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Understanding turbulence in the divertor leg of tokamaks is essential to predict the heat deposition profile on the divertor plate. This in turn is important for evaluating advanced divertor configurations, such as the super-X divertor. Within the divertor region, the private flux region is of interest because it is relatively unaffected by turbulence extending from the outboard midplane, so instabilities in this region could have a particularly pronounced effect on transport. These instabilities are modeled using the Arbitrary Topology Equation Reader (ArbiTER) eigenvalue code. Eigenmodes are examined further by comparing physics models to determine the fundamental mechanisms behind their formation and quantifying the effect of individual terms. This analysis is conducted on both conventional and super-X divertors to compare these effects. The resulting analysis reveals the presence of a geodesic curvature driven instability that is significantly more pronounced in the super-X configuration.

The two-dimensional fluid turbulence code SOLT is employed to study the role of midplane turbulence on the scrape-off-layer (SOL) heat flux width of tokamak plasmas. The physics simulated includes curvature-driven-interchange modes, sheath losses, and perpendicular turbulent diffusive and convective (blob) transport. Midplane SOL profiles of density, temperature and parallel heat flux are obtained from the simulation and compared with experimental results from the National Spherical Torus Experiment (NSTX) to study the scaling of the heat flux width with power and plasma current. It is concluded that midplane turbulence is the main contributor to the SOL width for the low power ELM-free H-mode discharges studied, while additional physics is required to explain the plasma current scaling of the SOL width observed experimentally in higher power discharges. Additional simulations predict a transition to a convectively-dominated SOL at critical values of power and connection length.

Major developments on the Mega Amp Spherical Tokamak (MAST) have enabled important advances in support of ITER and the physics basis of a spherical tokamak (ST) based component test facility (CTF), as well as providing new insight into underlying tokamak physics. For example, L–H transition studies benefit from high spatial and temporal resolution measurements of pedestal profile evolution (temperature, density and radial electric field) and in support of pedestal stability studies the edge current density profile has been inferred from motional Stark effect measurements. The influence of the q-profile and E × B flow shear on transport has been studied in MAST and equilibrium flow shear has been included in gyro-kinetic codes, improving comparisons with the experimental data. H-modes exhibit a weaker q and stronger collisionality dependence of heat diffusivity than implied by IPB98(y,2) scaling, which may have important implications for the design of an ST-based CTF. ELM mitigation, an important issue for ITER, has been demonstrated by applying resonant magnetic perturbations (RMPs) using both internal and external coils, but full stabilization of type-I ELMs has not been observed. Modelling shows the importance of including the plasma response to the RMP fields. MAST plasmas with q > 1 and weak central magnetic shear regularly exhibit a long-lived saturated ideal internal mode. Measured plasma braking in the presence of this mode compares well with neo-classical toroidal viscosity theory. In support of basic physics understanding, high resolution Thomson scattering measurements are providing new insight into sawtooth crash dynamics and neo-classical tearing mode critical island widths. Retarding field analyser measurements show elevated ion temperatures in the scrape-off layer of L-mode plasmas and, in the presence of type-I ELMs, ions with energy greater than 500 eV are detected 20 cm outside the separatrix. Disruption mitigation by massive gas injection has reduced divertor heat loads by up to 70%.

