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 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 highpower 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 componentsapproaches 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 a) Paper AR1 1, Bull. Am. Phys. Soc. 58, 21 (2013). b) Invited speaker.

Abstract. Experimental observations of lower hybrid current drive (LHCD) at high density on the Alcator C-Mod tokamak are presented in this paper. Bremsstrahlung emission from relativistic fast electrons in the core plasma drops suddenly above line averaged densities of 10 20 m −3 (ω/ω LH ∼ 3) in single null discharges with large (> 10 mm) plasma-inner wall gaps, well below the density limit previously observed on limited tokamaks (ω/ω LH ∼ 2). Modeling and experimental evidence suggest that the absence of LHCD driven fast electrons at high density may be due to parasitic collisional absorption in the scrape off layer. Experiments show that the population of fast electrons produced by LHCD at high density (n e > 10 20 m −3 ) can be increased significantly by operating with a plasma-inner wall gap of less than ∼ 5 mm with the strongest non-thermal emission in inner-wall limited plasmas. A change in plasma topology from single to double null produces a modest increase in non-thermal emission at high density. Increasing the electron temperature in the periphery of the plasma (0.8 > r/a > 1.0) also results in a modest increase in non-thermal electron emission above the density limit. Ray tracing/Fokker-Planck simulations of these discharges predict the observed sensitivity to plasma position when the effects of collisional absorption in the SOL are included in the model.

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Assessing the performance of lower hybrid current drive (LHCD) at high density is critical for developing non-inductive current drive systems on future steady-state experiments. Excellent LHCD efficiency has been observed during fully non-inductive operation (η = 2.0 − 2.5 × 10 19 AW −1 m −2 atn e = 0.5 × 10 20 m −3 ) on Alcator C-Mod [I. H. Hutchinson, et al, Physics of Plasmas, 1, 1511] under conditions (n e , magnetic field and topology, LHCD frequency) relevant to ITER [S. Shiraiwa, et al, Nuclear Fusion, 51, 103024 (2011)]. To extend these results to advanced tokamak regimes with higher bootstrap current fractions on C-Mod, it is necessary to increasen e to 1.0 − 1.5 × 10 20 m −3 . However, the number of current-carrying, non-thermal electrons generated by LHCD drops sharply in diverted configurations at densities that are well below the density limit previously observed on limited tokamaks. In these cases, changes in scrape off layer (SOL) ionization and density profiles are observed during LHCD, indicating that significant power is transferred from the LH waves to the SOL. Fokker-Planck simulations of these discharges utilizing ray tracing and full wave propagation codes indicate that LH waves in the high density, multi-pass absorption regime linger in the plasma edge and SOL region, where absorption near or outside the LCFS results in the loss of current drive efficiency. Modeling predicts that non-thermal emission increases with stronger single-pass absorption. Experimental data show that increasing T e in high density LH discharges results in higher non-thermal electron emission, as predicted by the models.

Ion cyclotron parametric decay instability (PDI) of lower hybrid (LH) waves is surveyed using edge Langmuir probes on the Alcator C-Mod tokamak. The measurement is carried out simultaneously at the high-field side (HFS) and low-field side (LFS) mid-plane of the tokamak, as well as in the outer divertor region. Different LH spectra are observed depending on the location of the probes and magnetic configuration in L-mode plasmas, with − → B × B drift direction downward. In lower single null (LSN) plasmas, strong ion cyclotron PDI occurring at the HFS is observed for the first time. This instability is characterized by a frequency separation in sidebands corresponding to the ion cyclotron frequency (ω ci ) near the HFS scrape-off layer and develops with threshold-like behavior as density increases. In inner wall limited (IWL) plasmas, this HFS instability shows a higher density threshold compared with that in LSN plasmas. The pump width becomes broadened even in the absence of the sidebands. In upper single null plasmas with similar plasma parameters, ion cyclotron PDI sidebands have a frequency separation corresponding to ω ci near the LFS and are weaker than those observed in the LSN and IWL plasmas. Correlation between the onset of ion cyclotron PDI and the observed loss of lower hybrid current drive efficiency (Wallace et al 2012 Phys. Plasmas 19 062505) is discussed.

