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It remains an open question to explain the dramatic change in intrinsic rotation induced by slight changes in electron density (White et al 2013 Phys. Plasmas 20 056106). One proposed explanation is that momentum transport is sensitive to the second derivatives of the temperature and density profiles (Lee et al 2015 Plasma Phys. Control. Fusion 57 125006), but it is widely considered to be impossible to measure these higher derivatives. In this paper, we show that it is possible to estimate second derivatives of electron density and temperature using a nonparametric regression technique known as Gaussian process regression. This technique avoids over-constraining the fit by not assuming an explicit functional form for the fitted curve. The uncertainties, obtained rigorously using Markov chain Monte Carlo sampling, are small enough that it is reasonable to explore hypotheses which depend on second derivatives. It is found that the differences in the second derivatives of and between the peaked and hollow rotation cases are rather small, suggesting that changes in the second derivatives are not likely to explain the experimental results.

Correlation ECE (CECE) is a diagnostic technique that allows measurement of small amplitude electron temperature, T[subscript e], fluctuations through standard cross-correlation analysis methods. In Alcator C-Mod, a new CECE diagnostic has been installed[Sung RSI 2012], and interesting phenomena have been observed in various plasma conditions. We find that local T[subscript e] fluctuations near the edge (ρ ~ 0:8) decrease across the linearto- saturated ohmic confinement transition, with fluctuations decreasing with increasing plasma density[Sung NF 2013], which occurs simultaneously with rotation reversals[Rice NF 2011]. T[subscript e] fluctuations are also reduced across core rotation reversals with an increase of plasma density in RF heated L-mode plasmas, which implies that the same physics related to the reduction of T[subscript e] fluctuations may be applied to both ohmic and RF heated L-mode plasmas. In I-mode plasmas, we observe the reduction of core T[subscript e] fluctuations, which indicates changes of turbulence occur not only in the pedestal region but also in the core across the L/I transition[White NF 2014]. The present CECE diagnostic system in C-Mod and these experimental results are described in this paper.

The physical mechanisms that cause tokamak plasmas to rotate toroidally without external momentum input are of considerable interest to the plasma physics community. This paper documents a substantial change in both the magnitude of the core-rotation frequency, −1 < ω(r/a = 0) < +10 kHz, and the sign of rotation shear at mid-radius, u' = −R[superscript 2] dω/dr/v[subscript th,i], which varies in the range −0.6 < u' < +0.8 in response to very small changes in the electron density. In 0.8 MA, 5.4 T Alcator C-Mod L-mode plasmas using 1.2 MW of on-axis ion-cyclotron resonance heating, plasmas with line-averaged densities in the range 1.0 < [bar over n][subscript e] < 1.2 X 10[superscript 20] m[superscript -3] exhibit a transition from a peaked intrinsic rotation profile to one that is hollow. Gradient scale lengths of the temperature and density profiles, the drive for plasma turbulence thought to play a role in intrinsic rotation, are indistinguishable within experimental uncertainties between the plasmas, and linear stability analysis using GYRO shows the plasmas to be in the ion temperature gradient-dominated turbulence regime. The impact of changes in the rotation profile in response to minor changes under target plasma conditions is discussed in relation to established analysis techniques and cross-machine rotation scaling studies, with comparisons made with existing ASDEX-Upgrade work on intrinsic rotation shear., United States. Dept. of Energy (Contract DE-FC02-99ER54512), United States. Dept. of Energy. Office of Fusion Energy Sciences (Postdoctoral Research Program)

This paper describes the use of nonlinear gyrokinetic simulations to assess the feasibility of a new correlation electron cyclotron emission (CECE) diagnostic that has been proposed for the Alcator C-Mod tokamak (Marmar et al 2009 Nucl. Fusion 49 104014). This work is based on a series of simulations performed with the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545). The simulations are used to predict ranges of fluctuation level, peak poloidal wavenumber and radial correlation length of electron temperature fluctuations in the core of the plasma. The impact of antenna pattern and poloidal viewing location on measurable turbulence characteristics is addressed using synthetic diagnostics. An upper limit on the CECE sample volume size is determined. The modeling results show that a CECE diagnostic capable of measuring transport-relevant, long-wavelength (k[subscript θ]ρ[subscript s] < 0.5) electron temperature fluctuations is feasible at Alcator C-Mod., United States. Dept. of Energy (DE-FC02-C99ER54512-CMOD)

