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International audience; Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

This paper summarizes recent progress in modeling the interaction between ion cyclotron range of frequency (ICRF) waves and edge plasma with application to ASDEX Upgrade. The basic theories, the development of ICRF and edge plasma codes, the integrated modeling methods and some key results are reviewed. In particular, the following physical aspects are discussed: (1) ICRF power coupling; (2) slow wave propagation; (3) ICRF-rectified sheath; (4) ICRF-induced convection; (5) ICRF-edge turbulence interaction. Moreover, comprehensive integrated modeling strategies by including all necessary codes in one package and solving multiple physical issues self-consistently are discussed.

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 2D scrape-off-layer turbulence code (nSOLT) includes 1D Boltzmann neutral–plasma interactions, a model of divertor recycling (introduced here), and a fixed source of plasma concentrated at the core-side boundary. Three fueling methods are considered herein: (1) neutral injection in the far-SOL is accomplished by specifying the density of Franck–Condon distributed neutrals streaming in from the boundary. (2) Divertor recycling is modeled by injecting a fraction of the particle parallel flux in the scrape-off layer (SOL) back into the edge region as a source of plasma. (3) A constant source fuels the edge plasma from the core-side boundary to model pellet injection. For machine parameters (B, Rm, and L//) illustrative of the MAST-U device, and for a deuterium plasma, turbulent equilibria are obtained that share the same plasma fueling rate for each of the three fueling methods, with only one of the sources on in each case. In the presence of self-consistent turbulence, quasi-steady plasma and neutral (deuterium) profiles, fueling efficiencies, SOL transparencies, and heat flux widths are compared. Characteristics of the turbulent fluctuations, including skewness, cross-phases, and power spectra, are described. The calculated fueling efficiencies, SOL transparencies to neutral penetration, and many of the turbulent properties are remarkably similar for all three fueling methods despite significant differences in the plasma profiles. The nonlinear states of the three cases are dominated by separatrix-spanning vortex cells that control particle and heat losses into the SOL.

This paper describes a number of deleterious interactions between radio-frequency ( rf ) waves and the boundary plasma in fusion experiments. These effects can lead to parasitic power dissipation, reduced heating efficiency, formation of hot spots at material boundaries, sputtering and self-sputtering, and arcing in the antenna structure. Minimizing these interactions is important to the success of rf heating, especially in future experiments with long-pulse or steady-state operation, higher power density, and high-Z divertor and walls. These interactions will be discussed with experimental examples. Finally, the present state of modeling and future plans will be summarized.

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.

In a magnetized plasma, such as in fusion devices or the Earth's magnetosphere, several different kinds of waves can simultaneously exist, having very different physical properties. Under the right conditions one wave can quite suddenly convert to another type. Depending on the case, this can be either a great benefit or a problem for the use of waves to heat and control fusion plasmas. Understanding and accurately modeling such behavior is a major computational challenge.

The stability of plasma blobs which have both density and temperature higher than the surrounding plasma, and can transport heat as well as particles, is considered. It is shown that the internal blob temperature profile Te(r) can drive azimuthal rotation or spin vθ(r) about the blob axis, which produces a robust m=2 rotational instability in the interchange limit (k∥=0). The theory includes the effects of the centrifugal and Coriolis forces, the sheared velocity vθ(r), and the axial sheath boundary condition. Estimates show that finite-Larmor-radius stabilization is ineffective, but the sheath conductivity can be strongly stabilizing. The blob rotational instability has only a small direct impact on the particle and energy transport, but it serves as a useful diagnostic for the underlying blob spin, which is an important variable in determining the blob’s radial velocity. A separate branch of temperature-gradient-driven sheath instabilities, predicted in the eikonal limit, is not observed for low mode nu...

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 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.

