstrate the accuracy of the method by presenting examples of two-fluid linear wave propagation, two-fluid linear eigenmodes of a tilting cylinder, and of a challenging nonlinear problem in two-fluid magnetic reconnection.

We demonstrate that in a 3D resistive magnetohydrodynamic simulation, for some parameters it is possible to form a stationary state in a tokamak where a saturated interchange mode in the center of the discharge drives a near helical flow pattern that acts to nonlinearly sustain the configuration by adjusting the central loop voltage through a dynamo action. This could explain the physical mechanism for maintaining stationary nonsawtoothing "hybrid" discharges, often referred to as "flux pumping."

Density pumpout and edge-localized mode (ELM) suppression by applied n=2 magnetic fields in low-collisionality DIII-D plasmas are shown to be correlated with the magnitude of the plasma response driven on the high-field side (HFS) of the magnetic axis but not the low-field side (LFS) midplane. These distinct responses are a direct measurement of a multimodal magnetic plasma response, with each structure preferentially excited by a different n=2 applied spectrum and preferentially detected on the LFS or HFS. Ideal and resistive magneto-hydrodynamic (MHD) calculations find that the LFS measurement is primarily sensitive to the excitation of stable kink modes, while the HFS measurement is primarily sensitive to resonant currents (whether fully shielding or partially penetrated). The resonant currents are themselves strongly modified by kink excitation, with the optimal applied field pitch for pumpout and ELM suppression significantly differing from equilibrium field alignment.

The Magnetic Nozzle Experiment (MNX) is a linear magnetized helicon-heated plasma device, with applications to advanced spacecraft-propulsion methods and solar-corona physics. This paper reviews ion and electron energy distributions measured in MNX with laser-induced fluorescence (LIF) and probes, respectively. Ions, cold and highly collisional in the main MNX region, are accelerated along a uniform magnetic field to sonic then supersonic speeds as they exit the main region through either mechanical or magnetic apertures. A sharp decrease in density downstream of the aperture(s) helps effect a transition from collisional to collisionless plasma. The electrons in the downstream region have an average energy somewhat higher than that in the main region. From LIF ion-velocity measurements, we find upstream of the aperture a presheath of strength Deltaphips=mrTe, where mrTe is the electron temperature in the main region, and length ~3 cm, comparable to the ion-neutral mean-free-path; immediately downstream of the aperture is an electrostatic double layer of strength DeltaphiDL=3-10 mrTe and length 0.3-0.6 cm, 30-600lambdaD. The existence of a small, ca. 0.1%, superthermal electron population with average energy ~10 mrTe is inferred from considerations of spectroscopic line ratios, floating potentials, and Langmuir probe data. The superthermal electrons are suggested to be the source for the large DeltaphiDL

Using a two-dimensional two-fluid numerical model with finite electron inertia, we have observed turbulence to occur in simulations of plasmas undergoing magnetic reconnection when the plasma β is sufficiently small. This turbulence is caused by secondary instabilities, which are excited by large gradients in the out-of-plane current. These gradients spontaneously form due to the dynamics of ion force balance across the layer, and first arise in the outflow regions downstream from the magnetic x point. This turbulence is not observed to have a substantial effect on the rate of reconnection.

Measurements show fast ion losses correlated with applied three-dimensional (3D) fields in a variety of plasmas ranging from L-mode to resonant magnetic perturbation (RMP) edge localized mode (ELM) suppressed H-mode discharges. In DIII-D L-mode discharges with a slowly rotating n = 2 magnetic perturbation, scintillator detector loss signals synchronized with the applied fields are observed to decay within one poloidal transit time after beam turnoff indicating they arise predominantly from prompt loss orbits. Full orbit following using M3D-C1 calculations of the perturbed fields and kinetic profiles reproduce many features of the measured losses and points to the importance of the applied 3D field phase with respect to the beam injection location in determining the overall impact on prompt beam ion loss. Modeling of these results includes a self-consistent calculation of the 3D perturbed beam ion birth profiles and scrape-off-layer ionization, a factor found to be essential to reproducing the experimental measurements. Extension of the simulations to full slowing down timescales, including fueling and the effects of drag and pitch angle scattering, show the applied n = 3 RMPs in ELM suppressed H-mode plasmas can induce a significant loss of energetic particles from the core. With the applied n = 3 fields, up to 8.4% of the injected beam power is predicted to be lost, compared to 2.7% with axisymmetric fields only. These fast ions, originating from minor radii ρ > 0.7, are predicted to be primarily passing particles lost to the divertor region, consistent with wide field-of-view infrared periscope measurements of wall heating in n = 3 RMP ELM suppressed plasmas. Edge fast ion Dα (FIDA) measurements also confirm a large change in edge fast ion profile due to the n = 3 fields, where the effect was isolated by using short 50ms RMP-off periods during which ELM suppression was maintained yet the fast ion profile was allowed to recover. The role of resonances between fast ion drift motion and the applied 3D fields in the context of selectively targeting regions of fast ion phase space is also discussed.