Linear and nonlinear gyrokinetic simulations are used to probe turbulent impurity transport in intrinsically rotating tokamak plasmas. For this simulation-based study, experimental input parameters are taken from a pair of ICRF heated Alcator C-Mod discharges exhibiting a change in the sign of the normalized toroidal rotation gradient at mid-radius (i.e. a change from hollow to peaked intrinsic rotation profiles). The simulations show that there is no change in the peaking of the calcium impurity between the plasmas with peaked and hollow rotation profiles, suggesting that the impurity transport and the shape of the rotation do not always change together. Furthermore, near mid-radius, r/a = 0.5 (normalized midplane minor radius), the linear and nonlinear gyrokinetic simulations exhibit no evidence of a transition from ion temperature gradient (ITG) to trapped electron mode dominance when the intrinsic rotation profile changes from peaked to hollow. Extensive nonlinear sensitivity analysis is performed, and there is no change in the ITG critical gradient or in the stiffness of ion heat transport with the change in the intrinsic toroidal rotation profile shape, which suggests that the shape of the rotation profile is not dominated by the ITG onset in these cases., United States. Department of Energy (contract DE-FC02-99ER54512-CMOD), United States. Department of Energy (Fusion Energy Postdoctoral Research Program)

The object of this review is to summarize the achievements of research on the Alcator C-Mod tokamak [Hutchinson et al., Phys. Plasmas 1, 1511 (1994) and Marmar, Fusion Sci. Technol. 51, 261 (2007)] and to place that research in the context of the quest for practical fusion energy. C-Mod is a compact, high-field tokamak, whose unique design and operating parameters have produced a wealth of new and important results since it began operation in 1993, contributing data that extends tests of critical physical models into new parameter ranges and into new regimes. Using only high-power radio frequency (RF) waves for heating and current drive with innovative launching structures, C-Mod operates routinely at reactor level power densities and achieves plasma pressures higher than any other toroidal confinement device. C-Mod spearheaded the development of the vertical-target divertor and has always operated with high-Z metal plasma facing components—approaches subsequently adopted for ITER. C-Mod has made ground-breaking discoveries in divertor physics and plasma-material interactions at reactor-like power and particle fluxes and elucidated the critical role of cross-field transport in divertor operation, edge flows and the tokamak density limit. C-Mod developed the I-mode and the Enhanced Dα H-mode regimes, which have high performance without large edge localized modes and with pedestal transport self-regulated by short-wavelength electromagnetic waves. C-Mod has carried out pioneering studies of intrinsic rotation and demonstrated that self-generated flow shear can be strong enough in some cases to significantly modify transport. C-Mod made the first quantitative link between the pedestal temperature and the H-mode's performance, showing that the observed self-similar temperature profiles were consistent with critical-gradient-length theories and followed up with quantitative tests of nonlinear gyrokinetic models. RF research highlights include direct experimental observation of ion cyclotron range of frequency (ICRF) mode-conversion, ICRF flow drive, demonstration of lower-hybrid current drive at ITER-like densities and fields and, using a set of novel diagnostics, extensive validation of advanced RF codes. Disruption studies on C-Mod provided the first observation of non-axisymmetric halo currents and non-axisymmetric radiation in mitigated disruptions. A summary of important achievements and discoveries are included., United States. Dept. of Energy (Cooperative Agreement DE-FC02-99ER54512), United States. Dept. of Energy (Cooperative Agreement DE-FG03-94ER-54241), United States. Dept. of Energy (Cooperative Agreement DE-AC02-78ET- 51013), United States. Dept. of Energy (Cooperative Agreement DE-AC02-09CH11466), United States. Dept. of Energy (Cooperative Agreement DE-FG02-95ER54309), United States. Dept. of Energy (Cooperative Agreement DE-AC02-05CH11231), United States. Dept. of Energy (Cooperative Agreement DE-AC52-07NA27344), United States. Dept. of Energy (Cooperative Agreement DE-FG02- 97ER54392), United States. Dept. of Energy (Cooperative Agreement DE-SC00-02060)

