Session NI1: Plasma Edge and Divertor

Superdense Plasma in LHD

In reduced recycling discharges using a Local Island Divertor (LID) in the Large Helical Device (LHD), a stable superdense plasma develops spontaneously when a series of pellets are injected. A core region with $\sim $ 4.5 x 10$^{20}$ m$^{-3 }$and temperature of 0.85 keV is maintained by an Internal Diffusion Barrier (IDB). The density gradient at the IDB (r/a $\sim $ 0.6) is very high, and the particle confinement time in the core region is $\sim $ 300 ms. The temperature profile inside the IDB (r/a $<$ 0.6) is flat, on the other hand, its gradient in the outer region is steep. Because of the increase in the central pressure, a large, stabilizing Shafranov shift up to $\sim $ 0.3 m is observed. The critical ingredients for IDB formation are a strongly pumped divertor to reduce edge recycling, and multiple pellet injection to ensure strong central fueling. Gas puffing results in broad, flat or slightly inverted density profiles, and does not lead to formation of a superdense plasma. Low density in the outer region helps to raise the edge temperature gradient there and hence the core temperature. In that sense, for the strong pumping, it does not take an LID to reduce the edge recycling, only if a conventional Helical Divertor (HD) has sufficient pumping capability. Similar discharges can actually be achieved in the HD configuration under exhaustive wall conditioning, although it cannot last for a long time because of the saturation of the pumping capability of the wall. Although use of the island divertor reduces the confinement volume by $\sim $40 {\%} from its nominal value, superdense LID discharges exhibit the highest performance (n$_{0}$T$_{0}\tau _{E}$ = 4.4 $\times $ 10$^{19 }$m$^{-3}\cdot $keV$\cdot $s) obtained so far in LHD. These plasmas provide unique opportunities for exploration of high-beta MHD stability in heliotron/stellarator configurations, and may extrapolate to a novel scenario for fusion ignition at very high density and relatively low temperature.   

Nonlinear dynamics of the tokamak edge plasmas

Transport in the edge appears to be mostly convective and intermittent. Ubiquitous coherent structures referred to as “blobs” that form in the steep-gradient region lead to cross-field transport that greatly enhances the SOL widths beyond those expected from simple diffusion models. In H-mode discharges, in addition to this background of blobby transport, filamentary structures, associated mostly with Type I ELMs, are observed to convectively transport significant portion of the stored energy in the pedestal to the far SOL. Blobs and ELM-generated filaments share many dynamical features, the most significant being their rapid radial propagation and interaction with the plasma facing components first, before their effects are felt in the divertor chamber. Here the nonlinear dynamics of both blob and ELM-generated filaments are examined with fluid models. An earlier study of blobs with a reduced 2D model showed how interchange-driven turbulence and the associated blobby transport can account for the observed SOL widths and their sometimes seen “two-tier” structure. A more recent 3D effort using the MHD code CTD shows that the ballooning/peeling mode generated “fingers” in the pedestal are quite similar to those of the blob studies: they rapidly convect plasma from the pedestal to the far SOL, while the “holes” between the fingers move inward, thus also affecting core confinement in some circumstances. An externally-imposed shear flow in the pedestal has a stabilizing influence on the linear modes involved; however, the modes in turn affect the flow, leading to a complex nonlinear coupling that is being investigated. Another effect under study is the role of resonant magnetic perturbations in ameliorating the effects of Type I ELM’s.   

Carbon Sources, Scrape-Off Layer Transport, and Deposition in DIII-D

Comprehensive studies of carbon production, transport, and deposition in the scrape-off layer (SOL) in DIII-D show that carbon produced in the main chamber is primarily deposited in the divertor on surfaces facing a cold and dense plasma. Controlling the carbon erosion and deposition are critical issues for future fusion devices with carbon PFCs, as tritium will be co-deposited with the carbon layer, potentially leading to an unacceptable tritium inventory. Carbon-13 tracer experiments were carried out in DIII-D L-mode and H-mode plasmas by injecting $^{13}CH_4$ into the main SOL, and analyzing tiles post-mortem for $^{13}C$ surface deposition. The main and divertor SOL of these plasmas were well characterized, including 2-D measurements of the carbon emission in the divertor and near the $^{13}CH_4$ injection location. In both confinement regimes a high $^{13}C$ deposition was observed in the inner divertor. However, in H-mode, the deposition extended across the private flux region to the intercept of the outer leg of the separatrix. Multiple diagnostics in the divertor region showed that the inner divertor SOL is partially detached in L- and H-mode, while the outer divertor SOL is attached in the L-mode, but partially detached in the H-mode plasma. Edge-localized modes were observed to modulate the divertor plasma conditions in H-mode, by periodically reattaching the inner and outer divertor plasma. Plasma simulations of the L-mode using the UEDGE code including $E\times B$ and $B\times\nabla B$ drifts predict carbon flow in the main SOL toward the outer target, and $^{13}C$ carbon deposition along the inner and outer divertor targets. Assuming a deuterium flow of $M\sim 0.5$ in the main SOL toward the inner divertor, interpretative studies with the OEDGE code are consistent with the main SOL carbon emission distributions and $^{13}C$ deposition profile.   

