Most auxiliary heating methods provide heating to more than one particle species (electrons, ions, impurities) in a fusion plasma. This can lead to substantial temperature differences between species, depending on conditions such as heating power to the different species and collisionality, with temperature differences between species limited by inter-species thermal equipartition and transport. The analysis of the steady-state electron-ion and impurity-ion power balances presented in this paper are used for consistency-checking experimental ion and electron temperature measurements and for inferring the main ion temperature from measured impurity temperatures. As ion temperature measurements by charge exchange spectroscopy (CXS) based on impurity ions have become more difficult and time-consuming since the installation of the ITER-like wall (ILW) with Be and W PFC's, knowing the maximum sustainable temperature difference between ions and electrons, |T-i - T-e| allows rejecting erroneous measurements. It also obviates the need for an ion temperature measurement, if an electron temperature measurement is available and |T-i - T-e| cannot be larger than the combined errors of the underlying measurements. A power balance analysis is also required for estimating the errors of the ion and electron heat fluxes prior to any species-resolved transport analysis. The ion-impurity temperature differences are usually found to be small due to strong thermal equipartition between ion species. However, they can approach 10% in JET-ILW low density, high power discharges, such the ones under development for a future JET deuterium-tritium campaign (Joffrin et al 2019 Nucl. Fusion). This has a generally small, but not always negligible effect on the calculation of fusion reaction rates, which depend on main ion temperatures. An important outcome of this analysis is that temperature differences between impurity species are always much smaller than between the impurities and hydrogenic species and can usually be neglected. The paper presents two methods for calculating the impurity-to-main ion temperature ratio. Finally, this analysis leads to a method for the reconstruction ion temperature profiles from ion temperature data available at only one or a small number of spatial locations.

This work reports observations of a tokamak plasma that experienced a thermal quench due to a large, transient high-Z influx but avoided a current quench. This is argued to be caused by the presence of lower hybrid range of frequency (LHRF) waves that sustain a non-thermal, current-carrying electron population. In Alcator C-Mod L-mode plasmas at I-p = 450 kA, (n) over bar (e) = 0.5 x 10(20) m(-3), nearly all of the current can be sustained non-inductively by injecting similar or equal to 700 kW of LHRF power at 4.6 GHz and n(parallel to) = 1.9. A sudden influx of a large amount of tungsten, n(z)/n(e) similar or equal to 0.0044, triggers a cooling wave that propagates at 2-3 m s(-1) all the way into the core, dropping on-axis T-e from 3 keV to temperatures less than measurement floor of 50 eV. An off-axis reheat begins after 100 ms, but T-e profiles remain hollow for 300-350 ms after the injection. Throughout this temperature evolution, the plasma density, current and shape remain unchanged to within 10%. Following the expulsion of the tungsten, the plasma returns to its baseline conditions and the plasma ends as planned with a controlled current ramp-down. Energy balance analysis shows the LHRF power continues to be absorbed in the plasma after the thermal quench, as a significant fraction of it is needed to be consistent with radiated power measurements. Examination of current relaxation time, T-R, and fast-electron slowing down time, T-S, indicate the LHRF must contribute to driving current, despite the low temperatures, as the current remains nominally stationary despite T-R < 5 ms and T-S < 50 ms for relativistic electrons. These measurements represent an important existence proof of a possible technique for avoidance of disruptions caused by sudden, unplanned influx of impurities in the form of dust or flakes of high-Z wall material. Implications and suggestions for future experimental and modeling and simulation work are summarized.

The ‘Super H-Mode’ regime is predicted to enable pedestal height and fusion performance substantially higher than standard H-Mode operation. This regime exists due to a bifurcation of the pedestal pressure, as a function of density, that is predicted by the EPED model to occur in strongly shaped plasmas above a critical pedestal density. Experiments on Alcator C-Mod and DIII-D have achieved access to the Super H-Mode (and Near Super H) regime, and obtained very high pedestal pressure, including the highest achieved on a tokamak ( p ped ~ 80 kPa) in C-Mod experiments operating near the ITER magnetic field. DIII-D Super H experiments have demonstrated strong performance, including the highest stored energy in the present configuration of DIII-D ( W ~ 2.2–3.2 MJ), while utilizing only about half of the available heating power ( P heat ~ 7–12 MW). These DIII-D experiments have obtained the highest value of peak fusion gain, Q DT,equiv ~ 0.5, achieved on a medium scale ( R < 2 m) tokamak. Sustained high performance operation ( β N ~ 2.9, H 98 ~ 1.6) has been achieved utilizing n = 3 magnetic perturbations for density and impurity control. Pedestal and global confinement has been maintained in the presence of deuterium and nitrogen gas puffing, which enables a more radiative divertor condition. A pair of simple performance metrics is developed to assess and compare regimes. Super H-Mode access is predicted for ITER and expected, based on both theoretical prediction and observed normalized performance, to allow ITER to achieve its goals ( Q = 10) at I p < 15 MA, and to potentially enable more compact, cost effective pilot plant and reactor designs.