For the first time, nonlinear gyrokinetic simulations spanning both the ion and electron spatio-temporal scales have been performed with realistic electron mass ratio ((m[subscript D] [over m [subscript e])[superscript 1 over 2] = 60.0), realistic geometry, and all experimental inputs, demonstrating the coexistence and synergy of ion (k[subscript θρs] ~O(1.0)) and electron-scale (k[subscript θρe] ~O(1.0)) turbulence in the core of a tokamak plasma. All multi-scale simulations utilized the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] to study the coupling of ion and electron-scale turbulence in the core (r/a = 0.6) of an Alcator C-Mod L-mode discharge shown previously to exhibit an under-prediction of the electron heat flux when using simulations only including ion-scale turbulence. Electron-scale turbulence is found to play a dominant role in setting the electron heat flux level and radially elongated (k[subscript r] ≪ k[subscript θ]) “streamers” are found to coexist with ion-scale eddies in experimental plasma conditions. Inclusion of electron-scale turbulence in these simulations is found to increase both ion and electron heat flux levels by enhancing the transport at the ion-scale while also driving electron heat flux at sub-ρ[subscript i] scales. The combined increases in the low and high-k driven electron heat flux may explain previously observed discrepancies between simulated and experimental electron heat fluxes and indicates a complex interaction of short and long wavelength turbulence., United States. Dept. of Energy. Office of Science (Contract DE-AC02-05CH11231), United States. Dept. of Energy (Contract DE-FC02-99ER54512-CMOD), United States. Dept. of Energy. Fusion Energy Postdoctoral Research Program (Oak Ridge Institute for Science and Education)

A novel “Shoelace” antenna has been used to inductively excite a short-wavelength edge fluctuation in a tokamak boundary layer for the first time. The principal design parameters, k[subscript ⊥] = 1.5 ± 0.1 cm[superscript −1] and 45 < f < 300 kHz, match the Quasi-Coherent Mode (QCM, k[subscript ⊥] ∼ 1.5 cm[superscript −1], f ∼ 50−150 kHz) in Alcator C-Mod, responsible for exhausting impurities in the steady-state, ELM-free Enhanced D[subscript α] H-mode. In H-mode, whether or not there is a QCM, the antenna drives coherent, field-aligned perturbations in density, [˜ over n][subscript e], and field, [˜ over B][subscript θ], which are guided by field lines, propagate in the electron diamagnetic drift direction, and exhibit a weakly damped (γ/ω[subscript 0] ∼ 5%−10%) resonance near the natural QCM frequency. This result is significant, offering the possibility that externally driven modes may be used to enhance particle transport. In L-mode, the antenna drives only a non-resonant [˜ over B][subscript θ] response. The facts that the driven mode has the same wave number and propagation direction as the QCM, and is resonant at the QCM frequency, suggest the antenna may couple to this mode, which we have shown elsewhere to be predominantly drift-mode-like [B. LaBombard et al., Phys. Plasmas 21, 056108 (2014)]., United States. Dept. of Energy (Cooperative Agreement DE-FC02-99ER54512)

We demonstrate that existing theories are insufficient to explain up/down asymmetries of argon x-ray emission in Alcator C-Mod ohmic plasmas. Instead of the poloidal variation, ñ[subscript z]/〈n[subscript z]〉, being of order the inverse aspect ratio, ϵ, and scaling linearly with B[subscript t][superscript _ over n][subscript e]/I[2 over p], it is observed over 0.8 < r/a < 1.0 to be of order unity and exhibits a threshold behaviour between 3.5, United States. Dept. of Energy (Contract DE-FC02-99ER54512), United States. Dept. of Energy (Fusion Research Postdoctoral Research Program)

Transport in ohmically heated plasmas in Alcator C-Mod was studied in both the linear (LOC) and saturated (SOC) ohmic L-mode confinement regimes and the importance of turbulent transport in the region r/a = 0.5–0.8 was established. After an extensive analysis with TGLF and GYRO, it is found that using an effective impurity ion species with Z[subscript i] = 8, and moderately high Z[subscript eff] (2.0–5.6), in the LOC regime electron transport becomes dominant due to TEM turbulence. The key ingredient in the present results is the observation that dilution of the main ion species (deuterium) by impurity species of moderate charge state reduces dominant ITG turbulence, in contrast to the SOC regime with little, if any dilution. The turbulent spectrum measured with the phase contrast imaging (PCI) diagnostic is in qualitative agreement with predictions of a synthetic PCI diagnostic adopted to Global GYRO. The toroidal rotation in the low-density LOC regime is in the co-current direction but as the density is raised in the SOC regime the rotation reverses to the counter current drive direction. The impurity content of the plasma was measured recently and an effective Z[subscript i] of 9 was deduced., United States. Dept. of Energy (Grant DE-FC02-99ER54512-CMOD)

For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E x B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E x B shear in GYRO simulations show that E x B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E x B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness. (C) 2015 AIP Publishing LLC.