The averaged toroidal flow of energetic minority ions during ICRF (ion cyclotron range of frequencies) heating is investigated in the Alcator C-Mod plasma by applying the GNET code, which can solve the drift kinetic equation with complicated orbits of accelerated energetic particles. It is found that a co-directional toroidal flow of the minority ions is generated in the region outside of the resonance location, and that the toroidal velocity reaches more than 40% of the central ion thermal velocity (Vtor ∼ 300 km/s with PICRF ∼ 2 MW). When we shift the resonance location to the outside of |r/a|∼0.5, the toroidal flow immediately inside of the resonance location is reduced to 0 or changes to the opposite direction, and the toroidal velocity shear is enhanced at r/a ∼ 0.5. A radial diffusion equation for toroidal flow is solved by assuming a torque profile for the minority ion mean flow, and good agreements with experimental radial toroidal flow profiles are obtained. This suggests that the ICRF driven minority ion flow is related to the experimentally observed toroidal rotation during ICRF heating in the Alcator C-Mod plasma.

This paper presents an overview of recent highlights from research on Alcator C-Mod. Significant progress has been made across all research areas over the last two years, with particular emphasis on divertor physics and power handling, plasma–material interaction studies, edge localized mode-suppressed pedestal dynamics, core transport and turbulence, and RF heating and current drive utilizing ion cyclotron and lower hybrid tools. Specific results of particular relevance to ITER include: inner wall SOL transport studies that have led, together with results from other experiments, to the change of the detailed shape of the inner wall in ITER; runaway electron studies showing that the critical electric field required for runaway generation is much higher than predicted from collisional theory; core tungsten impurity transport studies reveal that tungsten accumulation is naturally avoided in typical C-Mod conditions.

Results of ICRF heating experiments in Alcator C-Mod during the November 1994 June 1995 campaign are summarized. Efficient heating of high density ( , ; 3 x 1020 m-3 ) plasmas was demonstrated with high power densities (up to 5 MW/m 3 volume averaged, 0.6 MW/m 2 surface averaged). These experiments were carried out with RF powers up to 3.5 MW at 80 MHz, at magnetic fields up to 8 T and plasma currents up to 1.2 MA. For on-axis hydrogen minority heating at 5.3 T, near complete absorption is achieved. Energy confinement in L-mode plasmas was found to be consistent with the ITER89-P scaling. H-mode is routinely observed when the ion VB 1 2 Y Takase et al drift is directed toward the X-point. The H-mode power threshold was found to scale as low as P/S(MW/m2 ) = 0.02 eBT(1 20 m3 T), which is a factor of two lower than the scaling observed on other tokamaks. PEP modes with highly peaked density and ion temperature profiles and highly enhanced fusion reactivity were obtained with Li pellet injection followed by on-axis ICRF heating at both BT = 5.3 T (H minority heating) and 8 T (3He minority heating). In H-3He plasmas at BT = 6.5 T highly localized direct electron heating by the mode converted ion Bernstein wave was observed. Nearly complete absorption by electrons in a small volume resulted in an extremely high electron heating power density of Po , 30 MW/m 3 with FWHM ~0.2 a. PACS number(s): 5250, 5255, 5225F Submitted to Plasma Phys. Control. Fusion Date: 12 March 1996 Alcator C-Mod ICRF heating and enhanced performance modes

New results suggest that changes observed in the intrinsic toroidal rotation influence the internal transport barrier (ITB) formation in the Alcator C-Mod tokamak [E. S. Marmar and Alcator C-Mod group, Fusion Sci. Technol. 51, 261 (2007)]. These arise when the resonance for ion cyclotron range of frequencies (ICRF) minority heating is positioned off-axis at or outside of the plasma half-radius. These ITBs form in a reactor relevant regime, without particle or momentum injection, with Ti ≈ Te, and with monotonic q profiles (qmin < 1). C-Mod H-mode plasmas exhibit strong intrinsic co-current rotation that increases with increasing stored energy without external drive. When the resonance position is moved off-axis, the rotation decreases in the center of the plasma resulting in a radial toroidal rotation profile with a central well which deepens and moves farther off-axis when the ICRF resonance location reaches the plasma half-radius. This profile results in strong E × B shear (>1.5 × 105 rad/s) in the region where the ITB foot is observed. Gyrokinetic analyses indicate that this spontaneous shearing rate is comparable to the linear ion temperature gradient (ITG) growth rate at the ITB location and is sufficient to reduce the turbulent particle and energy transport. New and detailed measurement of the ion temperature demonstrates that the radial profile flattens as the ICRF resonance position moves off axis, decreasing the drive for the ITG the instability as well. These results are the first evidence that intrinsic rotation can affect confinement in ITB plasmas.

