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For the efficient and safe operation of experimental advanced superconducting tokamak (EAST), it is necessary to accurately identify and control the plasma current and its central position. In this article, neural network is used to identify the position of the plasma current center. The model trained by the basic back-propagation neural network can well match the relationship between the electromagnetic diagnostic signals and plasma current center positions. Both noisy simulation data and experimental data are applied to train and test the neural network inference model. Adding 0.1% noise to the training data is proven to improve the noise immunity of the inference model. Basic neural networks trained with both noisy simulation data and actual experimental data show good results with sufficient inputs; however, in both cases, the performance degrades significantly when only the poloidal field coil currents are given as inputs. For this kind of time-series problem, the dynamic neural network containing delay and feedback architecture is introduced, and an improved model requiring much fewer inputs is trained and tested for current center inference. Some parameters of this model are compared and analyzed in this article. With suitable neural network architecture, the mapping between the controlled variables (poloidal field coil currents) and response variables (plasma current center) can be well-established.

Both collisionless and collisional Landau fluid (LF) closure have been developed and implemented in two-fluid plasma simulation framework BOUT++, taking full advantage of the fast non-Fourier method (Dimits, 2014). The spectral range of good fit can be conveniently extended to larger domain by adding more Lorentzians. The scaling for upper limit of wavenumber resolved in collisionless LF operator and the fitting coefficients for the collisional LF operator, the later is extended to weakly collisional regime ( ν e ∗ ∼ 0 . 01 ), are presented in this paper. The flux limited expression q ∥ e FL is reduced to free streaming expression q ∥ e FS in collisionless limit and gives classical Spitzer–Harm result q ∥ e SH in collisional limit as we expected. The collisional LF closure recovers the classical Spitzer–Harm result q ∥ e SH in collisional limit and is same as the collisionless LF closure in collisionless limit. The test cases also obviously demonstrate the nonlocal effects from LF closures and responding to different boundary conditions in open surface region. This work will make it more applicable and possible to include the Landau damping kinetic effect in the fluid simulation of tokamak plasma.

A simulation study has been conducted of the physical mechanisms behind the weakly coherent mode (WCM) and its produced particle transport in the I-mode edge plasmas by using the BOUT++ code. The WCM is identified in our simulations by its poloidal and radial distributions as well as its frequency and wavenumber spectra. Its produced radial particle flux is calculated and compared with the experimental value. The good agreement indicates that the WCM is an important particle transport channel in the I-mode pedestal. It is found that the WCM can transport particles across the strong outer shear layer of the E r well established in the formation of I-mode, based on which a possible explanation is provided why I-mode does not feature a density pedestal. The key point lies in the change of the cross-phase between the electric potential and density fluctuations induced by the E × B Doppler shift. In the strong shear layer, although the electric potential fluctuation is significantly suppressed, the cross-phase is close to π/2, resulting in a strong drive of the density fluctuation and particle transport. To identify the physical nature of the WCM, a linear dispersion relation for drift Alfvén modes is derived in the slab geometry. A drift Alfvén wave instability is found to have similar dependence to the simulated linear instability behind the WCM on the resistivity and the parallel electron pressure gradient and thermal force terms in the parallel Ohm’s law.

Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture n=0 axisymmetric mode evolution in realistic tokamak configurations. These improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transient (e.g., ELM, disruption) and transport time-scale simulations., 26 pages, 14 figures

A study of a dataset of JET H-mode plasma with the Be/W ITER-like wall (JET-ILW) shows that reaching the edge MHD ballooning limit leads to confinement degradation. However, unlike JET plasmas with a carbon wall (JET-C), the JET-ILW plasmas stay in a marginal dithering phase for a relatively long period, associated with a higher (≈20%) H-mode density limit (HDL) than JET-C equivalents. This suggests that ITER could be operated in H-mode with higher density than the scaling based on carbon wall devices, but likely with a dithering phase plasma with lower confinement. A new, reliable estimator for JET E r, min has been derived by combining HRTS measurements of pedestal gradient and edge-SOL decay lengths. JET radial E r ETB wells are observed in the range of −15 to −60 kV m−1 in high performance H-modes, consistent with previous CXRS results in ASDEX Upgrade. The results imply that a higher positive E × B shear in the near SOL plays a role in sustaining a marginal phase in JET-ILW which leads to a higher HDL than that in JET-C. The results of the JET-ILW dataset show agreement with the Goldston finite collisionality HD model for SOL broadening at high collisionality. A hypothesis for the dithering H-mode phase is proposed: as n e,SOL increases, ν ∗,SOL increases, SOL broadens, E r shear decreases, triggers L-mode; n e drops, ν ∗,SOL decreases, SOL becomes narrower, and E r shear increases, triggering H-mode, resulting in a cycle of H–L–H- oscillations. For burning plasma devices, such as ITER, operating just below the MHD limit for the dithering phase could be a promising regime for maximising core density, and fusion performance while minimising plasma-material interaction. The oscillatory signal during the dithering phase could be used as a precursor of undesirable plasma performance for control purposes.

