Non-axisymmetric control coils and the so-called snowflake divertor configuration are two potential solutions proposed to solve two separate outstanding issues on the path towards self-sustained burning plasma operations, namely the transient energy bursts caused by edge localized modes and the steady state heat exhaust problem. In a reactor, these two proposed solutions would have to operate simultaneously and it is, therefore, important to investigate their compatibility and to identify possible conflicts that could prevent them from operating simultaneously. In this work, single- and two-fluid resistive magnetohydrodynamic calculations are used to investigate the effect of externally applied magnetic perturbations on the snowflake divertor configuration. The calculations are based on simulated NSTX-U plasmas and the results show that additional and longer magnetic lobes are created in the null-point region of the snowflake configuration, compared to those in the conventional single-null. The intersection of these longer and additional lobes with the divertor plates are expected to cause more striations in the particle and heat flux target profiles. In addition, the results indicate that the size of the magnetic lobes, in both single-null and snowflake configurations, are more sensitive to resonant magnetic perturbations than to non-resonant magnetic perturbations. The results also suggest that lower values of current in non-axisymmetric control coils would be required to suppress edge localized modes in plasmas with the snowflake configuration.
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, H-Mode accessed, magnetic error fields identified and mitigated, and the first physics research campaign carried out. During 10 run weeks of operation, NSTX-U surpassed NSTX-record pulse-durations and toroidal fields, and high-performance ~1MA 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 H98y2 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 (DECAF) code. Lastly, the Materials Analysis and Particle Probe (MAPP) 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.
Skinner, C.H.; Bedoya, F.; Scotti, F.; Allain, J.P.; Blanchard, W.; Cai, D.; Jaworski, M.; Koel, B.E.
Boronization has been effective in reducing plasma impurities and enabling access to higher density, higher confinement plasmas in many magnetic fusion devices. The National Spherical Torus eXperiment, NSTX, has recently undergone a major upgrade to NSTX-U in order to develop the physics basis for a ST-based Fusion Nuclear Science Facility (FNSF) with capability for double the toroidal field, plasma current, and NBI heating power and increased pulse duration from 1–1.5 s to 5–8 s. A new deuterated tri-methyl boron conditioning system was implemented together with a novel surface analysis diagnostic. We report on the spatial distribution of the boron deposition versus discharge pressure, gas injection and electrode location. The oxygen concentration of the plasma facing surface was measured by in-vacuo XPS and increased both with plasma exposure and with exposure to trace residual gases. This increase correlated with the rise of oxygen emission from the plasma.
This paper examines a method for real-time control of non-inductively sustained scenarios in NSTX-U by using TRANSP,
a time-dependent integrated modeling code for prediction and interpretive analysis of tokamak experimental data, as a
simulator. The actuators considered for control in this work are the six neutral beam sources and the plasma boundary
shape. To understand the response of the plasma current, stored energy, and central safety factor to these actuators
and to enable systematic design of control algorithms, simulations were run in which the actuators were modulated and
a linearized dynamic response model was generated. A multi-variable model-based control scheme that accounts for the
coupling and slow dynamics of the system while mitigating the effect of actuator limitations was designed and
simulated. Simulations show that modest changes in the outer gap and heating power can improve the response time of
the system, reject perturbations, and track target values of the controlled values.
Yoo, Jongsoo; Na, Byungkeun; Jara-Almonte, Jonathan; Yamada, Maasaki; Ji, Hantao; Roytershteyn, V.; Argall, M. R.; Fox, W.; Chen, Li-Jen
Electron heating and the energy inventory during asymmetric reconnection are studied in the laboratory plasma with a density ratio of about 8 across the current sheet. Features of asymmetric reconnection such as the large density gradients near the low-density-side separatrices, asymmetric in-plane electric field, and bipolar out-of-plane magnetic field are observed. Unlike the symmetric case, electrons are also heated near the low-density-side separatrices. The measured parallel electric field may explain the observed electron heating. Although large fluctuations driven by lower-hybrid drift instabilities are also observed near the low-density-side separatrices, laboratory measurements and numerical simulations reported here suggest that they do not play a major role in electron energization. The average electron temperature increase in the exhaust region is proportional to the incoming magnetic energy per an electron/ion pair but exceeds scalings of the previous space observations. This discrepancy is explained by differences in the boundary condition and system size. The profile of electron energy gain from the electric field shows that there is additional electron energy gain associated with the electron diamagnetic current besides a large energy gain near the X-line. This additional energy gain increases electron enthalpy, not the electron temperature. Finally, a quantitative analysis of the energy inventory during asymmetric reconnection is conducted. Unlike the symmetric case where the ion energy gain is about twice more than the electron energy gain, electrons and ions obtain a similar amount of energy during asymmetric reconnection.