Experiments on the Alcator C-Mod tokamak have utilized reactor-relevant magnetic fields to sustain substantially higher pedestal pressure than in other devices and allow close approach to the ITER H-mode baseline target pedestal pressure of 90 kPa. The EPED model, which couples the physics of transport driven by kinetic ballooning modes and MHD instabilities arising from peeling-ballooning modes, predicts the pressure profile at the onset of edge-localized modes (ELMs), and yields to lowest order a critical-beta(N) like behavior for the pedestal: p proportional to B-t x B-p (proportional to B-t(2) for fixed edge q). C-Mod routinely accesses edge plasma pressure in excess of 30 kPa, often by using a high-density ((n(e)) over bar > 3 x 10(20) m(-3)) approach to high confinement, taking advantage of a regime known as enhanced D-alpha (EDA) H-mode. In the EDA H-mode, plasma transport regulates both the pedestal profiles and the core impurity content, thus holding the pedestal stationary at just below the peeling-ballooning stability boundary. This stationary ELM-suppressed regime has approached the maximum pedestal predicted by EPED at these densities: 60 kPa. This in turn gives rise to volume-averaged core plasma pressure in excess of 0.2 MPa, a world record value for a magnetic fusion device. Another approach to achieving high pressure utilizes a pedestal limited by current-driven modes at low collisionality, in which pressure increases with density and which allows access to a higher EPED solution, termed 'super-H'. C-Mod experiments at reduced density ((n(e)) over bar < 2 x 1020 m-3) and strong plasma shaping (delta > 0.5) accessed this regime, producing pedestals with pressures up to 80 kPa (approximately 90% of the ITER target) and temperatures of nearly 2 keV. In a number of these hot H-modes, we observe strong edge instabilities at low toroidal mode number (n = 1) when pedestal pressure approaches predicted values from EPED, showing that current-driven MHD modes can serve as a limit on the pedestal in a metal-walled tokamak at high pressure and low collisionality.

This work discusses sources of uncertainty in the validation of lower hybrid wave current drive simulations against experiments, by evolving self-consistently the magnetic equilibrium and the heating and current drive profiles, calculated with a combined toroidal ray tracing code and 3D Fokker-Planck solver. The simulations indicate a complex interplay of elements, where uncertainties in the input plasma parameters, in the models and in the transport solver combine and-in some cases-compensate each other. It is concluded that ray-tracing calculations should include a realistic representation of the density and temperature in the region between the confined plasma and the wall, which is especially important in regimes where the LH waves are weakly damped and undergo multiple reflections from the plasma boundary. Uncertainties introduced in the processing of diagnostic data as well as uncertainties introduced by model approximations are assessed. It is shown that, by comparing the evolution of the plasma parameters in self-consistent simulations with available data, inconsistencies can be identified and limitations in the models or in the experimental data assessed.

Recent progress in understanding and mitigating parasitic wave absorption in edge plasmas is presented. Experimental observations collected on Alcator C-Mod suggest multiple physics mechanisms are involved in such losses. Localized measurement of parametric decay instabilities (PDIs) has been performed using RF Langmuir probes. The divertor heat flux due to LH and ionization power loss have been evaluated quantitatively. We observe that the LHCD efficiency can be recovered when the SOL density profile is controlled by operating the tokamak at high current. The experimental progresses motivated a re-examination of the LHCD simulation model based on the ray-tracing/Fokker-Planck code (GENRAY/CQL3D). The effect of introducing a relatively small wave number broadening in the launched power spectrum and using 2D SOL density and temperature profiles was investigated. Comparison with C-Mod experiment indicates that the new model can explain the experimental trend over a wider density range including the density regime where disagreement was seen previously, suggesting that including realistic SOL geometry is a key to improve the simulation accuracy.