We describe fully self-consistent time-dependent simulations of radio frequency (RF) generated ion distributions in the ion cyclotron range of frequencies and RF-generated electron distributions in the lower hybrid range of frequencies using combined Fokker-Planck and full wave electromagnetic field solvers. In each regime, the non-thermal particle distributions have been used in synthetic diagnostic codes to compare with diagnostic measurements from experiment, thus providing validation of the simulation capability. The computational intensive simulations require multiple full wave code runs that iterate with a Fokker-Planck code. We will discuss advanced algorithms that have been implemented to accelerate both the massively parallel full wave simulations as well as the iteration with the distribution code. A vector extrapolation method (Sidi A 2008 Comput. Math. Appl. 56) that permits Jacobian-free acceleration of the traditional fixed point iteration technique is used to reduce the number of iterations needed between the distribution and wave codes to converge to self-consistency. The computational burden of the parallel full wave codes has been reduced by using a more efficient two level parallel decomposition that improves the strong scaling of the codes and reduces the communication overhead.

Application of lower hybrid range of frequencies (LHRF) waves can induce both co-and counter-current directed changes in toroidal rotation in Alcator C-Mod plasmas, depending on the target plasma current, electron density, confinement regime and magnetic shear. For ohmic L-mode discharges with good core LH wave absorption, and significant current drive at a fixed LH power near 0.8 MW, the interior (r/a < 0.5) rotation increments (on a time scale of order the current relaxation time) in the counter-current direction if n e (10 20 m −3) > q 95 /11.5, and in the co-current direction if n e (10 20 m −3) < q 95 /11.5. All discharges with co-current rotation changes have q 0 > 1, indicating a good correlation with driven current fraction, unifying the results observed on various tokamaks. For high density (n e 1.2 × 10 20 m −3) L-mode target discharges, where core LH wave absorption is low, the rotation change is in the co-current direction, but evolves on a shorter momentum transport time scale, and is seen across the entire spatial profile. For H-mode target plasmas, both co-and counter-current direction increments have been observed with LHRF. The H-mode co-rotation is correlated with the pedestal temperature gradient, which itself is enhanced by the LH waves absorbed in the plasma periphery. The H-mode counter-rotation increment, a flattening of the peaked velocity profile in the core, is consistent with a reduction in the momentum pinch correlated with a steepening of the core density profile. Most of these rotation changes must be due to indirect transport effects of LH waves on various parameters, which modify the momentum flux.

Abstract. Parametric Decay Instabilities (PDI) appear to be an ubiquitous feature of Lower Hybrid Current Drive (LHCD) experiments at high density. In density ramp experiments in Alcator C-Mod and other machines the onset of PDI activity has been well correlated with a decrease in current drive efficiency and production of fast electron Bremsstrahlung. However whether PDI is the primary cause of the "density limit", and if so by exactly what mechanism (beyond the obvious one of pump depletion) has not been clearly established. In order to further understand the connection, the frequency spectrum of PDI activity occurring during Alcator C-Mod LHCD experiments has been explored in detail by means of a number of RF probes distributed around the periphery of the C-Mod tokamak including a probe imbedded in the inner wall. The results show that i) the excited spectra consists mainly of a few discrete ion cyclotron quasi-modes, which have higher growth than the ion sound branch; ii) PDI activity can begin either at the inner or outer wall, depending on magnetic configuration; iii) the frequencies of the IC quasi-modes correspond to the magnetic field strength close to the LFS or HFS separatrix; and iv) although PDI activity may initiate near the inner separatrix, the loss in fast electron Bremsstrahlung is best correlated with the appearance of IC quasimodes characteristic of the magnetic field strength near the LFS separatrix. These data, supported by growth rate calculations, point to the importance of the LFS SOL density in determining PDI onset and degradation in current drive efficiency. By minimizing the SOL density it is possible to extend the core density regime over which PDI can be avoided, thus potentially maximizing the effectiveness of LHCD at high density. Increased current drive efficiency at high density has been achieved in FTU and EAST through lithium coating and special fueling methods, and in recent C-Mod experiments by operating at higher plasma current. Another approach would be to locate the launcher in the inner wall with double null operation. This would reduce the SOL density by an order of magnitude or more and greatly mitigate the effects of PDI as well as other parasitic losses.