An impact of the equilibrium radial electric field on energy loss processes after pedestal collapse is numerically investigated using the BOUT++ framework. Using linear stability analysis, the resistive ballooning mode is shown to be stabilized by the radial shear of the equilibrium radial electric field. On the other hand, the energy loss level after the pedestal collapse increases if the equilibrium radial electric field is taken into account. The spatio‐temporal and phase diagram analyses show that the equilibrium radial electric field partially cancels the fluctuation‐driven toroidally axisymmetric radial electric field and weakens the E × B shearing rate after pedestal collapse, weakening the turbulence suppression by vortex shearing. The equilibrium radial electric field therefore increases turbulence intensity in nonlinear cyclic oscillations among pressure gradient, E × B shearing rate, and turbulence intensity, which gives rise to subsequent bursts of turbulent transport and increases the energy loss level.

We present a novel distributed union-find algorithm that features asynchronous parallelism and k-d tree based load balancing for scalable visualization and analysis of scientific data. Applications of union-find include level set extraction and critical point tracking, but distributed union-find can suffer from high synchronization costs and imbalanced workloads across parallel processes. In this study, we prove that global synchronizations in existing distributed union-find can be eliminated without changing final results, allowing overlapped communications and computations for scalable processing. We also use a k-d tree decomposition to redistribute inputs, in order to improve workload balancing. We benchmark the scalability of our algorithm with up to 1,024 processes using both synthetic and application data. We demonstrate the use of our algorithm in critical point tracking and super-level set extraction with high-speed imaging experiments and fusion plasma simulations, respectively., Accepted by IEEE Transactions on Visualization and Computer Graphics (IEEE TVCG Special Issue on IEEE PacificVis 2021)

The steady state radial electric field (Er) is calculated by coupling a plasma transport model with the quasi-neutrality constraint and the vorticity equation within the BOUT++ framework. Based on the experimentally measured plasma density and temperature profiles in Alcator C-Mod discharges, the effective radial particle and heat diffusivities are inferred from the set of plasma transport equations. The effective diffusivities are then extended into the scrape-off layer (SOL) to calculate the plasma density, temperature and flow profiles across the separatrix into the SOL with the electrostatic sheath boundary conditions (SBC) applied on the divertor plates. Given these diffusivities, the electric field can be calculated self-consistently across the separatrix from the vorticity equation with SBC coupled to the plasma transport equations. The sheath boundary conditions act to generate a large and positive Er in the SOL, which is consistent with experimental measurements. The effect of magnetic particle drifts is shown to play a significant role on local particle transport and Er by inducing a net particle flow in both the edge and SOL regions.

To study the transport of Li species in the plasma with real-time Li aerosol injection on EAST, a model has been developed by reducing Braginskii's equations, and implemented in the frame of BOUT++. The simulation results show that Li atoms propagate inwards since the Li injection, and their penetration depth depends on both the local plasma conditions along their path and initial injection velocity. It is also found that Li ions accumulate rapidly in the edge, and only a small fraction of Li species can transport cross the separatrix into the core. In the poloidal direction, Li ions drift swiftly downwards along the field lines, and transport much faster at the high field side than at the low field side. The interaction between background plasma and Li species plays a critical role in determining the edge plasma profile. It is found that real-time Li injection raises the plasma density in the pedestal region and reduces the plasma temperature, just as has been observed experimentally. Keywords: BOUT++, Lithium injection, Edge plasma

A generalized linear dispersion relation of electromagnetic slab universal modes is derived, taking into account arbitrary ion charge state, electron finite Larmor radius (FLR) effects, and Debye shielding effects. As a consequence, it provides more accurate predictions and is applicable to a wider range of plasmas. We find that electron FLR effects have a weakly stabilizing effect on the slab universal instability in electron-ion plasma, while Debye shielding strongly stabilizes this instability when $\lambda_D$ approaches $\rho_i$ ($\lambda_D$ is the Debye length and $\rho_i$ is the ion gyro-radius). In particular, we examine the stability criterion for this instability in electron-positron pair plasmas, and find that the instability persists in this simplest plasma system as long as the pair plasma number density exceeds the critical value $n_c=B^2/(8\pi m_e c^2)$., Comment: 31 pages, 11 figures

A reproducible stationary high-confinement regime with small ``edge-localized modes'' (ELMs) has been achieved recently in the Experimental Advanced Superconducting Tokamak, which has a metal wall and low plasma rotation as projected for a fusion reactor. We have uncovered that this small ELM regime is enabled by a wide edge transport barrier (pedestal) with a low density gradient and a high density ratio between the pedestal foot and top. Nonlinear simulations reveal, for the first time, that the underlying mechanism for the observed small ELM crashes is the upper movement of the peeling boundary induced by an initial radially localized collapse in the pedestal, which stops the growth of instabilities and further collapse of the pedestal, thus providing a physics basis for mitigating ELMs in future steady-state fusion reactors.