I) Introduction and motivation.Understanding the formation and stability of three-dimensional (3D) helical modes in the core of an otherwise, axisymmetric toroidal configuration, is still one of the challenges of current fusion research [1-5]. Small deviations from toroidal axisymmetry are well known to destabilize non-rotating tearing modes (a.k.a. locked modes), which can significantly impact plasma operation. Error-field induced locked-modes have been studied in several tokamak devices and are observed to result in a density pump-out, braking of core toroidal rotation, modification of sawtooth activity and significant reduction in energy and particle confinement. Locked modes frequently lead to disruptions and associated vertical displacements. Locked-mode excitation can be achieved in C-Mod (see Fig. 1 and ref. [6]) by using the control coils placed outside the vacuum vessel; so far, the locked-mode threshold studies have considered only engineering macroscopic parameters resulting in a scaling law of the form [6,8]. The determination of this dependence is useful for extrapolating low-aspect and standard-aspect ratio tokamaks results to ITER. However, the influence of drift-MHD as well as collisional and neoclassical flow-damping effects dependent on local kinetic profiles [8-10] can alter the predicted scaling and have not yet been considered. The experimental validation of new theoretical models sensitive to rotation [8] and viscous [11] effects different than that of ideal-MHD should also be addressed.

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.

The goal of this experiment is to characterize the effect of lower hybrid waves (LH) on the scrape-off-layer (SOL) of Alcator C-Mod plasmas through improved edge measurements. Availability of fast time and high spatial resolution measurements of the SOL provides a new window for characterizing LHRF effects near the density limit. Correlation of edge ionization to changes in SOL profiles will provide important data for calculating SOL power balance and damping behavior of LHCD in the SOL.

The goal of this experiment is to characterize the Greenwald limit and related phenomena as affected by LHRF power. While the Greenwald limit is well described with respect to macroscopic tokamak parameters, the underlying cause of the Greenwald limit has yet to be fully proven. LHRF will be used as an actuator in this MP. LHRF in high density plasma is damped in the edge creating non-monotonic electron density profiles in the scrape-off-layer (SOL) [9]. By changing the ionization front (as seen through Lyα measurements), LHRF provides a way of changing SOL power and particle balances in a way not previously available on Alcator C-Mod. The SOL parameters have been shown to be important for the character of the Greenwald density limit, and will be changed through LHRF to test the Greenwald limit dependencies (outside of Ip, and a).

Recent research on the Alcator C-Mod tokamak has focused on a range of scientific issues with particular emphasis on ITER needs and on detailed comparisons between experimental measurements and predictive models. Research on ICRF (ion cyclotron range of frequencies) heating emphasized the origins and mitigation of metallic impurities while work on lower hybrid current drive experiments have focused on linear and nonlinear wave interactions that limit efficiency at high densities in regimes with low single pass absorption. Experiments in core turbulence and transport focused on quantitative, multi-field comparisons between nonlinear gyro-kinetics simulations and experimental measurements of profiles, fluxes and fluctuations. Experiments into self-generated rotation observed spontaneous flow reversal at a critical density identical to the transition density between linear ohmic confinement and saturated ohmic confinement regimes. H-mode studies have measured pedestal widths consistent with kinetic-ballooning-mode-like instabilities, while the pedestal heights quantitatively match the EPED code predictions. Experiments with I-mode have increased the operating window for this promising edge-localized-mode-free regime. Extrapolation of I-mode to ITER suggests that the fusion gain Q ∼ 10 could be possible in ITER. Investigations into the physics and scaling of the power exhaust channel width in attached enhanced D-alpha H-mode and L-mode plasma showed a direct connection between the midplane pressure-folding length and the outer divertor target footprint. The width was found to scale inversely with IP, while being independent of conducted power, BT or q95 and insensitive to the scrape-off layer connection length—a behaviour that suggests critical-gradient physics sets both pressure and heat-flux profiles.

New observations of the formation and dynamics of long-lived impurity-induced helical "snake" modes in tokamak plasmas have recently been carried out on Alcator C-Mod. The snakes form as an asymmetry in the impurity ion density that undergoes a seamless transition from a small helically displaced density to a large crescent-shaped helical structure inside q<1, with a regularly sawtoothing core. The observations show that the conditions for the formation and persistence of a snake cannot be explained by plasma pressure alone. Instead, many features arise naturally from nonlinear interactions in a 3D MHD model that separately evolves the plasma density and temperature.