The National Spherical Torus Experiment (NSTX) is currently being upgraded to operate at twice the toroidal field and plasma current (up to 1 T and 2 MA), with a second, more tangentially aimed neutral beam (NB) for current and rotation control, allowing for pulse lengths up to 5 s. Recent NSTX physics analyses have addressed topics that will allow NSTX-Upgrade to achieve the research goals critical to a Fusion Nuclear Science Facility. These include producing stable, 100% non-inductive operation in high-performance plasmas, assessing plasma–material interface (PMI) solutions to handle the high heat loads expected in the next-step devices and exploring the unique spherical torus (ST) parameter regimes to advance predictive capability. Non-inductive operation and current profile control in NSTX-U will be facilitated by co-axial helicity injection (CHI) as well as radio frequency (RF) and NB heating. CHI studies using NIMROD indicate that the reconnection process is consistent with the 2D Sweet–Parker theory. Full-wave AORSA simulations show that RF power losses in the scrape-off layer (SOL) increase significantly for both NSTX and NSTX-U when the launched waves propagate in the SOL. Toroidal Alfven eigenmode avalanches and higher frequency Alfven eigenmodes can affect NB-driven current through energy loss and redistribution of fast ions. The inclusion of rotation and kinetic resonances, which depend on collisionality, is necessary for predicting experimental stability thresholds of fast growing ideal wall and resistive wall modes. Neutral beams and neoclassical toroidal viscosity generated from applied 3D fields can be used as actuators to produce rotation profiles optimized for global stability. DEGAS-2 has been used to study the dependence of gas penetration on SOL temperatures and densities for the MGI system being implemented on the Upgrade for disruption mitigation. PMI studies have focused on the effect of ELMs and 3D fields on plasma detachment and heat flux handling. Simulations indicate that snowflake and impurity seeded radiative divertors are candidates for heat flux mitigation in NSTX-U. Studies of lithium evaporation on graphite surfaces indicate that lithium increases oxygen surface concentrations on graphite, and deuterium–oxygen affinity, which increases deuterium pumping and reduces recycling. In situ and test-stand experiments of lithiated graphite and molybdenum indicate temperature-enhanced sputtering, although that test-stand studies also show the potential for heat flux reduction through lithium vapour shielding. Non-linear gyro kinetic simulations have indicated that ion transport can be enhanced by a shear-flow instability, and that non-local effects are necessary to explain the observed rapid changes in plasma turbulence. Predictive simulations have shown agreement between a microtearing-based reduced transport model and the measured electron temperatures in a microtearing unstable regime. Two Alfven eigenmode-driven fast ion transport models have been developed and successfully benchmarked against NSTX data. Upgrade construction is moving on schedule with initial physics research operation of NSTX-U planned for mid-2015.

Externally launched ion Bernstein wave (IBW) experiments have demonstrated localized electron heating, sheared flows and transport barriers in several tokamaks. Experiments in the tokamak fusion test reactor (TFTR) showed that IBW waves launched from low-field side IBW antennas could drive a velocity shear layer in the central plasma, but the power coupled to the IBW was not sufficient to achieve a transport barrier. This experiment raised important questions concerning where the radio-frequency (rf) power went and whether the anomalous loss channels are more important in larger machines. Recently, it was proposed that the power loss was due to a coaxial electron plasma wave (EPW) mode excited in the low density plasma halo near the vessel wall (Myra et al 2000 Phys. Plasmas 7 283). This mode could dissipate a significant power fraction by sheath and collisional mechanisms, fits more easily in larger machines like TFTR and has the phasing dependence observed in the experiments. Here we extend that work by demonstrating the existence and phasing dependence of the coaxial mode (CM) in a realistic rf coupling calculation. A three-dimensional finite-element electromagnetic code couples a detailed model of the antenna geometry with a plasma dielectric model that retains CM physics. Quantitative results show the dependence of the CM rf fields and power dissipation on the phasing of the multiple-strap array. Unlike conventional rf coupling codes, this paper enables the antenna limiters to be immersed in tenuous plasma, an important feature for correctly modelling parasitic coupling to the CM.

This paper summarizes the recent work on JET in the three areas of heating, current drive and energetic particles. The achievements have extended the possibilities of JET, have a direct connection to ITER operation and provide new and interesting physics. Toroidal rotation profiles of plasmas heated far off axis with little or no refuelling or momentum input are hollow with only small differences on whether the power deposition is located on the low field side or on the high field side. With LH current drive the magnetic shear was varied from slightly positive to negative. The improved coupling (through the use of plasma shaping and CD4) allowed up to 3.4 MW of PLH in internal transport barrier (ITB) plasmas with more than 15 MW of combined NBI and ICRF heating. The q-profile with negative magnetic shear and the ITB could be maintained for the duration of the high heating pulse (8 s). Fast ions have been produced in JET with ICRF to simulate alpha particles: by using third harmonic 4He heating, beam injected 4He at 120 kV were accelerated to energies above 2 MeV, taking advantage of the unique capability of JET to use NBI with 4He and to confine MeV class ions. ICRF heating was used to replicate the dynamics of alpha heating and the control of an equivalent Q = 10 'burn' was simulated.

The linear behavior of resistive ballooning modes in the edge and scrape-off layer of diverted tokamaks is explored in the context of a collisional fluid model. It is shown that the large magnetic shear and small poloidal field in the X-point region act to increase the wave number, and hence the importance of resistivity, near the X point. The resulting “disconnection” of the eigenmodes across the X point profoundly influences the unstable spectrum. A new class of modes called resistive X-point (RX) modes exploits this synergism between resistivity and the X-point geometry, giving rise to robust growth rates at moderate-to-low mode numbers. Relative to an equivalent limited plasma, the diverted plasma is shown to be more unstable in the edge (inside the separatrix), and more stable in the scrape-off layer.