Author(s): Menard, JE; Allain, JP; Battaglia, DJ; Bedoya, F; Bell, RE; Belova, E; Berkery, JW; Boyer, MD; Crocker, N; Diallo, A; Ebrahimi, F; Ferraro, N; Fredrickson, E; Frerichs, H; Gerhardt, S; Gorelenkov, N; Guttenfelder, W; Heidbrink, W; Kaita, R; Kaye, SM; Kriete, DM; Kubota, S; Leblanc, BP; Liu, D; Lunsford, R; Mueller, D; Myers, CE; Ono, M; Park, JK; Podesta, M; Raman, R; Reinke, M; Ren, Y; Sabbagh, SA; Schmitz, O; Scotti, F; Sechrest, Y; Skinner, CH; Smith, DR; Soukhanovskii, V; Stoltzfus-Dueck, T; Yuh, H; Wang, Z; Waters, I; Ahn, JW; Andre, R; Barchfeld, R; Beiersdorfer, P; Bertelli, N; Bhattacharjee, A; Brennan, D; Buttery, R; Capece, A; Canal, G; Canik, J; Chang, CS; Darrow, D; Delgado-Aparicio, L; Domier, C; Ethier, S; Evans, T; Ferron, J; Finkenthal, M; Fonck, R; Gan, K; Gates, D; Goumiri, I; Gray, T; Hosea, J; Humphreys, D; Jarboe, T; Jardin, S; Jaworski, MA; Koel, B; Kolemen, E; Ku, S; La Haye, RJ; Levinton, F; Luhmann, N; Maingi, R; Maqueda, R; McKee, G; Meier, E; Myra, J; Perkins, R | Abstract: The National Spherical Torus Experiment (NSTX) has undergone a major upgrade, and the NSTX Upgrade (NSTX-U) Project was completed in the summer of 2015. NSTX-U first plasma was subsequently achieved, diagnostic and control systems have been commissioned, the H-mode accessed, magnetic error fields identified and mitigated, and the first physics research campaign carried out. During ten run weeks of operation, NSTX-U surpassed NSTX record pulse-durations and toroidal fields (TF), and high-performance ∼1 MA H-mode plasmas comparable to the best of NSTX have been sustained near and slightly above the n = 1 no-wall stability limit and with H-mode confinement multiplier H98y,2 above 1. Transport and turbulence studies in L-mode plasmas have identified the coexistence of at least two ion-gyro-scale turbulent micro-instabilities near the same radial location but propagating in opposite (i.e. ion and electron diamagnetic) directions. These modes have the characteristics of ion-temperature gradient and micro-tearing modes, respectively, and the role of these modes in contributing to thermal transport is under active investigation. The new second more tangential neutral beam injection was observed to significantly modify the stability of two types of Alfven eigenmodes. Improvements in offline disruption forecasting were made in the areas of identification of rotating MHD modes and other macroscopic instabilities using the disruption event characterization and forecasting code. Lastly, the materials analysis and particle probe was utilized on NSTX-U for the first time and enabled assessments of the correlation between boronized wall conditions and plasma performance. These and other highlights from the first run campaign of NSTX-U are described.

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.

In recent ion Bernstein wave (IBW) heating experiments on the Tokamak Fusion Test Reactor (TFTR) [J. R. Wilson. R. E. Bell, S. Bernabei, K. Hill et al., Phys. Plasmas 5, 1721 (1998)] a velocity shear layer in the plasma core was obtained. The magnitude of velocity shear was believed to be too small to create an internal transport barrier, because of parasitic edge processes which reduced the power coupled to the core. In this paper we investigate these rf (radio frequency) edge processes by employing a model which includes both coaxial modes and their dissipation in rf plasma sheaths. The coaxial mode (here, an electron plasma wave trapped in the halo plasma between the lower hybrid layer and the vessel wall) can propagate at low poloidal wave numbers. This feature is shown to relate to the observed poloidal phasing dependence of the antenna loading. Results of analytical models and a three-dimensional antenna code are presented. The experimentally observed loading is also nonlinear, being larger at very ...

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.