In order to study the distribution and evolution of the transient heat flux on HL-2A during edge-localized-mode (ELM) bursts, the BOUT++ electromagnetic six-field two-fluid model is used to simulate the pedestal collapse under the lower single-null divertor geometry. The equilibrium profiles of HL-2A ELMy H-mode discharge No. 24 953 are adopted as the initial condition in the original case. In this case, linear analysis shows that the resistive ballooning mode (RBM) and drift-Alfven wave are unstable to this equilibrium, and RBM is the dominant instability. The evolutions of the radial heat fluxes at the outer mid-plane and heat fluxes to the inner and outer targets during the ELM event are presented. Six more equilibria are constructed based on the original case to find out the influence of the pedestal profiles on the peak electron heat flux. The results indicate that the heat flux increases with temperature and/or density, and the theoretical analysis and simulation results consistently show that the heat flux q∥e is proportional to ne0,SEPTe0,SEP32.

In this work, the kinetic Landau-fluid (LF) closure with collision and periodic boundary condition is used in the development of the deep learning (DL) surrogate model. A classical neural network, namely, feedforward neural network or sometimes termed multilayer perceptron, is constructed and trained to learn the kinetic LF closure in the static limit and arbitrary mean free path in configuration space. The preliminary relation between best hyperparameters and critical parameters for data generation is found. Compared with the numerical approach (non-Fourier method) of the LF closure, the deep learning surrogate model shows an order of magnitude of improvement in terms of accuracy. Perhaps most importantly, the surrogate model closure has been integrated for the first time with fluid simulations. Our DL-enabled fluid simulations, for the first time, give the correct Landau damping rate for a wide range of wave vectors, while the Hammett–Perkins closure cannot produce the correct damping rate. We correctly connect the collisionless Hammett–Perkins closure and collisional Braginskii closure to reproduce the intrinsic nonlocal feature of the heat flux with DL techniques. We address the most concerning error accumulation problem and find that simulations with the deep learning surrogate model are as good as, if not better than, simulations with the analytic closure in terms of long-term numerical stability in the linear Landau damping test.

The first result of applying the machine/deep learning technique to the fluid closure problem is presented in this paper. As a start, three different types of neural networks (multilayer perceptron (MLP), convolutional neural network (CNN) and two-layer discrete Fourier transform (DFT) network) were constructed and trained to learn the well-known Hammett-Perkins Landau fluid closure in configuration space. We find that in order to train a well-preformed network, a minimum size of the training data set is needed; MLP also requires a minimum number of neurons in the hidden layers that equals the degrees of freedom in Fourier space despite the fact that training data is fed in configuration space. Out of the three models, DFT performs the best for the clean data, most likely due to the existence of the simple Fourier expression for Hammett-Perkins closure, but it is the least robust with respect to input noise. Overall, with appropriate tuning and optimization, all three neural networks are able to accurately predict the Hammett-Perkins closure and reproduce the intrinsic \textit{nonlocal} feature, suggesting a promising path to calculating more sophisticated closures with the machine/deep learning technique.

The dependence of shaping effects on the growth rate of collisionless and resistive ballooning mode (CBM/RBM) is numerically investigated. That of the drift ballooning modes (DCBM/DRBM) is also investigated by taking kinetic effects into account. Resistivity scans of linear growth rates of CBM/RBM and DCBM/DRBM in a circular geometry show that both modes have 3 branches in accordance with decreasing resistivity, fast, re- sistive and collisionless branch. The last two branches are in the edge relevant resistivity regime and are in the scope of this paper. For CBM/RBM, shaping effect on the growth rate becomes weak with increasing resistivity and the growth rate monotonically increases with decrease of the elongation and increase of the triangularity, on the other hand, the opposite tendency appears on the triangularity for DCBM, namely it weakly decreases with increase of the triangularity. This fact indicates that the inverted D-shaped equilibrium can be unstable against DCBM compared with the D-shaped equilibrium.