It is shown that the boundary (edge and scrape-off-layer) plasma in a typical low (L) mode diverted tokamak discharge is unstable to a new class of modes called resistive X-point (RX) modes. The RX mode is a type of resistive ballooning mode that exploits a synergism between resistivity and the magnetic geometry of the X-point region. The RX modes are shown to give robust instabilities at moderate mode numbers, and therefore are expected to be the dominant contributors to turbulent diffusion in the boundary plasma of a diverted tokamak.

Results are presented from the 3-D non-local electromagnetic turbulence code BOUT and the linearized shooting code BAL for studies of turbulence in tokamak boundary plasmas and its relationship to the L-H transition, in a realistic divertor plasma geometry. The key results include: (1)?the identification of the dominant resistive X?point mode in divertor geometry; (2)?turbulence suppression in the L-H transition by shear in the E ? B drift velocity, ion diamagnetism and finite polarization; (3) the fact that calculated values of the thermal diffusivities such as ?i are comparable to those inferred from the experimentally measured plasma density and temperature profiles. On the basis of simulation results, a parameterization of the transport is given that includes the dependence on the relevant physical parameters.

Reciprocating Langmuir probes are used to investigate the structure of electrostatic potentials, E x B drifts, and fluctuations in the edge (ρ < 1), scrape-off layer (SOL) and divertor of single null diverted discharges in the DIII-D tokamak. These measurements demonstrate that the X-point geometry suppresses potential fluctuations in the drift wave range of frequencies (20 kHz ≤f≤ 300 kHz) as predicted by theory [N. Mattor and R.N. Cohen, Phys. Plasmas 2 (1995) 4042], and suppresses quasi-coherent modes in the edge of H-modes. Consequently, edge turbulence and ballooning mode stability calculations, such as those used in L-H transition and H mode pedestal theories, must incorporate realistic X-point magnetic geometry to quantitatively reproduce experimental results. In the divertor plasma, root-mean-square potential fluctuations o fl . are found to be larger in H mode than in L mode, and in detached versus attached divertor plasmas. These measurements have been used to benchmark turbulence simulations with two unique codes that incorporate realistic X-point magnetic geometry: the 3-D boundary turbulence code BOUT and the BAL shooting code with high-n ballooning formalism.

We simulate boundary plasma turbulence using a 3D turbulence code BOUT and a linearized electromagnetic instability shooting code BAL. The code BOUT solves fluid equations for plasma vorticity, density, ion temperature and parallel momentum (along the magnetic field), electron temperature, and parallel momentum. A realistic DIII-D X-point magnetic geometry is used. The focus is on the possible local linear instability drives and turbulence suppression mechanisms involved in the L–H transition and on the consistency of the computed turbulence with observed temperature and density profiles. Comparison is made with data from the DIII-D tokamak where probe measurements provide turbulence statistics in the boundary plasma and transport modeling.

The present work is motivated by the importance of r.f. sheaths in determining the antenna-plasma interaction and the sensitivity of the sheaths to the complicated three-dimensional structure of modern ion cyclotron range of frequency (ICRF) antennas. To analyze r.f. sheaths on the plasma facing regions of the launcher, we first calculate the contact points of the tokamak magnetic field lines on the surface of the antenna Faraday screen and nearby limiters for realistic three-dimensional magnetic flux surface and antenna geometries. Next, the r.f. voltage that can drive sheaths at the contact points is determined and used to assess the resulting sheath power dissipation, r.f.-driven sputtering, and r.f.-induced convective cells (which produce edge profile modification). The calculations are embodied in a computer code, ansat (Antenna Sheath Analysis Tool), and sample ansat runs are shown to highlight the physics and geometry-dependent characteristics of the r.f. sheaths and their relationship to the antenna design. One use of ansat is therefore as a design tool, to assess the strengths and weaknesses of a given design with respect to critical voltage handling and edge plasma interaction issues. Additionally, examples are presented where ansat has been useful in the analysis and interpretation of ICRF experiments

Here, the structure and motion of discrete plasma blobs (a.k.a. filaments) in the edge and scrape-off layer of NSTX is studied for representative Ohmic and H-mode discharges. Individual blobs were tracked in the 2D radial versus poloidal plane using data from the gas puff imaging diagnostic taken at 400 000 frames s-1. A database of blob amplitude, size, ellipticity, tilt, and velocity was obtained for ~45 000 individual blobs. Empirical relationships between various properties are described, e.g. blob speed versus amplitude and blob tilt versus ellipticity. The blob velocities are also compared with analytic models.

