Session GI1: H-Mode Pedestal

H-mode pedestal and threshold studies over an expanded operating space on Alcator C-Mod

Understanding of the transition to, and pedestal structure in, the H-mode regime is both critically important for extrapolation to burning plasmas, and incomplete. H-mode studies on Alcator C-Mod exploit state-of-the-art high resolution edge diagnostics. Past studies have focused primarily on operating regimes with B$_{T}\sim $5.4 T, using D(H) heating, and with ion $B\times \nabla B$drift towards the closed divertor, favorable for H-mode. These show pedestal widths to be very narrow, typically 3-5 mm, and fairly constant, with gradients scaling primarily with I$_{p}$. The quiescent Enhanced D-Alpha H-mode regime is most typical. Experiments in recent campaigns, using varied ICRF frequencies and heating scenarios, have greatly expanded the parameter space, with B$_{T}$ varied from 2.6-8 T. At 8 T, L-H thresholds in edge T as well as power are much increased. Pedestals are accordingly also hot, with T$_{ped}$ up to 0.8 keV, while widths remain narrow. Likely as a result of the decreased collisionality, these H-modes are typically ELM-free. Similarly, when I and B are reversed, producing drifts away from the divertor, threshold powers, temperatures and gradients are again much higher, particularly at low n. Grad T gradually increases to H-mode-like values ($\sim $100 keV/m), with decreasing thermal conductivity before the transition in particle confinement. Past experiments varying topology with fixed drift direction have shown a connection of thresholds to SOL flows and core toroidal rotation [1]; the new results confirm and extend this picture with improved measurements. Extended experimental pedestal scalings will be presented and compared with models which consider both neutral penetration and plasma transport [2]. [1] B. LaBombard et al, Phys. Plasmas \textbf{12}, 056111, 2005. [2] J.W. Hughes et al, Phys. Plasmas \textbf{13}, 056103, 2006.   

Study of Turbulence and Radial Electric Field Transitions in ASDEX Upgrade using Doppler Reflectometry

The radial electric field is recognised as an important factor in the performance of magnetically confined fusion plasmas. On ASDEX Upgrade microwave Doppler reflectometry has been developed to directly measure $E_r$ profiles, its shear and its fluctuations. Here a poloidally tilted antenna selects via Bragg a specific turbulence wavenumber giving a frequency shift directly proportional to the perpendicular rotation velocity $u_\perp = v_{E \times B} + v_{\rm turb}$ of the turbulence moving in the plasma. Turbulence simulations show $v_{E \times B} \gg v_{\rm turb}$ allowing simple extraction of $E_r$ with good accuracy. In the scrape-off-layer $E_r$ is positive, but reverses across the separatrix due to the pedestal pressure gradient to form a negative well. The strength of the well scales directly with confinement, typically -50V/cm for ohmic/L-mode, rising to -300V/cm for H-mode and in excess of -500V/cm for improved H-modes. Without NBI $v_{E \times B} \approx v_{\rm turb}$ which allows the turbulence behaviour to be investigated. For example the core rotation reverses from ion to electron direction when plasma collisionality is raised while matched gyro-kinetic turbulence simulations show the dominant turbulence changing from TEM to ITG with corresponding $v_{\rm turb}$ reversal, which implies the core $E_r$ reverses sign with the turbulence. Also of major importance to confinement are zonal flows and GAMs - radially localised oscillating $E \times B$ flows. $E_r$ fluctuations directly measured by Doppler refl. reveal coherent modes in the edge gradient region where turbulence vorticity and $E_r$ shear are largest. The mode frequency scales as sound speed over major radius but is sensitive to plasma shape and local $q$. So far GAMs have not been seen in H-modes, nor in the plasma core. In each topic, the synergetic combination of experiment, theory and numerical simulation aids interpretation shows $E_r$ is interlinked with turbulence and the mean plasma profiles. \newline Collaborators: J.Schirmer, W.Suttrop, C.Angioni, R.Dux, F.Jenko, E.Holzhauer, S.Klenge, B.Kurzan, C.Maggi, A.G.Peeters, M.Reich, F.Ryter, B.Scott, C.Tr\"oster, E.Wolfrum, H.Zohm and the ASDEX~Upgrade~Team.   

Gyrocenter shift and H-mode transition

Since the first observation of the H-mode, there has been much experimental and theoretical work studying the role of boundary neutrals on the L-H transition. In addition, it is believed that turbulence suppression due to ErxB shear can also play an important role in the L-H transition, despite a lack of complete understanding~of the origin of the radial electric field. The gyrocenter shift of thermal ions is the basis of a theoretical model that connects these two problems of L-H transition theory: the role of neutrals and the origin of the radial electric field. The radial gradient of the charge-exchange microscopic reaction rate of thermal ions in the presence of a neutral density gradient gives rise to a radial force. This force in turn gives rise to a radial current and electric field, which can be computed by taking the average of the ion velocity at the time of the charge-exchange reaction averaged over the gyromotion. This model can be applied to the interplay between the neutral density gradient and the plasma density gradient, which affects neutral penetration. This paper will integrate the details of the theory and related neoclassical effects with a neutral transport calculation in order to develop a time-dependent picture of the L-H transition, specifically for NSTX. Calculations of the radial electric fields based on this theory show good agreement with experimental results from NSTX and DIII-D.   

