Search

Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin–Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared $\boldsymbol{E}\times \boldsymbol{B}$ flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at, and just outside of, the separatrix as a result of the distribution of magnetic shear. Finally implications for reduced edge turbulence modelling codes are discussed.

A numerical code that solves self-consistent radio-frequency (RF) sheath–plasma interactions in the ion cyclotron range of frequencies is developed based on a nonlinear finite element technique. The present code solves for plasma waves based on the cold plasma model subject to a sheath boundary condition. The finite element procedure has been implemented for one- and two-dimensional analyses using simplified models for the poloidal plane of a tokamak. The results show good accuracy and generalize previous analytical calculations. The present algorithmic approach shows promise for developing a code to predict RF sheath potentials in the scrape-off layer of RF-heated fusion experiments.

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.

A new radio-frequency (rf) sheath boundary condition (BC) is described and applied to the problem of far field sheaths. The new BC generalizes the one presently used in rf codes to include: (1) an arbitrary magnetic field angle, (2) the full complex impedance, (3) mobile ions, (4) unmagnetized ions, and (5) the magnetic pre-sheath. For a given wave-propagation (macro) problem, root-finding is used to match the impedance of the rf wave with that of the micro-sheath problem. For a model far-field sheath problem, it is shown that the structure of the (multiple) roots with the new BC is similar to that with the capacitive BC, but the location of the resonance changes when the full impedance is used.

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.

Global wave solutions with self-consistent velocity distributions are calculated for ion cyclotron heating in non-Maxwellian plasmas. The all-orders spectral algorithm (AORSA) global wave solver 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 field and used to calculate ion velocity distribution functions with the CQL3D Fokker–Planck code. Alternatively, the quasi-linear coefficients can be calculated numerically by integrating the Lorentz force equations along particle orbits. Self-consistency between the wave electric field and resonant ion distribution function is achieved by iterating between the global-wave and Fokker–Planck solutions.

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...

Nonlinear rf-driven sheared flows are of interest for turbulence control and basic physics experiments. Short-wavelength slow modes are required for efficient coupling of wave momentum to the plasma, requiring a kinetic hot-plasma theory. Here, a guiding-center formulation is developed which calculates the nonlinear particle and energy fluxes, energy absorption, and nonlinear forces on the plasma using a kinetic moment approach that is valid to first order in the ratio of the gyroradius compared to the wave envelope scale length and the plasma equilibrium scale length. Both the stress tensor and Lorentz force contribute to the net force on a fluid element. The forces driving flux-surface-averaged flows in a tokamak are extracted from the parallel and toroidal components. It is shown that flux-surface-averaged flows are driven by two classes of terms: direct absorption of wave momentum and dissipative stresses. Furthermore, the general kinetic expression for the force is shown to reduce to the standard cold-fluid ponderomotive force in an appropriate limit, but in this limit no flows are driven.

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.

Significant efforts have been made to quantitatively benchmark the sheath sub-grid model used in our time-domain simulations of plasma-immersed antenna near fields, which includes highly detailed three-dimensional geometry, the presence of the slow wave, and the non-linear evolution of the sheath potential. We present both our quantitative benchmarking strategy, and results for the ITER antenna configuration, including detailed maps of electric field, and sheath potential along the entire antenna structure. Our method is based upon a time-domain linear plasma model [1], using the finite-difference electromagnetic Vorpal/Vsim software [2]. This model has been augmented with a non-linear rf-sheath sub-grid model [3], which provides a self-consistent boundary condition for plasma current where it exists in proximity to metallic surfaces. Very early, this algorithm was designed and demonstrated to work on very complicated three-dimensional geometry, derived from CAD or other complex description of actual hard...

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

A novel mechanism for feedback stabilization of external kink modes and disruptions is proposed in which modulated radio‐frequency (RF) antennas apply a stabilizing ponderomotive force (PF) to the plasma. The RF power required for n=1 kink stabilization in the Princeton Beta Experiment‐Modified (PBX‐M) [Phys. Fluids B 2, 1271 (1990)] is estimated, and it is shown that the idea can be tested with the existing antenna system. A simulation of a preliminary n=0 modulation experiment on PBX‐M also shows that the PF can balance applied vertical field oscillations.