Progress is reviewed on the simulation of wave-particle interactions in the ion cyclotron range of frequencies (ICRF). Two important aspects of this problem are described. First, mode conversion from a long wavelength fast magnetosonic wave to short wavelength ion Bernstein waves (IBW) and ion cyclotron waves (ICW) is simulated and validation tests of the simulations against experiment are presented. Second, simulations of the quasilinear evolution of nonthermal ion tails during the minority heating are reviewed and experimental validation tests are also discussed. In this paper we describe how access to teraflop computing capability has made it possible to advance the state of the art in this area. We also discuss two aspects of the wave-particle interaction where future work is needed and where in particular access to sub-petaflop and petaflop computing capability would be highly desirable. This work involves the interaction of ICRF waves with energetic neutral beam ions at high ion cyclotron harmonic number and addresses the inclusion of finite ion drift orbit effects in the nonthermal ion tail evolution and the inclusion of nonlinear effects such as RF sheaths in the antenna – edge plasma coupling.

Self‐consistent solutions for the wave electric field and particle distribution function are calculated for ion cyclotron heating in non‐Maxwellian plasmas. The all‐orders wave solver AORSA is generalized to treat non‐thermal velocity distributions arising from fusion reactions, neutral beam injection, and wave driven diffusion in velocity space. Quasi‐linear diffusion coefficients are derived directly from the wave electric fields and used to calculate velocity distribution functions with the CQL3D Fokker‐Planck code. Self‐consistent results are obtained by iterating the full‐wave and Fokker‐Planck solutions.

The use of mixed(monopole–dipole)-phasing of a set of ion cyclotron range of frequency antennas is potentially useful to optimize tokamak performance. However, recent mixed-phasing experiments on JET, described here, showed undesirable antenna–plasma interactions under certain circumstances. A possible physical mechanism to explain the experimental results is discussed, namely, rf-driven dc parallel currents flowing between adjacent antennas with different phasings can lead to arcing on the antenna with the largest sheath voltage. Means of controlling the interaction are discussed.

The edge and scrape-off layer (SOL) region of a tokamak plasma is considered, with emphasis on sheared flow generation and the dynamics of blob-filaments. Both numerical simulations and experimental data analysis are employed. The simulations use the fluid-based two-dimensional (2D) curvature-interchange model embedded in the SOLT code. A blob-tracking algorithm based on 2D time-resolved images from the gas puff imaging diagnostic has also been developed and applied to NSTX, Alcator C-Mod and simulation data. The algorithm is able to track the blob motion and changes in blob structure, such as elliptical deformations, that can be affected by sheared flows. Results of seeded blob simulations and quasi-steady turbulence simulations are compared with the experimental data to determine the role of plasma parameters on the blob tracks and to evaluate the exchange of momentum between the blobs and flows. The simulations are shown to reproduce many qualitative and quantitative features of the data including size, scale-length and direction of perpendicular (approximately poloidal) flows, the inferred Reynolds acceleration and residual stress, poloidal reversal of blob tracks, and blob trapping and/or ejection. Mechanisms related to blob motion, SOL currents and radial inhomogeneity are shown to be sufficient to explain the presence or absence of mean and oscillating zonal sheared flows in selected shots.

Reduced-model scrape-off layer turbulence (SOLT) simulations of an enhanced D-alpha (EDA) H-mode shot observed in the Alcator C-Mod tokamak were conducted to compare with observed variations in the scrape-off-layer (SOL) width of the parallel heat flux profile. In particular, the role of the competition between sheath- and conduction-limited parallel heat fluxes in determining that width was studied for the turbulent SOL plasma that emerged from the simulations. The SOL width decreases with increasing input power and with increasing separatrix temperature in both the experiment and the simulation, consistent with the strong temperature dependence of the parallel heat flux in balance with the perpendicular transport by turbulence and blobs. The particularly strong temperature dependence observed in the case analyzed is attributed to the fact that these simulations produce SOL plasmas which are in the conduction-limited regime for the parallel heat flux. A persistent quasi-coherent (QC) mode dominates the SOLT simulations and bears considerable resemblance to the QC mode observed in C-Mod EDA operation. The SOLT QC mode consists of nonlinearly saturated wave-fronts located just inside the separatrix that are convected poloidally by the mean flow, continuously transporting particles and energy and intermittently emitting blobs into the SOL.