When the density at the ion Bernstein wave (IBW) antenna is relatively low, mode transformation of the electron plasma wave to the IBW is sensitive to the density gradient scale length, and hence to ponderomotive effects. A second-order nonlinear ordinary differential equation that describes mode transformation at the lower-hybrid layer, including self-consistent ponderomotive density profile modification, is solved for the rf electrostatic potential in front of the IBW antenna, for the particular case of heating just below the second harmonic of the deuterium cyclotron frequency. The complex antenna impedance and a local reflectivity are calculated, assuming vacuum within the antenna box. These calculations reveal diminished antenna coupling to the IBW with increasing ponderomotive density expulsion, as compared to the linear prediction. The ponderomotive force increases the density gradient in the edge plasma, thus enhancing reflection and lowering the loading resistance. The model also describes the di...

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.

The National Spherical Torus Experiment (NSTX) produces plasmas, with toroidal aspect ratio as low as 1.25 and plasma currents up to 1.5 MA, which can be heated by up to 6 MW High‐Harmonic Fast Waves and up to 7 MW of deuterium Neutral Beam Injection. With these capabilities, NSTX has already made considerable progress in advancing the scientific understanding of high performance plasmas needed for low‐aspect‐ratio reactor concepts and for ITER. In transport and turbulence research on NSTX, the role of magnetic shear is being elucidated in discharges in which electron energy transport barriers are observed. Scaling studies indicate a weaker dependence on plasma current than at conventional aspect ratio and a significant dependence on toroidal field (BT).

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.

This paper describes the range of variations in edge and SOL turbulence observed using a gas puff imaging (GPI) diagnostic in NSTX discharges. The database consists of 140 shots including Ohmic, L-mode, and H-mode plasmas measured during steady-state conditions (e.g. without ELMs). Turbulence quantities were evaluated using both cross-correlation analysis and blob tracking. Relative fluctuation levels varied from –1.0, correlation times were –40 μs, correlation lengths were –10 cm, and turbulence velocities were km s−1 and km s−1 outwards. These variations were evaluated with respect to both the global and local edge plasma parameters, and compared with simplified theoretical models.

The most common method for treating wave propagation in tokamaks in the lower hybrid range of frequencies (LHRF) has been toroidal ray tracing, owing to the short wavelengths (relative to the system size) found in this regime. Although this technique provides an accurate description of 2D and 3D plasma inhomogeneity effects on wave propagation, the approach neglects important effects related to focusing, diffraction, and finite extent of the RF launcher. Also, the method breaks down at plasma cutoffs and caustics. Recent adaptation of full‐wave electromagnetic field solvers to massively parallel computers has made it possible to accurately resolve wave phenomena in the LHRF. One such solver, the TORIC code, has been modified to simulate LH waves by implementing boundary conditions appropriate for coupling the fast electromagnetic and the slow electrostatic waves in the LHRF. In this frequency regime the plasma conductivity operator can be formulated in the limits of unmagnetized ions and strongly magnetized electrons, resulting in a relatively simple and explicit form. Simulations have been done for parameters typical of the planned LHRF experiments on Alcator C‐Mod, demonstrating fully resolved fast and slow LH wave fields using a Maxwellian non‐relativistic plasma dielectric. Significant spectral broadening of the injected wave spectrum and focusing of the wave fields have been found, especially at caustic surfaces. Comparisons with toroidal ray tracing have also been done and differences between the approaches have been found, especially for cases where wave caustics form. The possible role of this diffraction‐induced spectral broadening in filling the spectral gap in LH heating and current drive will be discussed.

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.

Edge turbulence images have been made using an ultra-high speed CCD camera on both NSTX and Alcator C-Mod. In both cases, the D-alpha or HeI (587.6 nm) line emission from localized deuterium or helium gas puffs was viewed along a local magnetic field line near the outer midplane. Fluctuations in this line emission reflect fluctuations in electron density and/or electron temperature through the atomic excitation rates, which can be modeled using the DEGAS-2 code. The 2-D structure of the measured turbulence can be compared with theoretical simulations based on 3-D fluid models.