Precise delivery of mass to burning plasmas is a problem of growing interest in magnetic fusion. The answers to how much mass is necessary and sufficient can vary depending on parameters such as the type of atoms involved, the type of applications, plasma conditions, mass injector, and injection timing. Motivated by edge localized mode (ELM) control in H-mode plasmas, disruption mitigation and other applications in magnetic fusion, we report progress and new possibilities in mass delivery based on hollow pellets. Here, a hollow pellet refers to a spherical shell mass structure with a hollow core. Based on an empirical model of pellet ablation, coupled with BOUT++ simulations of ELM triggering threshold, hollow pellets are found to be attractive in comparison with solid spheres for ELM control. By using hollow pellets, it is possible to tailor mass delivery to certain regions of edge plasmas while minimizing core contamination and reducing the total amount of mass needed. We also include experimental progress in mass delivery experiments, in-situ diagnostics and hollow pellet fabrication, and emphasize new experimental possibilities for ELM control based on hollow pellets. A related application is the disruption mitigation scheme using powder encapsulated inside hollow shells. Further experiments will also help to resolve known discrepancies between theoretical predictions and experiments in using mass injection for ELM control and lead to better predictive models for ELM stability and triggering., Comment: Manuscript prepared for reviews by {\it Nuclear Fusion}, following the initial presentation in the 27th IAEA FEC, Gandhinagar, India, Oct. 22 - 27, 2018

An interplay between fluctuation driven toroidal axisymmetric flows (convective cell modes) and resistive ballooning mode turbulence after the pedestal collapse is numerically studied by a four-field reduced MHD model in the BOUT++ framework. The strong flow shear suppresses the radial transport of pressure filaments, and the pressure profile in the pedestal region is partially recovered. As a result, a secondary instability is quasilinearly excited, which yields a secondary collapse. The subsequent damped oscillation is also analyzed by phase diagram analysis.

Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al., Phys. Plasmas 23, 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E × B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E × B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the Er shear. Adopting the much more general shape of E × B shear (ωE=Er/RBθ) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode.

The geodesic acoustic mode (GAM) is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the second order and the finite β effect. The general dispersion relation is derived from the gyro-kinetic equations in the presence of nonzero δ A ∥, the parallel component of the perturbed magnetic vector potential. Transparent and concise expressions for the GAM frequency and Landau damping rate in the presence of the second order FOW effect and finite β effect are first presented. It is clearly shown that the m = ±2 harmonics dominant δ A ∥ and the kinetic expression of δ A ∥ have the same form as the fluid one. For the real frequency, the electromagnetic effect introduces a term on the order of q2β, which is comparable to the second order electrostatic terms, namely, the terms introduced by the second order FOW resonance effect. While for the collisionless damping rate, δ A ∥ does not directly introduce β–dependent terms, but affects the damping rate via modifying the real frequency. Besides, our analytical result shows good agreement with the numerical examinations.

The kinetic Landau-fluid (LF) closure which can be regarded as the exact closure is derived. For Maxwellian plasma, the kinetic closure is the same as Hammett-Perkins closure in static limit and totally the same with Chang-Callen closure. A new LF closure for arbitrary frequency response constructed with harmonic average technique is presented in this paper. This new LF closure bridges the existing LF closures in the low and high frequency limits: it recovers Hammett-Perkins closure when weight coefficient κ = 0 and converges to Chang-Callen closure at high frequency when weight coefficient κ = 1. By picking an appropriate κ, the harmonic average closure contains both nonlocal transport and local transport and the resulting fluid response function of a three moment fluid model well matches the exact kinetic response function within the entire frequency range. On the computational side, a sum of diffusion-convection solves (SDCS) method is developed to facilitate numerical implementation of the harmonic average LF closure. By using SDCS method, good agreement is achieved for the response functions between driven initial-value simulations and matrix eigenvalue calculations within the BOUT++ framework. The harmonic average closure of shifted-Maxwellian is also outlined.

By using the specific co-neutral beam injection (co-NBI) and counter-NBI systems on EAST, an alternating flow shear discharge has been obtained to study the impact of the flow shear on ballooning-driven edge localized modes (ELMs) at a fixed high collisionality (). The results reveal that the increased flow shear can significantly mitigate ELMs, or even totally suppress ELMs when the shear is large enough. Our simulations with BOUT support the observations on EAST, and further indicate that the increased can both reduce the linear growth rate of the ballooning mode and shorten its growth time (phase coherence time, PCT). The enhanced nonlinear interactions shorten the PCT of the ballooning mode, as validated by the bispectrum study on EAST. All those studies suggest a new way to control ELMs.

We have performed linear and nonlinear simulations to study the drive mechanism of the quasi-coherent modes (QCM) during the inter-edge localized mode period in HL-2A. With an unstable Resistive-Ballooning mode from linear simulations, the nonlinear simulation has successfully reproduced the QCM inside the separatrix at the outer mid-plane. The poloidal wave number and frequency from fluctuation analysis are almost the same as the experimental results. The phase shift between the electrical potential and the density fluctuation matches. Linear and nonlinear global profile scans show that the QCM is triggered by the density gradient. Based on these scans, some other experimental observations of the QCM are explained.