Linear stability analysis of the national spherical torus experiment (NSTX) Li-conditioned
ELM-free H-mode equilibria is carried out in the context of the extended
magneto-hydrodynamic (MHD) model in NIMROD. The purpose is to investigate the physical
cause behind edge localized mode (ELM) suppression in experiment after the Li-coating of
the divertor and the first wall of the NSTX tokamak. Besides ideal MHD modeling, including
finite-Larmor radius effect and two-fluid Hall and electron diamagnetic drift contributions,
a non-ideal resistivity model is employed, taking into account the increase of Z eff after
Li-conditioning in ELM-free H-mode. Unlike an earlier conclusion from an eigenvalue code
analysis of these equilibria, NIMROD results find that after reduced recycling from divertor
plates, profile modification is necessary but insufficient to explain the mechanism behind
complete ELMs suppression in ideal two-fluid MHD. After considering the higher plasma
resistivity due to higher Z eff , the complete stabilization could be explained. A thorough
analysis of both pre-lithium ELMy and with-lithium ELM-free cases using ideal and
non-ideal MHD models is presented, after accurately including a vacuum-like cold halo
region in NIMROD to investigate ELMs.
Stotler, D.P.; Battaglia, D.J.; Hager, R.; Kim, K.; Koskela, T.; Park, G.; Reinke, M.L.
Modifications of the drift-kinetic transport code XGC0 to include the
transport, ionization, and recombination of individual charge states,
as well as the associated radiation, are described. The code is first
applied to a simulation of an NSTX H-mode discharge with carbon
impurity to demonstrate the approach to coronal equilibrium. The
effects of neoclassical phenomena on the radiated power profile are
examined sequentially through the activation of individual physics
modules in the code. Orbit squeezing and the neoclassical inward
pinch result in increased radiation for temperatures above a few
hundred eV and changes to the ratios of charge state emissions at a
given electron temperature. Analogous simulations with a neon
impurity yield qualitatively similar results.
In this paper we present data from experiments on NSTX-U where it is shown for the first time that small amounts of high pitch-angle beam ions can strongly suppress the counter-propagating Global Alfvén Eigenmodes (GAE). GAE have been implicated in the redistribution of fast ions and modification of the electron power balance in previous experiments on NSTX. The ability to predict the stability of Alfvén modes, and developing methods to control them, is important for fusion reactor like the International Tokamak Experimental Reactor (ITER) which are heated by a large population of non-thermal, super-Alfvénic ions consisting of fusion generated alphas and beam ions injected for current profile control. We present a qualitative interpretation of these observations using an analytic model of the Doppler-shifted ion-cyclotron resonance drive responsible for GAE instability which has an important dependence on k⊥ρL. A quantitative analysis of this data with the HYM stability code predicts both the frequencies and instability of the GAE prior to, and suppression of the GAE after the injection of high pitch-angle beam ions.
Bejjanki, Vikranth R.; da Silveira, Rava Azeredo; Cohen, Jonathan D.; Turk-Browne, Nicholas B.
Multivariate decoding methods, such as multivoxel pattern analysis (MVPA), are highly effective at extracting information from brain imaging data. Yet, the precise nature of the information that MVPA draws upon remains controversial. Most current theories emphasize the enhanced sensitivity imparted by aggregating across voxels that have mixed and weak selectivity. However, beyond the selectivity of individual voxels, neural variability is correlated across voxels, and such noise correlations may contribute importantly to accurate decoding. Indeed, a recent computational theory proposed that noise correlations enhance multivariate decoding from heterogeneous neural populations. Here we extend this theory from the scale of neurons to functional magnetic resonance imaging (fMRI) and show that noise correlations between heterogeneous populations of voxels (i.e., voxels selective for different stimulus variables) contribute to the success of MVPA. Specifically, decoding performance is enhanced when voxels with high vs. low noise correlations (measured during rest or in the background of the task) are selected during classifier training. Conversely, voxels that are strongly selective for one class in a GLM or that receive high classification weights in MVPA tend to exhibit high noise correlations with voxels selective for the other class being discriminated against. Furthermore, we use simulations to show that this is a general property of fMRI data and that selectivity and noise correlations can have distinguishable influences on decoding. Taken together, our findings demonstrate that if there is signal in the data, the resulting above-chance classification accuracy is modulated by the magnitude of noise correlations.