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.

Transport and turbulence profiles were directly evaluated using probes for the first time in the edge and scrape-off layer (SOL) of NSTX [Ono et al., Nucl. Fusion 40, 557 (2000)] in low (L) and high (H) confinement, low power (Pin∼ 1.3 MW), beam-heated, lower single-null discharges. Radial turbulent particle fluxes peak near the last closed flux surface (LCFS) at ≈4×1021 s−1 in L-mode and are suppressed to ≈0.2×1021 s−1 in H mode (80%–90% lower) mostly due to a reduction in density fluctuation amplitude and of the phase between density and radial velocity fluctuations. The radial particle fluxes are consistent with particle inventory based on SOLPS fluid modeling. A strong intermittent component is identified. Hot, dense plasma filaments 4–10 cm in diameter, appear first ∼2 cm inside the LCFS at a rate of ∼1×1021 s−1 and leave that region with radial speeds of ∼3–5 km/s, decaying as they travel through the SOL, while voids travel inward toward the core. Profiles of normalized fluctuations feature levels o...

In the course of this grant, Lodestar has collaborated with the TFTR ICRF team to carry out an extensive investigation of rf-edge physics relevant to the understanding and operation of the TFTR fast wave (FW) and ion Bernstein wave (IBW) antennas. Their FW work covered four main areas: rf sheath geometry on TFTR, ICRF convective cells and edge profile modifications, impurity production, and plasma glow and Fermi acceleration. Their IBW work, carried out over the last two years, was in support of the IBW transport barrier and poloidal flow generation experiments. A theoretical survey of rf-edge physics expected to be critical for these antennas was carried out. While the physics that was known to be important for FW systems was considered (especially sheath power dissipation, edge density modifications, and impurities), additional physics enters for IBW waves because of the shorter wavelength, slower group velocity, larger electric fields and the different polarization. In particular, ponderomotive forces, while normally negligible in the FW context, can be substantial for the IBW, but the jitter excursion distance of an electron is too large for validity of the usual theory. A new model for the resulting electron heating and density expulsion was developed. A newmore » model of antenna coupling to the electron plasma wave, mode transformation to the IBW, and the effect of reflected waves at the lower hybrid layer was also developed.« less

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.

Two-dimensional (2D) turbulence simulations are reported in which the balancing of the parallel and perpendicular currents is modified by changing the axial boundary condition (BC) to vary the sheath conductivity. The simulations are carried out using the 2D scrape-off-layer turbulence (SOLT) code. The results are compared with recent experiments on the controlled shear de-correlation experiment (CSDX) in which the axial BC was modified by changing the composition of the end plate. Reasonable qualitative agreement is found between the simulations and the experiment. When an insulating axial BC is used, broadband turbulence is obtained and an inverse cascade occurs down to low frequencies and long spatial scales. Robust sheared flows are obtained. By contrast, employing a conducting BC at the plate resulted in coherent (drift wave) modes rather than broadband turbulence, with weaker inverse cascade, and smaller zonal flows. The dependence of the two instability mechanisms (rotationally driven interchange mode and drift waves) on the axial BC is also discussed.

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.

A synthetic gas puff imaging (GPI) diagnostic has been added to the scrape-off layer turbulence (SOLT) simulation code, enabling comparisons with GPI data from the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)]. The edge and scrape-off layer are modeled in the radial and poloidal (bidirectional) dimensions of the outboard midplane region of NSTX. A low-confinement mode discharge is simulated by choosing reference parameters, including radial density and temperature profiles, to be consistent with those of the shot (no. 112825). NSTX and simulation GPI data are submitted to identical analyses. It is demonstrated that the level of turbulent fluctuations in the simulation may be adjusted to give synthetic GPI radial intensity profiles similar to those of the experiment; for a “best-case” simulation, SOLT and NSTX probability distribution functions of blob radial locations, widths, and GPI image velocities are compared. For the simulation, synthetic GPI image velocity ...