New results suggest that changes observed in the intrinsic toroidal rotation influence the internal transport barrier (ITB) formation in the Alcator C-Mod tokamak. The ITBs arise when the resonance for ICRF minority heating is positioned off-axis at or outside of the plasma half-radius. These ITBs form in a reactor relevant regime, without particle or momentum injection, with Ti≈Te, and with monotonic q profiles (qmin < 1). C-Mod H-mode plasmas exhibit strong intrinsic co-current rotation that increases with increasing stored energy without external drive. When the resonance position is moved off-axis, the rotation decreases in the center of the plasma resulting in a radial toroidal rotation profile with a central well, which then deepens and moves farther off-axis when the ICRF resonance location reaches the plasma half-radius. This profile results in strong E×B shear (>1.5x105 Rad/sec) in the region where the ITB foot is observed. Gyrokinetic analyses indicate that this spontaneous shearing rate is comparable to the linear ion temperature gradient (ITG) growth rate at the ITB location and is sufficient to reduce the turbulent particle and energy transport. Detailed measurement of the ion temperature demonstrates that the radial profile flattens as the ICRF resonance position moves off axis, which reduces the drive for ITG instability. These results are the first evidence that intrinsic rotation can affect confinement in ITB plasmas, and suggest that this regime could be achievable on ITER and future reactor experiments. This work was supported by US-DoE DE-FC02-99ER54512, DE-FG03-96ER5437 and DE-AC02-09CH11466

Ohmic energy confinement saturation is found to be closely related to core toroidal rotation reversals in Alcator C-Mod tokamak plasmas. Rotation reversals occur at a critical density, depending on the plasma current and toroidal magnetic field, which coincides with the density separating the linear Ohmic confinement regime from the saturated Ohmic confinement regime. The rotation is directed co-current at low density and abruptly changes direction to counter-current when the energy confinement saturates as the density is increased. Since there is a bifurcation in the direction of the rotation at this critical density, toroidal rotation reversal is a very sensitive indicator in the determination of the regime change. The reversal and confinement saturation results can be unified, since these processes occur in a particular range of the collisionality.

Direction reversals of intrinsic toroidal rotation have been observed in Alcator C-Mod ohmic L-mode plasmas following modest electron density or toroidal magnetic field ramps. The reversal process occurs in the plasma interior, inside of the q = 3/2 surface. For low density plasmas, the rotation is in the co-current direction, and can reverse to the counter-current direction following an increase in the electron density above a certain threshold. Reversals from the co- to counter-current direction are correlated with a sharp decrease in density fluctuations with k R ⩾ 2 cm−1 and with frequencies above 70 kHz. The density at which the rotation reverses increases linearly with plasma current, and decreases with increasing magnetic field. There is a strong correlation between the reversal density and the density at which the global ohmic L-mode energy confinement changes from the linear to the saturated regime.

Internal transport barriers (ITBs) are seen under a number of conditions in Alcator C-Mod plasmas. Most typically, radio frequency power in the ion cyclotron range of frequencies (ICRFs) is injected with the second harmonic of the resonant frequency for minority hydrogen ions positioned off-axis at r/a > 0.5 to initiate the ITBs. They can also arise spontaneously in ohmic H-mode plasmas. These ITBs typically persist tens of energy confinement times until the plasma terminates in radiative collapse or a disruption occurs. All C-Mod core barriers exhibit strongly peaked density and pressure profiles, static or peaking temperature profiles, peaking impurity density profiles and thermal transport coefficients that approach neoclassical values in the core. The strongly co-current intrinsic central plasma rotation that is observed following the H-mode transition has a profile that is peaked in the centre of the plasma and decreases towards the edge if the ICRF power deposition is in the plasma centre. When the ICRF resonance is placed off-axis, the rotation develops a well in the core region. The central rotation continues to decrease as long as the central density peaks when an ITB develops. This rotation profile is flat in the centre (0 < r/a < 0.4) but rises steeply in the region where the foot in the ITB density profile is observed (0.5 < r/a < 0.7). A correspondingly strong E × B shear is seen at the location of the ITB foot that is sufficiently large to stabilize ion temperature gradient instabilities that dominate transport in C-Mod high density plasmas.