We present the linear simulations of edge plasma instabilities using the 3-field peeling-ballooning model and gyro-Landau-fluid model under the BOUT++ framework. A series of realistic equilibria of shifted circular geometry are generated by a global equilibrium solver CORSICA, where the Shafranov shift, elongation effects, and bootstrap current are included. The linear growth rate spectrum of the peeling-ballooning modes is shown in a wide range of pressure gradient and parallel current density in the pedestal region. The results show that the bootstrap current stabilizes high beta ballooning modes. The simulations with different fractions of bootstrap current indicate a trend for the existence of the high beta peeling-ballooning mode stability region. Taking the kinetic effects into account, the linear simulations of kinetic peeling-ballooning mode using the gyro-Landau-fluid model show that this region can be accessed.We present the linear simulations of edge plasma instabilities using the 3-field peeling-ballooning model and gyro-Landau-fluid model under the BOUT++ framework. A series of realistic equilibria of shifted circular geometry are generated by a global equilibrium solver CORSICA, where the Shafranov shift, elongation effects, and bootstrap current are included. The linear growth rate spectrum of the peeling-ballooning modes is shown in a wide range of pressure gradient and parallel current density in the pedestal region. The results show that the bootstrap current stabilizes high beta ballooning modes. The simulations with different fractions of bootstrap current indicate a trend for the existence of the high beta peeling-ballooning mode stability region. Taking the kinetic effects into account, the linear simulations of kinetic peeling-ballooning mode using the gyro-Landau-fluid model show that this region can be accessed.

The heat flux distributions on divertor targets in H-mode plasmas are serious concerns for future devices. We seek to simulate the tokamak boundary plasma turbulence and heat transport in the edge localized mode-suppressed regimes. The improved BOUT++ model shows that not only Ip but also the radial electric field Er plays an important role on the turbulence behavior and sets the heat flux width. Instead of calculating Er from the pressure gradient term (diamagnetic Er), it is calculated from the plasma transport equations with the sheath potential in the scrape-off layer and the plasma density and temperature profiles inside the separatrix from the experiment. The simulation results with the new Er model have better agreement with the experiment than using the diamagnetic Er model: (1) The electromagnetic turbulence in enhanced Dα H-mode shows the characteristics of quasi-coherent modes (QCMs) and broadband turbulence. The mode spectra are in agreement with the phase contrast imaging data and almost has no change in comparison to the cases which use the diamagnetic Er model; (2) the self-consistent boundary Er is needed for the turbulence simulations to get the consistent heat flux width with the experiment; (3) the frequencies of the QCMs are proportional to Er, while the divertor heat flux widths are inversely proportional to Er; and (4) the BOUT++ turbulence simulations yield a similar heat flux width to the experimental Eich scaling law and the prediction from the Goldston heuristic drift model.

Results presented here are from 6-field Landau-Fluid simulations using shifted circular cross-section tokamak equilibria on BOUT++ framework. Linear benchmark results imply that the collisional and collisionless Landau resonance closures make a little difference on linear growth rate spectra which are quite close to the results with the flux limited Spitzer-Harm parallel flux. Both linear and nonlinear simulations show that the plasma current profile plays dual roles on the peeling-ballooning modes that it can drive the low-n peeling modes and stabilize the high-n ballooning modes. For fixed total pressure and current, as the pedestal current decreases due to the bootstrap current which becomes smaller when the density (collisionality) increases, the operational point is shifted downwards vertically in the Jped – α diagram, resulting in threshold changes of different modes. The bootstrap current can slightly increase radial turbulence spreading range and enhance the energy and particle transports by increasing the perturbed amplitude and broadening cross-phase frequency distribution.Results presented here are from 6-field Landau-Fluid simulations using shifted circular cross-section tokamak equilibria on BOUT++ framework. Linear benchmark results imply that the collisional and collisionless Landau resonance closures make a little difference on linear growth rate spectra which are quite close to the results with the flux limited Spitzer-Harm parallel flux. Both linear and nonlinear simulations show that the plasma current profile plays dual roles on the peeling-ballooning modes that it can drive the low-n peeling modes and stabilize the high-n ballooning modes. For fixed total pressure and current, as the pedestal current decreases due to the bootstrap current which becomes smaller when the density (collisionality) increases, the operational point is shifted downwards vertically in the Jped – α diagram, resulting in threshold changes of different modes. The bootstrap current can slightly increase radial turbulence spreading range and enhance the energy and particle transports by incre...