Two-dimensional scrape-off layer turbulence (SOLT) code simulations are compared with an L-mode discharge on the Alcator C-Mod tokamak [Greenwald et al., Phys. Plasmas 21, 110501 (2014)]. Density and temperature profiles for the simulations were obtained by smoothly fitting Thomson scattering and mirror Langmuir probe (MLP) data from the shot. Simulations differing in turbulence intensity were obtained by varying a dissipation parameter. Mean flow profiles and density fluctuation amplitudes are consistent with those measured by MLP in the experiment and with a Fourier space diagnostic designed to measure poloidal phase velocity. Blob velocities in the simulations were determined from the correlation function for density fluctuations, as in the analysis of gas-puff-imaging (GPI) blobs in the experiment. In the simulations, it was found that larger blobs moved poloidally with the E × B flow velocity, vE, in the near-SOL, while smaller fluctuations moved with the group velocity of the dominant linear (interc...

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.

The effect of lithium (Li) wall coatings on scrape-off-layer (SOL) turbulence in the National Spherical Torus Experiment (NSTX) is modeled with the Lodestar SOLT (SOL Turbulence) code. Specifically, the implications for the SOL heat flux width of experimentally observed, Li-induced changes in the pedestal profiles are considered. The SOLT code used in the modeling has been expanded recently to include ion temperature evolution and ion diamagnetic drift effects. This work focuses on two NSTX discharges occurring pre- and with-Li deposition. The simulation density and temperature profiles are constrained, inside the last closed flux surface only, to match those measured in the two experiments, and the resulting drift-interchange-driven turbulence is explored. The effect of Li enters the simulation only through the pedestal profile constraint: Li modifies the experimental density and temperature profiles in the pedestal, and these profiles affect the simulated SOL turbulence. The power entering the SOL measu...

Interactions between propagating fast waves and radio-frequency (RF) sheaths in the ion cyclotron range of frequencies are numerically investigated based on a cold fluid plasma model coupled with a sheath boundary condition. In this two-dimensional study, the capability of the finite element code rfSOL, which was developed in previous numerical work, is extended to analyze self-consistent RF sheath-plasma interaction problems in a tokamak with a non-circular cross-section. It is found that a large sheath voltage is generated near the edges of the limiter-shaped deformation as a result of the conversion from fast to slow waves on the sheaths. The sheath voltage associated with this conversion is particularly significant in the localized region where the contact angle between the magnetic field line and the conducting wall varies rapidly along the curved sheath surface, which is consistent with the results in previous one-dimensional theoretical work. The dependences of the RF sheaths on various parameters in plasma such as the toroidal wavenumber, edge plasma density, and the degree of the RF wave absorption in the core region are also examined in detail.

The physics of radio-frequency (rf) sheaths near a conducting surface is studied for plasmas immersed in a magnetic field that makes an oblique angle θ with the surface. A set of one-dimensional equations is developed that describes the dynamics of the time-dependent magnetic presheath and non-neutral Debye sheath. The model employs Maxwell-Boltzmann electrons, and the magnetization and mobility of the ions is determined by the magnetic field strength, and wave frequency, respectively. The angle θ, assumed to be large enough to insure an electron-poor sheath, is otherwise arbitrary. Concentrating on the ion-cyclotron range of frequencies, the equations are solved numerically to obtain the rectified (dc) voltage, the rf voltage across the sheath, and the rf current flowing through the sheath. As an application of this model, the sheath voltage-current relation is used to obtain the rf sheath impedance, which in turn gives an rf sheath boundary condition for the electric field at the sheath-plasma interface that can be used in rf wave codes. In general, the impedance has both resistive and capacitive contributions, and generalizes previous sheath boundary condition models. The resistive part contributes to parasitic power dissipation at the wall.

