Session PI2: Pedestal, SOL and Divertor

Transport-driven toroidal rotation in the tokamak edge

The edge of H-mode tokamak plasmas without external momentum input almost always rotates toroidally in the co-current direction, which has prompted a theoretical search for non-diffusive momentum transport mechanisms. In contrast to these efforts, the present work treats a model drift-kinetic ion equation for the pedestal and SOL containing only parallel free streaming, magnetic drifts, and spatially inhomogeneous but purely diffusive transport. The solution demonstrates that passing-ion orbits and spatially inhomogeneous diffusion interact to cause a variation of the orbit-averaged diffusivities that depends on the sign of $v_{\parallel}$, typically resulting in preferential transport of counter-current ions. If the plasma at the boundary with the core is allowed to rotate toroidally to annihilate toroidal momentum transport, the resulting pedestal-top rotation reaches experimentally relevant values and exhibits several features in qualitative agreement with experiment. It is almost always in the co-current direction, with a rate that is proportional to $T_{i}|_{\rm{ped-top}}/B_{\rm{pol}}L_{Te}$ for small $q\rho_{i}/L_{Te}$, thus inversely proportional to $I_{p}$ in accord with Rice scaling. It is independent of the toroidal velocity and its radial gradient, representing a residual stress. The $T_{i}|_{\rm{ped-top}}/B_{\rm{pol}}L_{Te}$ scaling implies co-current spin-up at the transition to H-mode, as $T_{i}$ increases and the gradient of $T_{e}$ steepens. Untested predictions of the model include a sensitivity of the rotation to the major-radial position of the X-point, with a more inboard X-point leading to stronger co-current rotation. Beyond intrinsic rotation predictions, comparison of heat and momentum transport reveals that neutral beam injection must be significantly unbalanced in the counter-current direction to cause zero toroidal rotation at the pedestal top.   

Predator-Prey Oscillations and Zonal Flow-Induced Turbulence Suppression Preceding the L-H Transition

Understanding the L- to H-mode transition and the density/rotation dependence of the H-mode power threshold is important for the design and predictive modeling of burning plasma experiments. We present here direct experimental evidence of the importance of predator-prey oscillations and turbulence/transport regulation by low frequency zonal flows (ZFs) at the L-H transition. Near the H-mode power threshold, a narrow oscillating flow layer develops at/inside the separatrix in a neutral beam-heated DIII-D plasma. Toroidal and radial correlation of the $E\times B$ velocity, as measured by Doppler backscattering (DBS), increase at the transition to this ``dithering'' state. The observed oscillation is consistent with a radially propagating ZF with a frequency much below the expected local GAM frequency. Periodic turbulence suppression due to ZF shearing is first observed when the turbulence decorrelation rate decreases sharply (within 0.1$\,$ms) at the transition to the dithering state and the increasing ZF shearing rate locally surpasses the decorrelation rate. The flow layer then expands radially inwards. The ZF amplitude lags the density fluctuation amplitude by 90$^{\circ}$. The ``final" H-mode transition (sustained turbulence/transport reduction) appears linked to increasing equilibrium flow shear due to the increasing ion pressure gradient. Both features are consistent with the predator-prey model of the L-H transition [1]. The transition dynamics is revealed with high time ($<$1$\,\mu$s) and spatial resolution ($<$0.5$\,$cm), combining eight channel and five channel DBS systems, separated 180$^{\circ}$ toroidally, with fast profile reflectometry.\par \vskip3pt \noindent [1] E.J. Kim and P.H. Diamond, Phys. Rev. Lett. {\bf 90}, 185006 (2003).   

H-mode Pedestal Evolution in ELMy and ELM-free discharges in NSTX

Most tokamaks operate in ELMy H-mode, since ELM-free regimes typically have narrow and transient operational windows. In contrast, in NSTX, sustained ELM-free regimes are routinely accessed with a wide operating window by evaporating lithium onto the divertor plates between discharges [1]. In this work, we use this widened operating window to investigate the governing physics of the pedestal density, temperature, and pressure profiles. As part of the FY11 DoE multi-facility Joint Research Target, we contrast the pedestal structure evolution, transport, and fluctuations in ELMy and ELM-free regimes, building on previous studies [2]. Counter to intuition, the pedestal pressure width and height are found to be larger in ELM-free than ELMy discharges. During the inter-ELM phase in ELMy discharges, the pedestal pressure height saturates early in the ELM cycle and the maximum pressure gradient is clamped around 20{\%} of the ELM cycle, similar in part to DIII-D observations [3]. Meanwhile the pedestal width continues to expand until the onset of ELMs [4]. The inter-ELM edge fluctuations, using BES and reflectometer measurements in the pedestal region, show a decrease of the fluctuations just prior to the onset of the ELM. This reduction of edge fluctuations is sustained when transitioning to ELM-free regimes. In the ELM-free discharges, the electron density pedestal width and height grow slowly with time, while the electron pedestal temperature appears clamped; hence, the pedestal pressure also grows slowly, evolving to a favorable parabolic-shaped profile. Nevertheless, peeling-ballooning theory appears to set an upper limit to the pressure gradients in both ELM-free and ELMy discharges.\\[4pt] [1] H. Kugel, et al. Phys. of Plasmas \textbf{15} (2008) 056118\\[0pt] [2] J. Canik, et al., Phys. of Plamas \textbf{18} (2011) 056118\\[0pt] [3] R. Groebner, et al. Nucl. Fusion \textbf{4} (2009) 064002\\[0pt] [4] A. Diallo, et al. Nucl. Fusion \textbf{50} (2011) \textit{at press}   