A high-order finite-volume algorithm is developed for the Fokker-Planck Operator (FPO) describing Coulomb collisions in strongly magnetized plasmas. The algorithm uses a generic fourth-order reconstruction scheme on an unstructured grid in the velocity space spanned by parallel velocity and magnetic moment. By analytically mapping between different coordinates, it produces an accurate and density-conserving numerical FPO for an arbitrary choice of velocity space coordinates. A linearized FPO in constants-of-motion coordinates is implemented as an example of the present algorithm combined with a cut-cell merging procedure. Numerical tests include the thermalization of a test distribution with a background Maxwellian at a different temperature, and the return to isotropy for a distribution initialized with a velocity space loss-cone. Utilization of the method for a nonlinear FPO is straightforward but requires evaluation of the Trubnikov-Rosenbluth potentials.

Theoretical and computational investigations of boundary-plasma microturbulence which take into account important effects of the geometry of diverted tokamaks—in particular, the effect of X-point magnetic shear and the termination of field lines on divertor plates—are presented. We first generalize our previous 'heuristic boundary condition' which describes, in a lumped model, the closure of currents in the vicinity of the X-point region to encompass three current-closure mechanisms. We then use this boundary condition to derive the dispersion relation for low-beta flute-like modes in the divertor-leg region under the combined drives of curvature, sheath impedance and divertor tilt effects. The results indicate the possibility of strongly growing instabilities, driven by sheath boundary conditions, and localized in either the private or common flux region of the divertor leg depending on the radial tilt of divertor plates. We revisit the issue of X-point effects on blobs, examining the transition from blobs terminated by X-point shear to blobs that extend over both the main SOL and divertor legs. We find that, for a main-SOL blob, this transition occurs without a free-acceleration period as previously thought, with X-point termination conditions applying until the blob has expanded to reach the divertor plate. We also derive propagation speeds for divertor-leg blobs. Finally, we present fluid simulations of the C-Mod tokamak from the BOUT edge fluid turbulence code, which show main-SOL blob structures with similar spatial characteristics to those observed in the experiment, and also simulations which illustrate the possibility of fluctuations confined to divertor legs.

Results are presented for turbulence simulations with the fluid edge turbulence code BOUT [X.Q. Xu, R.H. Cohen, Contr. Plas. Phys. 36 (1998) 158]. The present study is focussed on turbulence in the divertor leg region and on the role of the X-point in the structure of turbulence. Results of the present calculations indicate that the ballooning effects are important for the divertor fluctuations. The X-point shear leads to weak correlation of turbulence across the X-point regions, in particular for large toroidal wavenumber. For the saturated amplitudes of the divertor region turbulence it is found that amplitudes of density fluctuations are roughly proportional to the local density of the background plasma. The amplitudes of electron temperature and electric potential fluctuations are roughly proportional to the local electron temperature of the background plasma.

The edge-plasma profiles and fluxes to the divertor and walls of a tokamak with a magnetic X-point are simulated by coupling a 2D transport code (UEDGE) and a 3D turbulence code (BOUT). A relaxed iterative coupling scheme is used where each code is run on its characteristic time scale, resulting in a statistical steady state. Plasma variables of density, parallel velocity, and separate ion and electron temperatures are included, together with a fluid neutral model for recycling neutrals at material surfaces. Results for the DIII-D tokamak parameters show that the turbulence is preferentially excited in the outer radial region of the edge where magnetic curvature is destabilizing, yielding substantial plasma particle flux to the main chamber walls. The coupled transport/turbulence simulation technique provides a strategy to achieve physics-based predictions for future device performance.

An overview of the research capabilities and the future plans on the MA-class National Spherical Torus Experiment (NSTX) at Princeton is presented. NSTX research is exploring the scientific benefits of modifying the field line structure from that in more conventional aspect ratio devices, such as the tokamak. The relevant scientific issues pursued on NSTX include energy confinement, MHD stability at high beta, non-inductive sustainment, solenoid-free start-up, and power and particle handling. In support of the NSTX research goal, research tools are being developed by the NSTX team. In the context of the fusion energy development path being formulated in the US, an ST-based Component Test Facility (CTF) and, ultimately a high beta Demo device based on the ST, are being considered. For these, it is essential to develop high performance (high beta and high confinement), steady-state (non-inductively driven) ST operational scenarios and an efficient solenoid-free start-up concept. We will also briefly describe the Next-Step-ST (NSST) device being designed to address these issues in fusion-relevant plasma conditions.