Understanding the responsible mechanisms and resulting scaling of the scrape-off layer (SOL) heat flux width is important for predicting viable operating regimes in future tokamaks and for seeking possible mitigation schemes. In this paper, we present a qualitative and conceptual framework for understanding various regimes of edge/SOL turbulence and the role of turbulent transport as the mechanism for establishing the SOL heat flux width. Relevant considerations include the type and spectral characteristics of underlying instabilities, the location of the gradient drive relative to the SOL, the nonlinear saturation mechanism, and the parallel heat transport regime. We find a heat flux width scaling with major radius R that is generally positive, consistent with the previous findings [Connor et al., Nucl. Fusion 39, 169 (1999)]. The possible relationship of turbulence mechanisms to the neoclassical orbit width or heuristic drift mechanism in core energy confinement regimes known as low (L) mode and high (H) mode is considered, together with implications for the future experiments.

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.

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 mitigating impact of thermal and rectified radio frequency (RF) sheath potentials on the peeling-ballooning modes is studied non-linearly by employing a two-fluid three-field simulation model based on the BOUT++ framework. Additional shear flow and the Kelvin-Helmholtz effect due to the thermal and rectified RF sheath potential are induced. It is found that the shear flow increases the growth rate while the K-H effect decreases the growth rate slightly when there is a density gradient, but the energy loss of these cases is suppressed in the nonlinear phase. The stronger external electrostatic field due to the sheaths has a more significant effect on the energy loss suppression. From this study, it is found the growth rate in the linear phase mainly determines the onset of edge-localized modes, while the mode spectrum width in the nonlinear phase has an important impact on the turbulent transport. The wider mode spectrum leads to weaker turbulent transport and results in a smaller energy loss. Due to the thermal sheath and rectified RF sheath potential in the scrape-off-layer, the modified shear flow tears apart the peeling-ballooning filament and makes the mode spectrum wider, resulting in less energy loss. The perturbed electric potential and the parallel current near the sheath region is also suppressed locally due to the sheath boundary condition.

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...

Computer simulations of radio-frequency (RF) waves propagating across a two-dimensional (2D) magnetic field into a conducting boundary are described. The boundary condition for the RF fields at the metal surface leads to the formation of an RF sheath, which has previously been studied in one-dimensional models. In this 2D study, it is found that rapid variation of conditions along the sheath surface promote coupling of the incident RF branch (either fast or slow wave) to a short-scale-length sheath-plasma wave (SPW). The SPW propagates along the sheath surface in a particular direction dictated by the orientation of the magnetic field with respect to the surface, and the wave energy in the SPW accumulates near places where the background magnetic field is tangent to the surface.

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.

This paper is motivated by the recent measurement of large (>100 V) plasma potentials in Alcator C-Mod during ion cyclotron range of frequency (ICRF) heating. The plasma potential is measured on field lines that intersect a limiter but do not pass near a powered ICRF antenna. The measured potential correlates with the local ICRF fast wave electric field and is a prime candidate to cause increased Mo sputtering from the limiter surface. In this paper, it is shown that a theory of 'far-field' radio-frequency (rf) sheaths can qualitatively explain this experimental observation. The theory describes rf-sheath formation when unabsorbed fast ICRF waves are incident on a conducting boundary far from the antenna. It is shown that the rf-sheath drive is sensitive to the angle between the surface normal and the equilibrium magnetic field. The main conclusion of this work is that the rapid tangential variation in the B field-limiter geometry near the tip of the limiter promotes the formation of large sheath potentials of the same order as the measured ones.

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 new finite element numerical scheme for analyzing self-consistent radio-frequency (RF) sheath-plasma interaction problems in the ion cyclotron range of frequencies is applied to various problems represented by simplified models for the tokamak scrape-off layer. The present code incorporates a modified boundary condition, which is called a sheath boundary condition, that couples the radio-frequency waves and sheaths at the material boundaries by treating the sheath as a thin vacuum layer. A series of numerical analyses in one- and two-dimensional domains show several important physical properties, such as the existence of multiple roots, hysteresis effects, presence and characteristics of the sheath-plasma waves, and the phase shift of a reflected slow wave, some of which are newly identified by introducing a spatially varying plasma density and background magnetic field.