Recent progress on lower hybrid current drive (LHCD) experiment and simulation towards steady-state (t >= 3-5 x tau(r), where tau(r) is the current relaxation time) regimes on Alcator C-Mod is presented. Highly non-inductive reversed shear plasmas are obtained with spontaneous generation of internal transport barriers at the density close to what is expected on ITER steady-state scenarios. Progress has been made to better understand and mitigate the unexpected degradation of LHCD efficiency at high densities, which poses an issue both for extending the non-inductive plasmas to advanced tokamak regimes (with a high bootstrap current fraction, f(BS)) on C-Mod and for predicting the performance of LHCD on future devices such as ITER. Several physics mechanisms that potentially contribute anomalous losses of LHCD power have been studied extensively. Numerical modelling of collisional absorption in cold scrape-off layer plasmas has been integrated into a ray-tracing code. The LHEAF full-wave code clarifies that full-wave effects move the power deposition profile closer to the separatrix than a calculation based on the WKB approximation, leading to a lower efficiency. Non-linear wave interactions were studied experimentally by LH wave spectral measurements using Langmuir probes, suggesting parametric decay instabilities to explain the remaining difference between experiments and simulations. An experimental demonstration of recovery of good LHCD efficiency at high densities is also reported. Improving the single pass absorption is proposed as a key to recover LHCD efficiency. A wave physics design of additional launcher (LH3) has been developed in order to demonstrate an improved LHCD performance by realizing high (similar to 80%) single pass absorption, in which the synergistic interaction in the velocity space with the existing launcher is maximized.

X-ray imaging crystal spectrometers with high spectral and spatial resolution are currently being used on magnetically confined fusion devices to infer the time history profiles of ion and electron temperatures as well as plasma flow velocities. The absolute measurement of flow velocities is important for optimizing various discharge scenarios and evaluating the radial electric field in tokamak and stellarator plasmas. Recent studies indicate that the crystal temperature must be kept constant to within a fraction of a degree to avoid changes of the interplanar 2d-spacing by thermal expansion that cause changes in the Bragg angle, which could be misinterpreted as Doppler shifts. For the instrumental parameters of the x-ray crystal spectrometer on Alcator C-Mod, where those thermal effects were investigated, a change of the crystal temperature by 1 degrees C causes a change of the lattice spacing of the order of Delta d = 1 x 10(-5) angstrom introducing a fictitious velocity drift of the order of similar to 3 km s(-1). This effect must be considered for x-ray imaging crystals spectrometers installed on LHD, KSTAR, EAST, J-TEXT, NSTX and, in the future, W7-X and ITER.

Long-lived (1, 1) 'snake' modes were discovered nearly three decades ago, but basic questions regarding their formation, stability, and superb particle confinement-shown by surviving tens to hundreds of sawtooth cycles-have remained unanswered. High-resolution spectroscopic imaging diagnostics permit studies of heavy-impurity-ion snakes with unprecedented temporal and spatial resolution, making it possible to positively identify the SXR signals with specific ion charge states and to infer, for the first time, the perturbed impurity density, Z(eff), and resistivity at the centre of these long-lived helical modes. The results show a new scenario for the formation of heavy-impurity-ion snakes, which can begin as a broad 1/1 kink asymmetry of the central impurity-ion density, that grows and undergoes a seamless transition to a large crescent-shaped helical island-like structure inside q < 1, with a regularly sawtoothing core. This type of formation departs strongly from the nonlinear island model based on a modified Rutherford equation proposed originally to describe the pellet-induced snakes and expanded further to account for the impurity effects (e. g. <(P)over tilde>(rad) and (Z) over tilde (eff)). These new high-resolution observations show details of their evolution and the accompanying sawtooth oscillations that suggest important differences between the density and temperature dynamics, ruling out a purely pressure-driven process. Instead, many features arise naturally from nonlinear interactions in a 3D MHD model that separately evolves the plasma density and temperature.

New experimental observations are reported on the structure and dynamics of short-lived periodic (1, 1) "fishbone"-like oscillations that appear during radio frequency heating and current-drive experiments in tokamak plasmas. For the first time, measurements can directly relate changes in the high energy electrons to the mode onset, saturation, and damping. In the relatively high collisionality of Alcator C-Mod with lower hybrid current drive, the instability appears to be destabilized by the non-resonant suprathermal electron pressure-rather than by wave-particle resonance, rotates toroidally with the plasma and grows independently of the (1, 1) sawtooth crash driven by the thermal plasma pressure. (C) 2015 AIP Publishing LLC.

In the absence of an internal particle source, plasma turbulence will impose an intrinsic relationship between an inwards pinch and an outwards diffusion resulting in a stationary density profile. The Alcator C-mod tokamak utilizes RF heating and current drive so that fueling only occurs in the vicinity of the separatrix. Discharges that transition from L-mode to I-mode are seen to maintain a self-similar stationary density profile as measured by Thomson scattering. For discharges with negative magnetic shear, an observed rise of the safety factor in the vicinity of the magnetic axis appears to be accompanied by a decrease of electron density, qualitatively consistent with the theoretical expectations.