Results of recent modeling of tokamak edge plasma with the turbulence code BOUT are presented. In previous studies with BOUT, the background profiles of plasma density and temperature were set as flux surface functions. However, in the divertor region of a tokamak, the temperature is typically lower and density is higher than those at the mid-plane. To account for this in the present study, a poloidal variation of background plasma density and temperature is included to provide a more realistic model. For poloidally uniform profiles of the background plasma, the calculated turbulence amplitude peaks near outer mid-plane, while in the divertor region the amplitude is small. However, present simulations show that as the background plasma profiles become more poloidally non-uniform, the amplitude of density fluctuations, n i , starts peaking in the divertor. It is found that in the divertor region the amplitude of n i fluctuations grows approximately linearly with the local density of the background plasma, n i0 , while the amplitudes of T e and Φ fluctuations are positively correlated with the local electron temperature, T e0 . Correlation analysis shows that plasma turbulence above and below the x-point is largerly uncorrelated.

The status of coupling the fluid 3D turbulence code BOUT and the fluid plasma/neutral 2D transport code UEDGE is reported, where both codes simulate the edge region of diverted tokamaks from several cm inside the magnetic separatrix to the far scrape-off layer (SOL), thereby including the magnetic X-point. Because the characteristic time scale of the turbulence is short (∼ 10 -5 - 10 -4 s) and the profile evolution time scale can be long (∼ 10 -2 - 10 -1 s owing to recycling), an iterative scheme is used that relaxes the turbulent fluxes passed from BOUT to LEDGE and the profiles from UEDGE to BOUT over many coupling steps. Each code is run on its own characteristic time scale, yielding a statistically averaged steady state. For this initial study, the ion and neutral densities and parallel velocities are evolved, while the temperature profiles are stationary. Here the turbulence code is run in the electrostatic approximation. For this example of self-consistent coupling with strong L-mode-like turbulence, the ion flux to the main-chamber exceeds that to the divertor plates.

Research on the Alcator C-Mod tokamak [1] is focused on high particle- and power-density plasma regimes to understand particle and energy transport in the core, the dynamics of the H-mode pedestal, and scrape-off layer and divertor physics. The auxiliary heating is provided exclusively by RF waves, and both the physics and technology of RF heating and current drive are studied. The momentum which is manifested in strong toroidal rotation, in the absence of direct momentum input, has been shown to be transported in from the edge of the plasma following the L–H transition, with timescale comparable to that for energy transport. In discharges which develop internal transport barriers, the rotation slows first inside the barrier region, and then subsequently outside of the barrier foot. Heat pulse propagation studies using sawteeth indicate a very narrow region of strongly reduced energy transport, located near r/a = 0.5. Addition of on-axis ICRF heating arrests the buildup of density and impurities, leading to quasi-steady conditions. The quasi-coherent mode associated with enhanced D-Alpha (EDA) H-mode appears to be due to a resistive ballooning instability. As the pedestal pressure gradient and temperature are increased in EDA H-mode, small ELMs appear; detailed modelling indicates that these are due to intermediate n peeling–ballooning modes. Phase contrast imaging has been used to directly detect density fluctuations driven by ICRF waves in the core of the plasma, and mode conversion to an intermediate wavelength ion cyclotron wave has been observed for the first time. The bursty turbulent density fluctuations, observed to drive rapid cross-field particle transport in the edge plasma, appear to play a key role in the dynamics of the density limit. Preparations for quasi-steady-state advanced tokamak studies with lower hybrid current drive are well underway, and time dependent modelling indicates that regimes with high bootstrap fraction can be produced.

Research on the spherical torus (or spherical tokamak) (ST) is being pursued to explore the scientific benefits of modifying the field line structure from that in more moderate aspect ratio devices, such as the conventional tokamak. The ST experiments are being conducted in various US research facilities including the MA-class National Spherical Torus Experiment (NSTX) at Princeton, and three medium sized ST research facilities: PEGASUS at University of Wisconsin, HIT-II at University of Washington, and CDX-U at Princeton. In the context of the fusion energy development path being formulated in the US, an ST-based Component Test Facility (CTF) and, ultimately a Demo device, are being discussed. For these, it is essential to develop high performance, steady-state operational scenarios. The relevant scientific issues are energy confinement, MHD stability at high beta (?), non-inductive sustainment, Ohmic-solenoid-free start-up, and power and particle handling. In the confinement area, the NSTX experiments have shown that the confinement can be up to 50% better than the ITER-98-pby2 H-mode scaling, consistent with the requirements for an ST-based CTF and Demo. In NSTX, CTF-relevant average toroidal beta values ?T of up to 35% with a near unity central ?T have been obtained. NSTX will be exploring advanced regimes where ?T up to 40% can be sustained through active stabilization of resistive wall modes. To date, the most successful technique for non-inductive sustainment in NSTX is the high beta poloidal regime, where discharges with a high non-inductive fraction (~60% bootstrap current+NBI current drive) were sustained over the resistive skin time. Research on radio-frequency (RF) based heating and current drive utilizing high harmonic fast wave and electron Bernstein wave is also pursued on NSTX, PEGASUS, and CDX-U. For non-inductive start-up, the coaxial helicity injection, developed in HIT/HIT-II, has been adopted on NSTX to test the method up to Ip ~ 500?kA. In parallel, start-up using a RF current drive and only external poloidal field coils are being developed on NSTX. The area of power and particle handling is expected to be challenging because of the higher power density expected in the ST relative to that in conventional aspect-ratio tokamaks. Due to its promise for power and particle handling, liquid lithium is being studied in CDX-U as a potential plasma-facing surface for a fusion reactor.

