Session TO9: Transport, Turbulence, and Magnetic Islands

Anomalous Transport in High Beta Poloidal DIII-D Discharges

Dominant instabilities that drive anomalous transport in high beta poloidal DIII-D discharges [A.M. Garofalo $et$ $al$. Proc. of 25th IAEA FEC (St. Petersburg, Russia, 2014) 657] are investigated using the MMM7.1 [T. Rafiq $et$ $al$. Phys. Plasmas 20 (2013) 032506], and TGLF models in the predictive integrated modeling TRANSP code. The ion thermal transport is found to be strongly reduced in these discharges, but turbulence driven by the ITG modes along with the neoclassical transport still play a role in determining the ion temperature profiles. The electron thermal transport driven by the ETG modes impact the electron temperature profiles. The $E\times B$ flow shear is found to have a small effect in reducing the electron thermal transport. The Shafranov shift is found to strongly reduce the anomalous transport in the high beta poloidal DIII-D discharges. The reduction of Shafranov shift can destroy the ion internal transport barrier and can result in significantly lower core temperatures. The MMM7.1 model predicts electron and ion temperature profiles reasonably well, but it fails to accurately predict the properties of electron internal transport barrier, which indicates that the ETG model in MMM7.1 needs to be improved in the high beta poloidal operational regime.   

Edge rotation as governed by momentum transport due to neutrals

Neutrals can strongly affect momentum transport even in relatively small concentrations due to their high cross-field mobility. We present a framework to calculate numerically the momentum transport due to charge-exchanging neutrals, in the closed field-line region. We couple a short mean-free-path solution of the neutral kinetic equation to neoclassical ions. We can then determine self-consistently the radial electric field and plasma rotation velocity, assuming that the neutrals dominate the momentum transport. We use the neoclassical solver PERFECT [Landreman et al 2014 PPCF 56 045005] to compute the ion distributions. Numerical solutions allow us to consider the full range of collisionalities; typical experimental parameters fall in the intermediate region that is not well described by analytical limits. We also compute the rotation velocities of minority impurity species, to facilitate experimental comparison of the results. We find that at a fixed collisionality, the important parameter determining the radial electric field and rotation is the major radius where the neutrals are localized. Therefore changes to the location of the peak neutral density, caused by altering the fuelling location or moving the X-point for example, should allow the rotation to be manipulated.   

Neoclassical transport in density pedestals with non-trace impurities

We study neoclassical transport in steady-state density pedestals with non-trace impurities using the Eulerian $\delta f$ code \textsc{Perfect}, with an emphasis on radially global effects and the effects of impurities. To properly describe transport in a tokamak pedestal, radial coupling must be included, which strongly affects the transport. We find that radial coupling reduces the pedestal heat flux compared to local predictions. Furthermore, the influence of the pedestal persists several orbit widths into the core. The electron flux is significant in the pedestal, and global neoclassical transport is not intrinsically ambipolar. Thus, the impurity flux is not simply opposing the ion flux. The resulting radial current gives a torque that is balanced by a non-negligible radial transport of toroidal momentum. The effective Prandtl number is comparable to typical turbulent values in the core ($0.1$--$0.3$), and is sensitive to the impurity content. Global effects have a strong contribution to the poloidal flows of low-$Z$ ions, which give rise to larger in-out flow asymmetries.   

Mechanisms of intrinsic toroidal rotation tested against ASDEX Upgrade observations

One of the major current challenges in the theory of tokamak turbulent transport is the quantitative prediction of intrinsic toroidal rotation. Symmetry breaking mechanisms connected with plasma rotation and with higher order effects must be included in the theoretical description of this transport channel. Many have been identified, however a systematic comparison of their predicted size against a comprehensive set of observations is largely missing. Presented will be a combined theoretical and experimental effort. The gyrokinetic code GKW has been increasingly upgraded to include the most important symmetry breaking mechanisms. Comparison is made to dedicated ASDEX Upgrade experiments which provide a database of 190 observations in Ohmic plasmas; an optimal test-bed to perform a comprehensive and systematic comparison of the predictions of many mechanisms against observations. The sum of the symmetry breaking mechanisms used in the local code, including neoclassical background flow effects, predicts mostly hollow rotation profiles, as observed, but rotation gradients have much smaller amplitudes. Larger flow gradients caused by profile shearing are found in global turbulence simulations with kinetic electrons, their reversal and parametric dependency will be discussed   

Magnetic activity and radial electric field during I-phase in ASDEX Upgrade plasmas