Kinetic modification of ideal stability theory from stabilizing resonances of mode-particle interaction has had success in explaining resistive wall mode (RWM) stability limits in tokamaks. With the goal of real-time stability forecasting, a reduced kinetic stability model has been implemented in the new Disruption Event Characterization and Forecasting (DECAF) code, which has been written to analyze disruptions in tokamaks. The reduced model incorporates parameterized models for ideal limits on beta, a ratio of plasma pressure to magnetic pressure, which are shown to be in good agreement with DCON code calculations. Increased beta between these ideal limits causes a shift in the unstable region of delta W_K space, where delta W_K is the change in potential energy due to kinetic effects that is solved for by the reduced model, such that it is possible for plasmas to be unstable at intermediate beta but stable at higher beta. Gaussian functions for delta W_K are defined as functions of E cross B frequency and collisionality, with parameters reflecting the experience of the National Spherical Torus Experiment (NSTX). The reduced model was tested on a database of discharges from NSTX and experimentally stable and unstable discharges were separated noticeably on a stability map in E cross B frequency, collisionality space. The reduced model only failed to predict an unstable RWM in 15.6% of cases with an experimentally unstable RWM and performed well on predicting stability for experimentally stable discharges as well.
Radio-frequency (RF) rectification is an important sheath phenomenon for wave heating of plasma in fusion devices and is proposed to be the mechanism responsible for converting highharmonic fast-wave (HHFW) power in the National Spherical Torus eXperiment (NSTX) into a heat ux to the divertor. RF rectification has two aspects: current rectification and voltage recti- fication, and, while the latter is emphasized in many application, we demonstrate the importance of current rectification in analysis of the NSTX divertor during HHFW heating. When rectified currents are accounted for in first-principle models for the heat ux to the tiles, we predict a sizeable enhancement for the heat ux in the presence of an RF field: for one case studied, the predicted heat ux increases from 0:103 MW=m2 to 0:209 MW=m2. We also demonstrate how this rectification scales with injected HHFW power by tracking probe characteristics during a HHFW power ramp; the rectified current may be clamped at a certain level. This work is important for minimizing SOL losses of HHFW power in NSTX-U but may also have implications for near-field studies of ICRF antennae: ignoring rectified current may lead to underestimated heat uxes and overestimated rectified voltages.
Reflectometry measurements of compressional (CAE) and global (GAE) Alfvén eigenmodes are analyzed to obtain the amplitude and spatial structure of the density perturbations associated with the modes. A novel analysis technique developed for this purpose is presented. The analysis also naturally yields the amplitude and spatial structure of the density contour radial displacement, which is found to be 2–4 times larger than the value estimated directly from the reflectometer measurements using the much simpler ‘mirror approximation’. The modes were driven by beam ions in a high power (6 MW) neutral beam heated H-mode discharge (#141398) in the National Spherical Torus Experiment. The results of the analysis are used to assess the contribution of the modes to core energy transport and ion heating. The total displacement amplitude of the modes, which is shown to be larger than previously estimated (Crocker et al 2013 Nucl. Fusion 53 43017), is compared to the predicted threshold (Gorelenkov et al 2010 Nucl. Fusion 50 84012) for the anomalously high heat diffusion inferred from transport modeling in similar NSTX discharges. The results of the analysis also have strong implications for the energy transport via coupling of CAEs to kinetic Alfvén waves seen in simulations with the Hybrid MHD code (Belova et al 2015 Phys. Rev. Lett. 115 15001). Finally, the amplitudes of the observed CAEs fall well below the threshold for causing significant ion heating by stochastic velocity space diffusion (Gates et al 2001 Phys. Rev. Lett. 87 205003).
Fully self-consistent hybrid MHD/particle simulations reveal strong energetic particle modifications to sub-cyclotron global Alfven eigenmodes (GAE) in low-aspect ratio, NSTX-like conditions. Key parameters defining the fast ion distribution function -- the normalized injection velocity v_0/v_A and central pitch -- are varied in order to study their influence on the characteristics of the excited modes. It is found that the frequency of the most unstable mode changes significantly and continuously with beam parameters, in accordance with the Doppler-shifted cyclotron resonances which drive the modes, and depending most substantially on v_0/v_A. This unexpected result is present for both counter-propagating GAEs, which are routinely excited in NSTX, and high frequency co-GAEs, which have not been previously studied. Large changes in frequency without clear corresponding changes in mode structure could indicate the existence of a new energetic particle mode, referred to here as an energetic-particle-modified GAE (EP-GAE). Additional simulations conducted for a fixed MHD equilibrium demonstrate that the GAE frequency shift cannot be explained by the equilibrium changes due to energetic particle effects.
Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfven eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n=4-9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfven wave (KAW) that occurs on the high-field side at the Alfven resonance location. High-frequency Alfven eigenmodes are frequently observed in beam-heated NSTX plasmas, and have been linked to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam-driven CAEs dissipate their energy at the resonance location,
therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.