Transport of plasma from the edge pedestal gradient region into the scrape-off layer (SOL) forms the heat exhaust channel. The properties of this channel are critical for future tokamak devices. The SOL heat-flux width is believed to be set by a competition between classical parallel transport and turbulent cross-field transport. In previous work, (Myra et al 2011 J. Nucl. Mat. 415 S605) focusing on modeling of the heat-flux width in the National Spherical Torus Experiment (NSTX), the possibility of a transition from quasi-diffusive to convective transport in the SOL was noticed. This transition, and the scaling of the heat-flux width, is explored here through additional SOL turbulence simulations using the SOLT code (Russell et al 2009 Phys. Plasmas 16 122304). At the transition, the transport becomes intermittent, and the SOL width is broadened due to blob emission. Critical parameters for the transition are investigated, including the power flux into the SOL, the field line pitch, the connection length and the plasma collisionality. An inverse dependence of the heat-flux width on the poloidal field, also seen routinely in experiments, is noted and explained qualitatively.

Reduced model simulations of turbulence in the edge and scrape-off-layer (SOL) region of a spherical torus or tokamak plasma are employed to address the physics of the scrape-off-layer heat-flux width. The simulation model is an electrostatic two-dimensional fluid turbulence model, applied in the plane perpendicular to the magnetic field at the outboard midplane of the torus. The model contains curvature-driven-interchange modes, sheath losses, and both perpendicular turbulent diffusive and convective (blob) transport. These transport processes compete with classical parallel transport to set the SOL width. Midplane SOL profiles of density, temperature, and parallel heat flux are obtained from the simulation and compared with experimental results from the National Spherical Torus Experiment [S. M. Kaye et al., Phys. Plasmas 8, 1977 (2001)] to study the scaling of the heat-flux width with power and plasma current. It is concluded that midplane turbulence is the main contributor to the SOL heat-flux width f...

Work on ICRF interaction with the edge plasma is reported. ICRF generated convective cells have been established as an important mechanism for influencing edge transport and interaction with the H-mode, and for controlling profiles in the tokamak scrape-off-layer. Power dissipation by rf sheaths has been shown to be significant for some misaligned ICRF and IIBW antenna systems. Near-field antenna sheath work has been extended to the far-field case, important for experiments with low single pass absorption. Impurity modeling and Faraday screen design support has been provided for the ICRF community. In the area of core-ICRF physics, the kinetic theory of heating by applied ICRF waves has been extended to retain important geometrical effects relevant to modeling minority heated tokamak plasmas, thereby improving on the physics base that is standard in presently employed codes. Both the quasilinear theory of ion heating, and the plasma response function important in wave codes have been addressed. In separate studies, it has been shown that highly anisotropic minority heated plasmas can give rise to unstable field fluctuations in some situations. A completely separate series of studies have contributed to the understanding of tokamak confinement physics. Additionally, a diffraction formalism has been produced which will bemore » used to access the focusability of lower hybrid, ECH, and gyrotron scattering antennas in dynamic plasma configurations.« less

Magnetically confined plasmas can contain significant concentrations of nonthermal plasma particles arising from fusion reactions, neutral beam injection, and wave-driven diffusion in velocity space. Initial studies in one-dimensional and experimental results show that nonthermal energetic ions can significantly affect wave propagation and heating in the ion cyclotron range of frequencies. In addition, these ions can absorb power at high harmonics of the cyclotron frequency where conventional two-dimensional global-wave models are not valid. In this work, the all-orders global-wave solver AORSA [E. F. Jaeger et al., Phys. Rev. Lett. 90, 195001 (2003)] is generalized to treat non-Maxwellian velocity distributions. Quasilinear diffusion coefficients are derived directly from the wave fields and used to calculate energetic ion velocity distributions with the CQL3D Fokker-Planck code [R. W. Harvey and M. G. McCoy, Proceedings of the IAEA Technical Committee Meeting on Simulation and Modeling of Thermonuclear ...