At the transition from the low (L-mode) to the high (H-mode) confinement regime, so called limit-cycle oscillations (LCOs) can occur at the edge of a fusion plasma. During the LCO evolution, which is also called I-phase, the relative importance of background flows and turbulence-generated zonal flows can change, and it is still unclear whether a large contribution of zonal flows is a necessary condition for triggering the H-mode. At ASDEX Upgrade, I-phases have been studied in a wide range of parameters. The modulation of flows and gradients during I-phase is accompanied by a strong magnetic activity with a specific poloidal and toroidal structure. The magnetic activity increases during the development of an edge pedestal during I-phase, and is preceded by type-III ELM-like precursors. During all phases of the I-phase, the radial electric field $E_r$ is found to be close to the neoclassical prediction of the electric field $E_{\rm r,neo}$. These results suggest that zonal flows do not contribute significantly to the LCO dynamics, and the burst like behavior is reminiscent of a critical-gradient driven instability like edge localized modes. These observations on ASDEX Upgrade seem to be inconsistent with LCO models based on an interaction between zonal flows and turbulence.   

Understanding TCV L-mode plasmas via global gyrokinetic GENE simulations

It is known that global effects can have a significant influence on turbulent transport driven by microintabilities, especially for small size machines like the TCV tokamak. The global version of the gyrokinetic GENE code has been extensively used to model TCV plasmas for which finite $\rho^*$ effects are expected to be crucial in order to recover the experimentally observed behaviour. We will address in particular: $(i)$ The effect of negative triangularity, which has been experimentally observed to lower up to a factor of two the heat flux through the lectron channel at all radial locations. Global effects and the inclusion of carbon impurities turn out to be the key elements required in order to match experiments and simulation results. $(ii)$ The formation of either radially coherent or dispersive axisymmetric density fluctuations, experimentally interpreted as Geodesic Acoustic Modes. GENE simulations reproduce the observed behaviour and allow to conclude that the modification of safety factor alone cannot explain the transition between these two different fluctuation regimes.   

Gyrokinetic simulation and analytic modeling of dissipative trapped electron mode in tokamak edge

Trapped electron mode (TEM), including collisionless TEM (CTEM) and dissipative TEM (DTEM), are major electrostatic candidates accounting for electron turbulent transport in tokamaks. The interests on DTEM have recently been re-invoked by the so called “edge coherent mode" in EAST experiments. Due to the low temperature in the pedestal region, DTEM may play an important role in electrostatic edge transport. In this work, we revise the previous DTEM theory by using a more realistic pitch angle scattering operator for collisions in the edge and the analytic result is further compared by the gyrokinetic simulation code GTC with a more complete collisional operator conserving both energy and momentum. The dependences of the DTEM instability on wavelength and collisional frequency are revealed by both simulation and theory and show good consistency between them. The linear growth is stabilized in the long wavelength limit, which is different from some of the previous studies, while consistent with traditional CTEM picture. The nonlinear wavelength cascade of DTEM is investigated by gyrokinetic simulation and will be reported in this presentation.   

Characterization of turbulent eddies and their associated transport

The internal electric field of turbulent eddies has been experimentally measured by a two-dimensional Langmiur probe array, which shows potential peak or valley in both radial and poloidal directions. This is consistent the expectation that the internal electric field of turbulent eddies either points towards the center or away from the center in both poloidal and radial directions. Fluctuating electron temperature and density associated with turbulent eddies have also been measured, in both L-mode and H-mode, and through the L-H transitions as well. The phase of the fluctuation velocity in all of the above discharges, including the case during ELMs, show that eddies mediated the turbulent momentum in such a way to enhance the mean ExB shear flow in the edge.   

Gyrokinetic simulation and theory for kinetic ballooning mode

The kinetic ballooning mode (KBM) plays an important role in H mode formation and edge-localized mode (ELM) physics and internal transport barrier. A thorough understanding of the linear KBM physics is crucial to understanding the nonlinear edge physics in tokamaks. The second stability regime in small shear and sufficiently large pressure gradient has been predicted by the ballooning MHD theory. In the present work, a kinetic ballooning mode is found for the second stability regime in s-alpha space. This KBM mode is characterized by a broad-spread eigenfunction in the ballooning space, and destabilized dramatically by the ion temperature gradient. Such KBM mode almost exists in the entire second stability regime. Also KBM has been found in the sufficiently small shear even with negative shear. The gyrokinetic code GTC is employed to study the KBM physics, and finds that the linear KBM growth rate and frequency are very sensitive to the equilibrium profile. The effect of parallel current and density has been investigated, and comparisons between gyrokinetic simulation and analytic theory are carried out. The results shows that parallel current response have a strong effect in stabilize KBM instability, which could have a large effect on nonlinear electromagnetic turbulent transport.   