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...

Fluctuations in the edge and scrape-off layer (SOL) of L-mode plasmas in the National Spherical Torus Experiment [Kaye et al., Phys. Plasmas 8, 1977 (2001)] as observed by the gas puff imaging (GPI) diagnostic are studied. Calculation of local, time resolved velocity maps using the hybrid optical flow and pattern matching velocimetry code enables analysis of turbulent flow and shear behavior. Periodic reversals in the direction of the poloidal flow near the separatrix are observed. Also, poloidal velocities and their radial shearing rate are found to be well correlated with the fraction of Dα light contained in the SOL, which acts as a measure of turbulent bursts. The spectra of GPI intensity and poloidal velocity both have a strong feature near 3 kHz, which appears to correspond with turbulent bursts. This mode exhibits a poloidal structure with poloidal wavenumber of 7.7 m−1 for GPI intensity and 3.4 m−1 for poloidal velocity, and the poloidal velocity fluctuations near 3 kHz remain coherent over length...

The relevance of rf-sheath-plasma interactions to ICRF operation in TFTR has been studied. Screen-screen and screen-limiter rf sheaths have been identified and analyzed for the old and new Bay M geometries on TFIR, including sheath voltages driven by both feeders and the central antenna conductor. Calculations have been carried out to determine the effects of ICRF on edge transport (profile flattening by E {times} B convection), impurity influx ({delta}Z{sub eff}) and edge electron heating (FS glow phenomena) as a function of edge plasma parameters, rf power and antenna phasing. It was found that many of the experimentally observed ICRF-edge plasma interactions on TFIR are consistent with the predictions of rf sheath theory.

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

Saturation mechanisms for two-dimensional (2D) edge turbulence are studied in a Braginskii-type fluid model using the scrape-off-layer turbulence code. The simulations study the interaction of edge and scrape-off-layer (SOL) turbulence, blob generation, momentum transport, and shear flow generation in 2D turbulence. It is shown that a key parameter is the zonal flow shear damping rate, which controls both the level of saturated turbulence and the rate of blob generation. The flow shear profile is produced by a combination of the turbulent Reynold’s stress inside the last closed surface and the sheath-induced flow in the SOL. The turbulent properties are studied as a function of zonal flow damping. The role of other edge and SOL dissipation mechanisms are also discussed.

Turbulence in the vicinity of the last closed surface transports plasma momentum away from the core region toward the wall, and hence provides a momentum “source” that can induce net core plasma rotation as well as sheared flows in the edge. Here, numerical simulations of this process for the binormal (approximately poloidal) component of momentum are described that use a minimal two-dimensional model, in the plane perpendicular to the magnetic field, incorporating directionality (drift-waves), radial transport (Reynolds stress and blobs), and dissipation (sheath loss terms). A zonally averaged momentum conservation law is used to advance the zonal flows. The net momentum transferred to the core is shown to be influenced by a number of physical effects: dissipation, the competition between momentum transport by Reynolds stress and passive convection by particles, intermittency (the role of blobs carrying momentum), and velocity shear regulation of turbulence. It is shown that the edge momentum source adju...

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 ...

In this paper we compare the structure and motion of edge turbulence observed in L-mode vs. H-mode plasmas in the National Spherical Torus Experiment (NSTX) [M. Ono, M. G. Bell, R. E. Bell et al., Plasma Phys. Controlled Fusion 45, A335 (2003)]. The radial and poloidal correlation lengths are not significantly different between the L-mode and the H-mode in the cases examined. The poloidal velocity fluctuations are lower and the radial profiles of the poloidal turbulence velocity are somewhat flatter in the H-mode compared with the L-mode plasmas. These results are compared with similar measurements Alcator C-Mod [E. Marmar, B. Bai, R. L. Boivin et al., Nucl. Fusion 43, 1610 (2003)], and with theoretical models.