Leading resistive wall mode (RWM) stability codes MARS-K [Y. Liu, et al., Phys. Plasmas 15, 112503 (2008)] and MISK [B. Hu, et al., Phys. Plasmas 12, 057301 (2005)] have been previously benchmarked. The benchmarking has now been extended to include additional physics, and used to project the stability of ITER in a realistic operating space. Due to ITER's relatively low plasma rotation and collisionality, collisions and non-resonance rotational effects were both found to have little impact on stability, and these non-resonance rotational effects also will not self-consistently affect the ITER RWM eigenfunction. Resonances between thermal ions and electrons and the expected level of ITER toroidal rotation were found to be important to stability, as were alpha particles, which are not in rotational resonance. MISK calculations show that without alpha particles, ITER is projected to be unstable to the RWM, but the expected level of alphas is calculated to provide a sufficient level of stability.
Recent advances in experimental techniques have allowed the simultaneous recordings of
populations of hundreds of neurons, fostering a debate about the nature of the collective
structure of population neural activity. Much of this debate has focused on the
empirical findings of a phase transition in the parameter space of maximum entropy
models describing the measured neural probability distributions, interpreting this phase
transition to indicate a critical tuning of the neural code. Here, we instead focus on the
possibility that this is a first-order phase transition which provides evidence that the
real neural population is in a `structured', collective state. We show that this collective
state is robust to changes in stimulus ensemble and adaptive state. We find that the
pattern of pairwise correlations between neurons has a strength that is well within the
strongly correlated regime and does not require fine tuning, suggesting that this state is
generic for populations of 100+ neurons. We find a clear correspondence between the
emergence of a phase transition, and the emergence of attractor-like structure in the
inferred energy landscape. A collective state in the neural population, in which neural
activity patterns naturally form clusters, provides a consistent interpretation for our
Bertelli, N; Valeo, E.J.; Green, D.L.; Gorelenkova, M.; Phillips, C.K.; Podesta, M.; Lee, J.P.; Wright, J.C.; Jaeger, E.
At the power levels required for significant heating and current drive
in magnetically-confined toroidal plasma, modification of the particle distribution
function from a Maxwellian shape is likely [T. H. Stix, Nucl. Fusion, 15 737
(1975)], with consequent changes in wave propagation and in the location and
amount of absorption. In order to study these effects computationally, both the
finite-Larmor-radius and the high-harmonic fast wave (HHFW), versions of the
full-wave, hot-plasma toroidal simulation code TORIC [M. Brambilla, Plasma Phys.
Control. Fusion 41, 1 (1999) and M. Brambilla, Plasma Phys. Control. Fusion
44, 2423 (2002)], have been extended to allow the prescription of arbitrary velocity
distributions of the form f(v||, v_perp, psi , theta). For hydrogen (H) minority heating of a
deuterium (D) plasma with anisotropic Maxwellian H distributions, the fractional
H absorption varies significantly with changes in parallel temperature but is
essentially independent of perpendicular temperature. On the other hand, for
HHFW regime with anisotropic Maxwellian fast ion distribution, the fractional
beam ion absorption varies mainly with changes in the perpendicular temperature.
The evaluation of the wave-field and power absorption, through the full wave
solver, with the ion distribution function provided by either aMonte-Carlo particle
and Fokker-Planck codes is also examined for Alcator C-Mod and NSTX plasmas.
Non-Maxwellian effects generally tends to increase the absorption with respect to
the equivalent Maxwellian distribution.
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 , 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.
Lunsford, R.; Bortolon, A.; Roquemore, A.L.; Mansfield, D.K.; Jaworski, M.A.; Kaita, R.; Maingi, R.; Nagy, A.
By employing a neutral gas shielding (NGS) model to characterize impurity granule
injection the pedestal atomic deposition for three different species of granule:
lithium, boron, and carbon are determined. Utilizing the duration of ablation
events recorded on experiments performed at DIII-D to calibrate the NGS model we
are able to quantify the ablation rate and mass deposition location with respect
to the plasma density profile. The species specific granule shielding constant
is then used to model granule ablation within NSTX-U discharges. Simulations of
300, 500 and 700 micron diameter granules injected at 50 m/sec are presented for
NSTX-U L-mode type plasmas as well as H-mode discharges with low natural ELM
frequencies. Additionally, ablation calculations of 500 micron granules of each
species are presented at velocities ranging from 50 � 150 m/sec. In H-mode type
discharges these simulations show that the majority of the injected granule is
ablated within or just past the steep gradient region of the discharge. At this
radial position, the perturbation to the background plasma generated by the ablating
granule can lead to conditions advantageous for the rapid triggering of an ELM crash