Recent experiments on DIII-D have increased confidence in the ability to suppress edge-localized modes (ELMs) using edge-resonant magnetic perturbations (RMPs) in ITER, including an improved physics basis for the edge response to RMPs as well as expansion of RMP ELM suppression to more ITER-like conditions. Complete ELM suppression has been achieved utilizing n = 3 RMPs in the ITER baseline scenario. In addition, RMP ELM suppression has been expanded to include plasmas with helium concentrations near 25% and the use of n = 2 RMPs. Analysis of the kinetic profile response suggests that ELM suppression is correlated with the co-alignment of the ω⊥e = 0 location, an n = 3 rational surface, and the top of the pedestal. Modelling predicts that such a co-alignment could potentially lead to island (or island chain) formation just inside the top of the pedestal, inhibiting the growth of the pedestal and thereby maintaining the ELM-free state. Detailed analysis of data obtained during toroidal phase variations of the applied n = 3 RMPs have provided further evidence of an island-like structure at the top of the pedestal. In addition, nearly matched discharges with co-neutral-beam-injection (co-NBI) and counter-NBI have demonstrated the importance of the presence of the ω⊥e = 0 location for ELM suppression. In the counter-NBI cases, the toroidal rotation profile is such that there is no ω⊥e = 0 location and ELMs are not suppressed in conditions in which ELM suppression is generally observed with co-NBI.

Edge Localised Modes (ELMs) in ITER Q = 10 H-mode plasmas are likely to lead to large transient heat loads to the divertor. To avoid an ELM induced reduction of the divertor lifetime, the large ELM energy losses need to be controlled. In ITER, ELM control is foreseen using magnetic field perturbations created by in-vessel coils and the injection of small D2 pellets. ITER plasmas are characterised by low collisionality at a high density (high fraction of the Greenwald density limit). These parameters cannot simultaneously be achieved in current experiments. Therefore, the extrapolation of the ELM properties and the requirements for ELM control in ITER relies on the development of validated physics models and numerical simulations. In this paper, we describe the modelling of ELMs and ELM control methods in ITER. The aim of this paper is not a complete review on the subject of ELM and ELM control modelling but rather to describe the current status and discuss open issues.