Achievement of Low Recycling and High Power Density Handling in CDX-U with Lithium Plasma-Facing Components

The CDX-U spherical tokamak research program has focused on lithium as a large area plasma-facing component (PFC). The CDX-U experiments have used a toroidal lithium limiter and evaporated lithium wall coatings up to 100 nm thick. Under these conditions, a particle pumping rate of 1 - 2 x 10$^{21}$ particles/second was achieved from an active wall area of 0.4 m$^{2}$. The energy confinement times deduced from plasma equilibrium reconstructions showed a nearly six-fold improvement over discharges without lithium PFC's. This was an increase of up to a factor three over ITER98P(y,1) scaling, and reflect the largest enhancement in confinement ever seen in Ohmic plasmas. Recycling coefficients (R) of 0.3 or below were deduced from spectroscopic measurements. These are the lowest values of R observed to date in magnetically-confined plasmas, and for the first time, the wall was not the dominant source of fueling. The process of generating lithium evaporative coatings also showed the effectiveness of liquid lithium in redistributing heat loads at extremely high power densities. An electron beam was used to deposit about 1.5 kW of power on a 6 mm spot on the toroidal lithium limiter. Lithium evaporation was not localized to this spot, but occurred only after the entire volume of lithium was raised to the evaporation temperature. Infrared camera images showed that even with a lithium depth of 3 mm, convection due to the Marangoni effect was able to distribute a heat load of about 50 MW/m$^{2}$ for the 240 second duration of the electron beam pulse. This could have significant consequences for PFC's in burning plasma devices, where high power densities are a concern.   

Characterization of Zonal Flows and Their Dynamics in Experiment and Simulation

Using newly developed algorithms, the {\em nonlinear} transfer of internal energy $\vert\tilde{n}\vert^2$ due to convection of drift-wave turbulence by a geodesic acoustic mode (GAM, a finite-frequency zonal flow) has now be measured directly in a high-power device. By combining spatially resolved density fluctuation measurements obtained via an upgraded beam emission spectroscopy (BES) system in the edge region of the DIII-D machine with a velocity inference algorithm, the convection of turbulent fluctuations by the GAM has been directly measured. These measurements indicate that GAM convection leads to a transfer of internal energy from low to high frequencies, in agreement with expectations from theory and simulation. In addition, the GAM is found to modulate the intensity of the density fluctuations, providing further support for the idea that the GAM is a significant player in the edge turbulence dynamics. The upgrades to the BES system have also allowed us to identify and characterize the zero mean frequency (ZMF) zonal flow branch for the first time in the core of a tokamak plasma. Calculations of the measured nonlinear interactions in long run-time simulations of the gyrokinetic code GYRO are found to be in good agreement with the experimental observations, and are used to develop new insights into the roles of GAM and ZMF flows in regulating drift-wave turbulence in different regions of parameter space. Complementing these measurements of how the zonal flows affect the turbulence are measurements of the turbulent momentum balance in a linear plasma column, which explicitly demonstrate the generation of a collisionally damped zonal flow by the Reynolds stress.\par \vskip3pt \noindent In collaboration with G.R. Tynan (UCSD); R.J. Fonck, G.R. McKee (U. Wisc.); J. Candy, and R.E. Waltz (GA).   

Geometric Gyrokinetic Theory for Edge Plasmas

A set of generalized gyrokinetic equations valid for the edge plasmas has been derived using a geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. In its most general form, gyrokinetic theory is about a symmetry called gyro-symmetry. The objective of geometric gyrokinetic theory is to decouple the gyro-phase dynamics by finding the gyro-symmetry. This is fundamentally different from the conventional gyrokinetic concept of ``averaging out'' the ``fast gyro-motion.'' The starting point is the Poincar\'e-Cartan-Einstein 1-form on the 7D phase space which determines particles' dynamics and realizes the velocity integrals in kinetic theory as fiber integrals. The infinitesimal generator of the gyro-symmetry is then constructed by applying the Lie coordinate perturbation method. General gyrokinetic equations are then developed as the Vlasov- Maxwell equations in the gyrocenter coordinate system, rather than a set of new equations. Because the general gyrokinetic system is geometrically the same as the Vlasov-Maxwell equations, all the coordinate-independent properties of the Vlasov-Maxwell equations, such as energy conservation, momentum conservation, and phase space volume conservation, are automatically carried over to the general gyrokinetic system by the pullback transformation. With subsidiary orderings, explicit and practical results can be obtained from the new formalism. For example, the pullback transformation in the gyrokinetic Poisson equation can be explicitly expressed in terms of moments of the gyrocenter distribution function, with the important gyro-orbit squeezing effect due to the large electric field shearing in the edge and the full finite Larmour radius effect for short wavelength fluctuations.