Internal particle and thermal energy transport barriers are produced in Alcator C-Mod with off-axis ICRF heating, with core densities exceeding 10 21 m −3 , without core fueling, and with little change in the temperature profile. Applying on-axis ICRF heating controls the core density gradient and rate of rise. The present study employs linear and nonlinear gyrokinetic simulations of trapped electron mode (TEM) turbulence to explore mechanisms for ITB formation and control in Alcator C-Mod ITB experiments. Anomalous pinches are found to be negligible in our simulations; further, the collisional Ware pinch is sufficient to account for the slow density rise, lasting many energy confinement times. The simulations have revealed new nonlinear physics of TEM turbulence. The critical density gradient for onset of TEM turbulent transport is nonlinearly up-shifted by zonal flows. As the density profile peaks, during ITB formation, this nonlinear critical gradient is eventually exceeded, and the turbulent particle diffusivity from GS2 gyrokinetic simulations matches the particle diffusivity from transport analysis, within experimental errors. A stable equilibrium is then established when the TEM turbulent diffusion balances the Ware pinch in the ITB. This equilibrium is sensitive to temperature through gyroBohm scaling of the TEM turbulent transport, and the collisionality dependence of the neoclassical pinch, providing for control of the density rate of rise with on-axis RF heating. With no core particle fueling, and ∼1 mm between density spatial channels, the C-Mod experiments provide a nearly ideal test bed for particle transport studies. The pure TEM is the only unstable drift mode in the ITB, producing particle transport driven by the density gradient.

Following the application of lower hybrid current drive (LHCD) power, the core toroidal rotation in Alcator C-Mod L- and H-mode plasmas is found to increment in the counter-current direction, in conjunction with a decrease in the plasma internal inductance, l i . Along with the drops in l i and the core rotation velocity, there is peaking of the electron and impurity density profiles, as well as of the ion and electron temperature profiles. The mechanism generating the counter-current rotation is unknown, but it is consistent in sign with an inward shift of energetic electron orbits, giving rise to a negative core radial electric field. The peaking in the density, toroidal rotation (in the counter-current direction) and temperature profiles occurs over a time scale similar to the current relaxation time but slow compared with the energy and momentum confinement times. Most of these discharges exhibit sawtooth oscillations throughout, with the inversion radius shifting inward during the LHCD and profile evolution. The magnitudes of the changes in the internal inductance and the central rotation velocity are strongly correlated and found to increase with increasing LHCD power and decreasing electron density. The maximum effect is obtained with a waveguide phasing of 60° (a launched parallel index of refraction n ‖ ∼ 1.5), with a significantly smaller magnitude at 120° ( n ‖ ∼ 3.1), and with no effect for negative or heating (180°) phasing. Regardless of the plasma parameters and launched n ‖ of the waves, there is a strong correlation between the rotation velocity and l i changes, possibly providing a clue for the underlying mechanism.

Abstract Turbulent particle transport is investigated with a quasilinear theory that is motivated by the boron impurity transport experiments in the Alcator C-Mod. Eigenvalue problems for sets of reduced fluid equations for multi-component plasmas are solved for the self-consistent fluctuating field vectors composed of the electric potential φ, the main ion density δni, the impurity density δnz and the ion temperature fluctuation δTi. For Alcator C-Mod parameters, we investigate two drift wave models: (1) the density-gradient-driven impurity drift wave and (2) the ion-temperature-gradient-driven ion temperature gradient (ITG) mode. Analytic and numerical results for particle transport coefficients are derived and compared with the transport data and the neoclassical theory. We explore the ability of the model to explain impurity density profiles in three confinement regimes: H-mode, I-mode and internal transport barrier (ITB) regime in C-Mod. Related experiments reported on the Large Helical Device are briefly discussed.