Investigation of Edge Localized Modes in Alcator C-Mod

Characteristics of discrete ELMs produced in Alcator C-Mod discharges of low edge collisionality and high triangularity are examined. These discharges have high values for central T$_{e}$ and n$_{e}$ (reaching 4.5 keV and 2x10$^{20}$ m$^{-3}$ respectively) and good confinement, consistent with ITER98y2 ELMy H-mode scaling. Pedestal temperature heights reach 0.9 keV at densities above 1x10$^{20}$ m$^{-3}$. Studies of the stability of the pedestal profiles to peeling/ballooning modes will be presented. The energy lost per ELM from the H-mode pedestal is $\sim $10-20{\%} of the pedestal energy. These ELMs exhibit relatively long-lived precursor oscillations, often with two modes of intermediate (n$\sim $10) toroidal mode number present. At the ELM ``crash'' a high frequency ($\sim $0.5 MHz), short-lived magnetic oscillation is initiated, and multiple plasma filament structures are expelled into the Scrape-Off-Layer. The initial ELM filaments, ``primaries'', are large perturbations to the SOL. The perturbation increases the local D$_{\alpha }$ emission by factors ranging from 1.5 (just outside the LCFS) to $\sim $100. In the outboard midplane region the primary filaments have radial extents of 0.5-1 cm and typical radial propagation velocities of 1-2 km/s. The poloidal extent of the filaments is greater than the 4.5 cm diagnostic field-of-view. The initial filaments are followed (at intervals of $\sim $100$\mu $s) by multiple, less perturbing ``secondary'' filaments. The radial dynamics of the ELM are also studied at the \textit{inboard} midplane. The perturbation on the inboard edge appears to be a rapid profile relaxation and recovery. The onset of the inboard profile relaxation is sometimes observed to occur \textit{before} filaments are seen on the outboard side.   

Intrinsic Rotation in DIII-D

In the absence of any auxiliary torque input the DIII-D plasma is observed to have nonzero toroidal angular momentum. In Ohmic H-mode discharges the toroidal rotation profile is relatively flat, consistent with early C-Mod observations. In electron cyclotron heating (ECH) H-modes the velocity profile is hollow, directed in the direction of the plasma current on the outside and depressed, or actually directed counter to the plasma current near the plasma center, depending upon the ECH deposition profile. Such ``intrinsic" rotation has been observed on other tokamaks. Understanding this effect is important for making projections toward burning plasma performance, and design considerations, where neutral beam injection torque will be relatively small, or nonexistent. Theoretical treatments of intrinsic rotation based upon neoclassical off-diagonal transport coefficients, and upon turbulence-induced momentum transport have been done. A detailed match with theory is yet to emerge. An empirical scaling is being developed, relating the intrinsic rotation velocity to the ratio of stored energy to plasma current. It appears possible that some aspects of intrinsic rotation will be elucidated through cross-machine experiments using similarity in the dimensionless plasma parameters, allowing a projection to a burning plasma. Velocity is an important parameter since sufficient toroidal rotation tends to stabilize deleterious MHD modes and velocity shear promotes thermal confinement. We will describe measured intrinsic rotation profiles from a variety of DIII-D L- and H-mode conditions, scalings, and comparisons with applicable theories, where they exist. Cross-machine experiments along paths of dimensionless similarity will be described. The DIII-D results will also be compared with experimental results from other tokamaks.   

Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual

Sheared zonal flow is known to be the predominant saturation mechanism of plasma turbulence. Rosenbluth and Hinton\footnote{M.N. Rosenbluth and F.L. Hinton, Phys. Rev. Lett., 80, 724 (1998)} (R-H) have shown that the zonal flow level is inversely proportional to the plasma radial polarizability due to magnetic drift departure from a flux surface. In another calculation, Hinton and Rosenbluth\footnote{F.L. Hinton and M.N. Rosenbluth, Plasma Phys. Control. Fusion, 41, A653 (1999)Work supported by U.S. DoE} (H-R) considered the weakly collisional case in the banana regime and calculated the neoclassical polarization and associated zonal flow damping in the high and low collisionality limits. The work presented here extends R-H's calculation in several aspects. The neoclassical polarization for arbitrary radial wavelength zonal flows is evaluated with finite ion banana width and ion gyroradius retained. Plasma shaping effects are retained in the R-H collisionless calculation. Elongation is shown to strongly reduce the neoclassical polarization and thereby strongly increase the zonal flow residual, while the Shafranov shift and triangularity result in a more moderate increase in the zonal flow level. In addition, the H-R collisional calculation is extended by using an exact eigenfunction expansion of the collision operator to calculate the neoclassical polarization for the entire range of collisionality. A simple, semi-analytical fit of these exact results based on the lowest eigenfunction gives the polarization to within 15{\%} and allows the collisional zonal flow damping rate to be evaluated for arbitrary collisionality.