A blob-filament (or simply “blob”) is a magnetic-field-aligned plasma structure which is considerably denser than the surrounding background plasma and highly localized in the directions perpendicular to the equilibrium magnetic field B. In experiments and simulations, these intermittent filaments are often formed near the boundary between open and closed field lines, and seem to arise in theory from the saturation process for the dominant edge instabilities and turbulence. Blobs become charge-polarized under the action of an external force which causes unequal drifts on ions and electrons; the resulting polarization-induced E × B drift moves the blobs radially outwards across the scrape-off-layer (SOL). Since confined plasmas generally are subject to radial or outwards expansion forces (e.g., curvature and ∇B forces in toroidal plasmas), blob transport is a general phenomenon occurring in nearly all plasmas. This paper reviews the relationship between the experimental and theoretical results on blob form...

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...

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.

The next step toward fusion as a practical energy source is the design and construction of ITER [R. Aymar et al., Nucl. Fusion 41, 1301 (2001)], a device capable of producing and controlling the high-performance plasma required for self-sustaining fusion reactions, i.e., “burning plasma.” ITER relies in part on ion-cyclotron radio frequency power to heat the deuterium and tritium fuel to fusion temperatures. In order to heat effectively, the radio frequency wave fields must couple efficiently to the dense core plasma. Calculations in this paper support the argument that this will be the case. Three-dimensional full-wave simulations show that fast magnetosonic waves in ITER propagate radially inward with strong central focusing and little toroidal spreading. Energy deposition, current drive, and plasma flow are all highly localized near the plasma center. Very high resolution, two-dimensional calculations reveal the presence of mode conversion layers, where fast waves can be converted to slow ion cyclotron...

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...

A two-region model is proposed to study the effect of collisionality and magnetic geometry on electrostatic turbulence and on the propagation of filamentary coherent structures (blobs) in the edge and scrape-off layer. The model invokes coupled vorticity and continuity equations in two different spatial regions along the magnetic field, taking into account the effect of magnetic field fanning and shear, e.g., near magnetic X-points. A linear dispersion relation for unstable modes illustrates the physics of mode disconnection (ballooning) along the magnetic field and its dependence on collisionality and wave number (scale size). Employing an invariant scaling analysis, dimensionless parameters for the nonlinear model are developed and used to describe the regimes of the system. A blob correspondence rule is postulated to relate the linear mode growth rates and regimes to the convective velocity of blobs. Nonlinear numerical simulations of blob convection show good agreement with a blob dispersion relation ...

Predictive modeling of radio-frequency wave propagation in high-power fusion experiments requires accounting for nonlinear losses of wave energy in the plasma edge and at the wall. An important mechanism of “anomalous” power losses is the acceleration of ions into the walls by rf sheath potentials. Previous work computed the “sheath power dissipation” non-self-consistently by postprocessing fields obtained as the solution of models which did not retain sheaths. Here, a method is proposed for a self-consistent quantitative calculation of sheath losses by incorporating a sheath boundary condition (SBC) in antenna coupling and wave propagation codes. It obtains the self-consistent sheath potentials and spatial distribution of the time-averaged power loss in the solution for the linear rf fields. It can be applied for ion cyclotron and (in some cases) lower hybrid waves. The use of the SBC is illustrated by applying it to the problem of an electron plasma wave propagating in a waveguide. This model problem is...

High-speed high-spatial-resolution data obtained by the gas puff imaging (GPI) diagnostic on the National Spherical Torus Experiment [M. Ono, M.G. Bell, R.E. Bell et al. Plasma Phys. Control. Fusion 45, A335 (2003).] is analyzed and interpreted in light of recent theoretical models for electrostatic edge turbulence and blob propagation. The experiment is described in terms of theoretical regimes that predict different dependencies for the radial velocity of blob convection. Using the GPI data, atomic physics analysis, and blob tracking on a restricted dataset, it is shown that the observed blob velocities in the scrape-off layer are bounded by a theory-based minimum velocity associated with the sheath-connected regime. A similar maximum velocity bound associated with the resistive-ballooning regime is also observed. Turning to the question of blob creation, it is shown that blobs are born with a density and temperature characteristic of the plasma conditions where underlying linear edge drift-curvature instabilities are localized. Finally, statistical variations in blob properties and in the radial blob velocity for given edge conditions are significant, and tend to mask any systematic changes among discharges with different conditions.

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.