The National Spherical Torus Experiment (NSTX) is currently being upgraded to operate at twice the toroidal field and plasma current (up to 1 T and 2 MA), with a second, more tangentially aimed neutral beam (NB) for current and rotation control, allowing for pulse lengths up to 5 s. Recent NSTX physics analyses have addressed topics that will allow NSTX-Upgrade to achieve the research goals critical to a Fusion Nuclear Science Facility. These include producing stable, 100% non-inductive operation in high-performance plasmas, assessing plasma–material interface (PMI) solutions to handle the high heat loads expected in the next-step devices and exploring the unique spherical torus (ST) parameter regimes to advance predictive capability. Non-inductive operation and current profile control in NSTX-U will be facilitated by co-axial helicity injection (CHI) as well as radio frequency (RF) and NB heating. CHI studies using NIMROD indicate that the reconnection process is consistent with the 2D Sweet–Parker theory. Full-wave AORSA simulations show that RF power losses in the scrape-off layer (SOL) increase significantly for both NSTX and NSTX-U when the launched waves propagate in the SOL. Toroidal Alfven eigenmode avalanches and higher frequency Alfven eigenmodes can affect NB-driven current through energy loss and redistribution of fast ions. The inclusion of rotation and kinetic resonances, which depend on collisionality, is necessary for predicting experimental stability thresholds of fast growing ideal wall and resistive wall modes. Neutral beams and neoclassical toroidal viscosity generated from applied 3D fields can be used as actuators to produce rotation profiles optimized for global stability. DEGAS-2 has been used to study the dependence of gas penetration on SOL temperatures and densities for the MGI system being implemented on the Upgrade for disruption mitigation. PMI studies have focused on the effect of ELMs and 3D fields on plasma detachment and heat flux handling. Simulations indicate that snowflake and impurity seeded radiative divertors are candidates for heat flux mitigation in NSTX-U. Studies of lithium evaporation on graphite surfaces indicate that lithium increases oxygen surface concentrations on graphite, and deuterium–oxygen affinity, which increases deuterium pumping and reduces recycling. In situ and test-stand experiments of lithiated graphite and molybdenum indicate temperature-enhanced sputtering, although that test-stand studies also show the potential for heat flux reduction through lithium vapour shielding. Non-linear gyro kinetic simulations have indicated that ion transport can be enhanced by a shear-flow instability, and that non-local effects are necessary to explain the observed rapid changes in plasma turbulence. Predictive simulations have shown agreement between a microtearing-based reduced transport model and the measured electron temperatures in a microtearing unstable regime. Two Alfven eigenmode-driven fast ion transport models have been developed and successfully benchmarked against NSTX data. Upgrade construction is moving on schedule with initial physics research operation of NSTX-U planned for mid-2015.

Experiments have been executed in the DIII-D tokamak to extend suppression of Edge Localized Modes (ELMs) with Resonant Magnetic Perturbations (RMPs) to ITER-relevant levels of beam torque. The results support the hypothesis for RMP ELM suppression based on transition from an ideal screened response to a tearing response at a resonant surface that prevents expansion of the pedestal to an unstable width [Snyder et al., Nucl. Fusion 51, 103016 (2011) and Wade et al., Nucl. Fusion 55, 023002 (2015)]. In ITER baseline plasmas with I/aB = 1.4 and pedestal ν * ∼ 0.15, ELMs are readily suppressed with co- I p neutral beam injection. However, reducing the beam torque from 5 Nm to ≤ 3.5 Nm results in loss of ELM suppression and a shift in the zero-crossing of the electron perpendicular rotation ω ⊥ e ∼ 0 deeper into the plasma. The change in radius of ω ⊥ e ∼ 0 is due primarily to changes to the electron diamagnetic rotation frequency ω e * . Linear plasma response modeling with the resistive MHD code m3d-c1 in...

Recent experimental observations have found turbulent fluctuation structures that are non-axisymmetric in a tokamak with applied 3D fields. In this paper, two fluid resistive effects are shown to produce changes relevant to turbulent transport in the modeled 3D magnetohydrodynamic (MHD) equilibrium of tokamak pedestals with these 3D fields applied. Ideal MHD models are insufficient to reproduce the relevant effects. By calculating the ideal 3D equilibrium using the VMEC code, the geometric shaping parameters that determine linear turbulence stability, including the normal curvature and local magnetic shear, are shown to be only weakly modified by applied 3D fields in the DIII-D tokamak. These ideal MHD effects are therefore not sufficient to explain the observed changes to fluctuations and transport. Using the M3D-C1 code to model the 3D equilibrium, density is shown to be redistributed on flux surfaces in the pedestal when resistive two fluid effects are included, while islands are screened by rotation in this region. The redistribution of density results in density and pressure gradient scale lengths that vary within pedestal flux surfaces between different helically localized flux tubes. This would produce different drive terms for trapped electron mode and kinetic ballooning mode turbulence, the latter of which is expected to be the limiting factor for pedestal pressure gradients in DIII-D.