The intermittent turbulent transport in the scrape-off-layer (SOL) of Alcator C-Mod [I.H. Hutchinson, R. Boivin, P.T. Bonoli et al., Nucl. Fusion 41, 1391 (2001)] is studied experimentally by imaging with a very high density of spatial measurements. The two-dimensional structure and dynamics of emission from a localized gas puff are observed, and intermittent features (also sometimes called “filaments” or “blobs”) are typically seen. The characteristics of the spatial structure of the turbulence and their relationship to the time-averaged SOL profiles are discussed and compared with those measured on the National Spherical Torus Experiment [M. Ono, S. M. Kaye, Y.-K. M. Pong et al., Nucl. Fusion 40, 557 (2000)]. The experimental observations are compared also with three-dimensional nonlinear numerical simulations of edge turbulence. Radial profiles of the poloidal wave number spectra and the poloidal scale length from the simulations are in reasonable agreement with those obtained from the experimental ima...

A271 EXPERIMENTAL CHARACTERIZATION OF COHERENT, RADIALLY-SHEARED ZONAL FLOWS IN THE DIII-D TOKAMAK. Application of time-delay-estimation techniques to two-dimensional measurements of density fluctuations, obtained with beam emission spectroscopy in DIII-D plasmas, has provided temporally and spatially resolved measurements of the turbulence flow-field. Features that are characteristic of self-generated zonal flows are observed in the radial region near 0.85 {

A six-field two-fluid model has been used to simulate density fluctuations. The equilibrium is generated by experimental measurements for both Deuterium (D) and Hydrogen (H) plasmas at the lowest densities of DIII-D low to high confinement (L-H) transition experiments. In linear simulations, the unstable modes are found to be resistive ballooning modes with the most unstable mode number n = 30 or . The ion diamagnetic drift and convection flow are balanced when the radial electric field (E r ) is calculated from the pressure profile without net flow. The curvature drift plays an important role in this stage. Two poloidally counter propagating modes are found in the nonlinear simulation of the D plasma at electron density m−3 near the separatrix while a single ion mode is found in the H plasma at the similar lower density, which are consistent with the experimental results measured by the beam emission spectroscopy (BES) diagnostic on the DIII-D tokamak. The frequency of the electron modes and the ion modes are about 40 kHz and 10 kHz respectively. The poloidal wave number is about 0.2 cm −1 () for both ion and electron modes. The particle flux, ion and electron heat fluxes are ~3.5–6 times larger for the H plasma than the D plasma, which makes it harder to achieve H-mode for the same heating power. The change of the atomic mass number A from 2 to 1 using D plasma equilibrium make little difference on the flux. Increase the electric field will suppress the density fluctuation. The electric field scan and ion mass scan results show that the dual-mode results primarily from differences in the profiles rather than the ion mass.

Edge Localised Modes (ELMs) in ITER Q = 10 H-mode plasmas are likely to lead to large transient heat loads to the divertor. To avoid an ELM induced reduction of the divertor lifetime, the large ELM energy losses need to be controlled. In ITER, ELM control is foreseen using magnetic field perturbations created by in-vessel coils and the injection of small D2 pellets. ITER plasmas are characterised by low collisionality at a high density (high fraction of the Greenwald density limit). These parameters cannot simultaneously be achieved in current experiments. Therefore, the extrapolation of the ELM properties and the requirements for ELM control in ITER relies on the development of validated physics models and numerical simulations. In this paper, we describe the modelling of ELMs and ELM control methods in ITER. The aim of this paper is not a complete review on the subject of ELM and ELM control modelling but rather to describe the current status and discuss open issues.

The resistive X point mode is shown to be the dominant mode in boundary plasmas in X point divertor geometry. The poloidal fluctuation phase velocity from the simulation results of the resistive X point turbulence shows a structure across the separatrix that is experimentally measured in many fusion devices. The fluctuation phase velocity is larger than the E × B velocity in both L and H mode phases. It is also demonstrated that there is a strong poloidal asymmetry of particle flux in the proximity of the separatrix. Turbulence suppression in the L-H transition results when sources of energy and particles drive sufficient gradients, as in the experiments.