Theory of the generation of non-axisymmetric scrape-off-layer perturbations for controlling tokamak edge plasma profiles and stability

The ability to control both steady-state and transient divertor heat loads is a critical requirement for successful tokamak fusion reactors. We propose driving toroidally-asymmetric perturbations through the scrape-off layer (SOL) plasma both to control the edge pedestal pressure gradient by generating currents that drive resonant magnetic perturbations (RMPs) [1] and to broaden the SOL by generating potentials that drive radial convection [2]. Both types of perturbations can be superposed in the same divertor, but lower mode numbers are favored for generating strong RMPs, while higher mode numbers are favored for generating strong convective transport. Calculations show that choosing the appropriate width and phasing of the biasing region at the target plate can amplify the RMP generated by the SOL current. Steady-state cross-field transport on open field lines can be enhanced if the convection frequency exceeds the rate of parallel transport. Analytic estimates and calculations will be made for the MAST and NSTX tokamaks, which have already produced relevant experimental information. Generation of the necessary currents by electric biasing of mutually-insulated divertor segments is the most straightforward technique, but requires the use of in-vessel insulators that are poorly suited to the fusion reactor neutron environment. Therefore, passive current-drive mechanisms that rely on puffing and pumping of neutral gas and/or impurities in a toroidally asymmetric fashion are analyzed using reduced 1d and 2d numerical models. \\[4pt] [1] I. Joseph, R. H. Cohen and D. D. Ryutov, Phys. Plasmas \textbf{16}, 052510 (2009). \\[0pt] [2] R. H. Cohen and D. D. Ryutov. Nucl. Fusion \textbf{37}, 621 (1997).   

Analysis of a Multi-Machine Database on Divertor Heat Fluxes

A coordinated effort to measure divertor heat flux characteristics in fully attached, similarly shaped H-mode plasmas on C-Mod, DIII-D and NSTX was carried out in 2010 in order to construct a predictive scaling relation applicable to next step devices including ITER, FNSF, and DEMO. Few published scaling laws are available and those that have been published were obtained under widely varying conditions and divertor geometries, leading to conflicting predictions for this critically important quantity. This study was designed to overcome these deficiencies. Corresponding plasma parameters were systematically varied in each tokamak, resulting in a combined data set in which $I_p$ varies by a factor 3, $B_t$ varies by a factor of 14.5, and major radius varies by a factor of 2.6. The derived scaling relation consistently predicts narrower heat flux widths than relations currently in use. Analysis of the combined data set reveals that the primary dependence of the parallel heat flux width is robustly inverse with $I_p$. All three tokamaks independently demonstrate this dependence. The midplane SOL profiles in DIII-D are also found to steepen with higher $I_p$, similar to the divertor heat flux profiles. Weaker dependencies on the toroidal field and normalized Greenwald density, $f_{GW}$, are also found, but vary across devices and with the measure of the heat flux width used, either FWHM or integral width. In the combined data set, the strongest size scaling is with minor radius resulting in an approximately linear dependence on $a/I_p$. This suggests a scaling correlated with the inverse of the poloidal field, as would be expected for critical gradient or drift-based transport.   

Deuterium retention enhancement in lithiated graphite plasma-facing surfaces in fusion devices

Lithium conditioning has been adopted in a number of magnetic confinement devices resulting in significant effects on plasma performance. In NSTX for example effects include: reduction of ELMs, reduced edge neutral density, increased pedestal electron and ion temperature, and improved energy confinement [1]. The main assumption conjectured for the effects observed in NSTX plasmas is the retention of hydrogen by coatings of lithium on ATJ graphite tile surfaces. The main binding channel understood to be the ionic lithium hydride bond. However, the likelihood that the dominant retention mechanism is governed by lithium-hydride bonding seems less probable based on well-known intercalation effects of lithium in graphite. The observed effects on plasma behavior in NSTX, despite the strong chemical interaction of D, Li, O and carbon, indicate an enhanced mechanism for retaining hydrogen in addition to Li-D binding. This paper summarizes the key mechanisms understood today of enhanced hydrogen retention in lithium-treated ATJ graphite surfaces. The mechanisms are elucidated by four major efforts: 1) controlled in-situ off-line experiments at Purdue [2,3], 2) post-mortem NSTX tile analysis, 3) in-vacuo PMI probe data in NSTX, and 4) computational quantum-based atomistic simulations. Results show that a saturation limit of D pumping by lithium conditioning of ATJ graphite surfaces is reached in a few number of shots. Computational modeling using semi-empirical quantum mechanics of electrons and classical mechanics of nuclei elucidate on the polar-covalent interactions that emerge between lithium and the C-D-O system. \\[4pt] [1] H. Kugel et al. Phys. Plasmas 15, (2008) 056118 \newline [2] J.P. Allain et al. J. Nucl. Mater. 390-391 (2009) 942 \newline [3] C.N. Taylor et al. 109 (2011) 053306.