Author(s): Menard, JE; Allain, JP; Battaglia, DJ; Bedoya, F; Bell, RE; Belova, E; Berkery, JW; Boyer, MD; Crocker, N; Diallo, A; Ebrahimi, F; Ferraro, N; Fredrickson, E; Frerichs, H; Gerhardt, S; Gorelenkov, N; Guttenfelder, W; Heidbrink, W; Kaita, R; Kaye, SM; Kriete, DM; Kubota, S; Leblanc, BP; Liu, D; Lunsford, R; Mueller, D; Myers, CE; Ono, M; Park, JK; Podesta, M; Raman, R; Reinke, M; Ren, Y; Sabbagh, SA; Schmitz, O; Scotti, F; Sechrest, Y; Skinner, CH; Smith, DR; Soukhanovskii, V; Stoltzfus-Dueck, T; Yuh, H; Wang, Z; Waters, I; Ahn, JW; Andre, R; Barchfeld, R; Beiersdorfer, P; Bertelli, N; Bhattacharjee, A; Brennan, D; Buttery, R; Capece, A; Canal, G; Canik, J; Chang, CS; Darrow, D; Delgado-Aparicio, L; Domier, C; Ethier, S; Evans, T; Ferron, J; Finkenthal, M; Fonck, R; Gan, K; Gates, D; Goumiri, I; Gray, T; Hosea, J; Humphreys, D; Jarboe, T; Jardin, S; Jaworski, MA; Koel, B; Kolemen, E; Ku, S; La Haye, RJ; Levinton, F; Luhmann, N; Maingi, R; Maqueda, R; McKee, G; Meier, E; Myra, J; Perkins, R | Abstract: The National Spherical Torus Experiment (NSTX) has undergone a major upgrade, and the NSTX Upgrade (NSTX-U) Project was completed in the summer of 2015. NSTX-U first plasma was subsequently achieved, diagnostic and control systems have been commissioned, the H-mode accessed, magnetic error fields identified and mitigated, and the first physics research campaign carried out. During ten run weeks of operation, NSTX-U surpassed NSTX record pulse-durations and toroidal fields (TF), and high-performance ∼1 MA H-mode plasmas comparable to the best of NSTX have been sustained near and slightly above the n = 1 no-wall stability limit and with H-mode confinement multiplier H98y,2 above 1. Transport and turbulence studies in L-mode plasmas have identified the coexistence of at least two ion-gyro-scale turbulent micro-instabilities near the same radial location but propagating in opposite (i.e. ion and electron diamagnetic) directions. These modes have the characteristics of ion-temperature gradient and micro-tearing modes, respectively, and the role of these modes in contributing to thermal transport is under active investigation. The new second more tangential neutral beam injection was observed to significantly modify the stability of two types of Alfven eigenmodes. Improvements in offline disruption forecasting were made in the areas of identification of rotating MHD modes and other macroscopic instabilities using the disruption event characterization and forecasting code. Lastly, the materials analysis and particle probe was utilized on NSTX-U for the first time and enabled assessments of the correlation between boronized wall conditions and plasma performance. These and other highlights from the first run campaign of NSTX-U are described.

New experimental studies and modelling of the coherent edge harmonic oscillation (EHO), which regulates the conventional Quiescent H-mode (QH-mode) edge, validate the proposed hypothesis of edge rotational shear in destabilizing the low-n kink-peeling mode as the additional drive mechanism for the EHO. The observed minimum edge E × B shear required for the EHO decreases linearly with pedestal collisionality , which is favorable for operating QH-mode in machines with low collisionality and low rotation such as ITER. In addition, the QH-mode regime in DIII-D has recently been found to bifurcate into a new 'wide-pedestal' state at low torque in double-null shaped plasmas, characterized by increased pedestal height, width and thermal energy confinement (Burrell 2016 Phys. Plasmas 23 056103, Chen 2017 Nucl. Fusion 57 022007). This potentially provides an alternate path for achieving high performance ELM-stable operation at low torque, in addition to the low-torque QH-mode sustained with applied 3D fields. Multi-branch low-k and intermediate-k turbulences are observed in the 'wide-pedestal'. New experiments support the hypothesis that the decreased edge E × B shear enables destabilization of broadband turbulence, which relaxes edge pressure gradients, improves peeling-ballooning stability and allows a wider and thus higher pedestal. The ability to accurately predict the critical E × B shear for EHO and maintain high performance QH-mode at low torque is an essential requirement for projecting QH-mode operation to ITER and future machines.