Full wave simulations of microwave interactions with turbulence

The interaction between electromagnetic radiation and plasma perturbations in the case that the radiation wavelength is comparable to the size of the perturbations is not a fully-understood problem. Yet the use of microwaves in magnetic confinement fusion plasmas is widespread for heating, current drive and both passive and active diagnostics, including in regimes for which there exist microwave length-scale plasma perturbations. We present simulation results using the full-wave cold plasma finite difference time domain codes EMIT-3D and IPF-FDMC developed independently at York and Stuttgart, respectively. First we present a novel systematic study of the scattering of microwaves through turbulence: we quantified the relationship between the normalised turbulent correlation length and the scattered power. Additionally we found a quadratic relationship between the scattered wave power and the turbulence amplitude. We go on to present results to model the Doppler back-scattering of a broad microwave beam from a moving turbulent slab. This second problem is particularly important for interpreting data from the Synthetic Aperture Microwave Imaging (SAMI) diagnostic currently installed on NSTX-U.   

Multi-scale Simulations of DIII-D near-edge L-mode plasmas

In order to self-consistently describe the L-H transition we have to be able to quantitatively characterize near-edge L-mode plasmas ($\rho$=0.8). Instructed by a linear analysis, we perform nonlinear gyrokinetic simulations of a DIII-D L-mode discharge. Comparison between single-scale and multi-scale simulations reveals that stability of ion temperature gradient (ITG) turbulence affects cross-scale coupling. When ion transport is stabilized by zonal flows, electron temperature gradient (ETG) streamer amplitude is reduced but persists at sub-ion-scales, causing radial electron heat transport to dominate. When ITG modes are unstable, we find that ion heat transport dominates, in agreement with experimental data. Moreover, nonlinear de-stabilization of ion transport occurs at higher critical gradients for multi-scale than for single-scale simulations, showing an enhanced Dimits shift. All simulations are performed with the GENE code (genecode.org).   

3D plasma turbulence and neutral simulations using the Hermes model in BOUT$++$: a study of linear devices and the tokamak edge and divertor region

Understanding the transport processes in the low temperature plasma at the boundary region of magnetic confinement fusion (MCF) devices is crucial to the design and operation of future fusion reactor devices. It influences the divertor heat load, and probably the core confinement as well. The dominant source of this transport is turbulence, which serves to mix the high and low temperature regions of the plasma. The nature of this plasma turbulence is affected by not only the plasma parameters, but also the neutral species that also exist in these low temperature regions. The interaction of neutrals with the plasma turbulence is studied in linear device geometry (for its simplicity, yet similarity in plasma parameters), and the result is a strong interaction that impacts the local plasma and neutral densities, momenta and energies. The neutral gas is found to affect plasma edge turbulence primarily through momentum exchange, reducing the radial electric field and enhancing cross-field transport, with consequent implications for the SOL width and divertor heat loads. Therefore, turbulent plasma and fluid simulations have been performed in multiple tokamak geometries to more closely examine the effects of this interaction. These cases were chosen for the variety in configuration with ISTOK having a toroidal limiter (ie. no divertor), DIII-D having a standard divertor configuration, and MAST-U having a super-X divertor with extended outer divertor legs. Progress towards the characterization of neutral impact on detachment and edge behavior will be presented.   

Effect of asymmetric magnetic islands on profiles, flows, turbulence and transport in nonlinear gyrokinetic simulations

Neoclassical Tearing Modes (NTMs) are a major impediment in the development of operating scenarios of present toroidal fusion devices. We study the effect of radially asymmetric magnetic islands on profiles, flows, turbulence and transport via nonlinear gyrokinetic simulations with the GENE code for the first time. Gradients, turbulence as well as cross-field transport levels progressively decrease at the O-point as the island width is increased in qualitative agreement with recent DIII-D experiments [1]. The island asymmetry plays a key role in the strength of perpendicular shear flows developing just outside the island separatrices. The effect of these shear flows on turbulent structures entering the island interior as well as their effect on cross-field transport and NTM dynamics are discussed. \newline [1] L. Bard\'oczi \textit{et al}, PRL \textbf{116} 215001 (2016)   

Drift kinetic theory of neoclassical tearing mode physics

Orbit averaged equations for the particle responses to a small magnetic island are derived, expanding the drift kinetic equation in the ratio of island width to tokamak plasma minor radius, assumed small. Analytic solutions demonstrate that the particles follow drift orbits which have the same geometry as the magnetic island flux surfaces, but are shifted radially by an amount that is proportional to the poloidal Larmor radius (in opposite directions for opposite signs of parallel velocity). The distribution function is flattened across these drift island structures, rather than across the magnetic island. Numerical solutions of our equations confirm the existence of the drift orbits. We employ a model momentum-conserving collision operator to evaluate the consequences for neoclassical tearing mode threshold physics, implementing numerical solutions to our orbit-averaged drift kinetic equations in a ``Modified Rutherford Equation''.