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The mission of the low aspect ratio spherical tokamak NSTX-U is to advance the physics basis and technical solutions required for optimizing the configuration of next-step steady-state tokamak fusion devices. NSTX-U will ultimately operate at up to 2 MA of plasma current and 1 T toroidal field on axis for 5 seconds, and has available up to 15 MW of Neutral Beam Injection (NBI) power at different tangency radii and 6 MW of High Harmonic Fast Wave (HHFW) heating. With these capabilities NSTX-U will develop the physics understanding and control tools to ramp-up and sustain high performance fully non-inductive plasmas with large bootstrap fraction and enhanced confinement enabled via the low aspect ratio, high beta configuration. With its unique capabilities, NSTX-U research also supports ITER and other critical fusion development needs. Super-Alfvénic ions in beam-heated NSTX-U plasmas access energetic particle parameter space that is relevant for both -heated conventional and low aspect ratio burning plasmas. NSTX-U can also generate very large target heat fluxes to test conventional and innovative plasma exhaust and plasma facing component (PFC) solutions. This paper summarizes recent analysis, theory and modelling progress to advance the tokamak physics basis in the areas of macrostability and 3D fields, energetic particle stability and fast ion transport, thermal transport and pedestal structure, boundary and plasma material interaction, RF heating, scenario optimization and real-time control.

The purpose of these integrated ITER simulations is to identify dependencies that can impact the performance of ITER. The dependence of fusion power production, temperature and density pedestals, and core profiles on varying magnetic-\textit{q}, edge density fueling strength, neoclassical transport, magnetic field strength, and alpha heating, are examined. It is noted that ion modes usually dominate the interior, while electron modes dominate the barrier. The electron mode without flow shear is substantially stronger. The \textit{q} increase tends to cause more kinetic ballooning modes at the edge and the \textit{q} decrease means that the peeling is getting worse, but the ballooning is getting better. The large edge \textit{q} tends to provide hollow density while small edge \textit{q} gives normal density profile. This is consistent with the observation that the density of particles is inversely proportional to the density of the plasma current. The rise in the source of the edge particle increases the density of the edge and the reaction rate close to the edge increases temperature fluxes, resulting in weak pedestal barriers. When neoclassical transport is turned off or the strength of B-field is increased, the pronounced edge barriers are identified. In addition, a distinct effect on the magnetohydrodynamic (MHD) modes is observed due to the increased B-field. The interesting aspect is that the barrier collapses about \textit{q} = 2 as the stability of MHD has decreased to replace the barrier with a continuous slope but with roughly the same fusion power. This would actually be good for a reactor. The slope of the H-mode pedestal is found to be reduced due to the alpha heating. It is expected that the problem of edge-localized modes causing damage to the first wall will be eased. The effects of circular, elongated, and general geometry on plasma profiles are also compared and contrasted. The circular geometry has a hallow density profile and no edge or internal thermal transport barrier (ETB or ITB). However, both ETBs and ITBs can be found in the elongated geometry. In general geometry, there is a weaker ETB, comparable ITBs, but a higher edge particle transport barrier than in elongated geometry. Higher density near the edge, on the other hand, causes more wall erosion, so elongated geometry might be the best option.

The impact of adiabatic electrons on drift-wave turbulence, modelled by the Hasegawa-Wakatani equations, is studied using information length. Information length is a novel theoretical method for measuring distances between statistical states represented by different probability distribution functions (PDFs) along the path of a system. Specifically, the time-dependent PDFs of turbulent fluctuations for a given adiabatic index $A$ is computed. The changes in fluctuation statistics are then quantified in time by using information length. The numerical results provide time traces exhibiting intermittent plasma dynamics, and such behaviour is identified by a rapid change in the information length. The effects of $A$ are discussed., Comment: 23 pages submitted to Physics of Plasmas. arXiv admin note: text overlap with arXiv:1706.02849

Microtearing mode (MTM) real frequency, growth rate, magnetic fluctuation amplitude, and resulting electron thermal transport are studied in systematic NSTX scans of relevant plasma parameters. The dependency of the MTM real frequency and growth rate on plasma parameters, suitable for low and high collision NSTX discharges, is obtained by using the reduced MTM transport model [T. Rafiq et al., Phys. Plasmas 23, 062507 (2016)]. The plasma parameter dependencies are compared and found to be consistent with the results obtained from MTM using the gyrokinetic GYRO code. The scaling trend of collision frequency and plasma beta is found to be consistent with the global energy confinement trend observed in the NSTX experiment. The strength of the magnetic fluctuation is found to be consistent with the gyrokinetic estimate. In earlier studies, it was found that the version of the multi-mode (MM) anomalous transport model, which did not contain the effect of MTMs, provided an appropriate description of the electron temperature profiles in standard tokamak discharges and not in spherical tokamaks. When the MM model, which involves transport associated with MTMs, is incorporated in the TRANSP code and is used in the study of electron thermal transport in NSTX discharges, it is observed that the agreement with the experimental electron temperature profile is substantially improved.

The Multi-Mode Model (MMM7.1) for anomalous transport is tested in predictive modeling of temperature profiles of a high beta poloidal DIII-D discharge. This new H-mode plasma regime, with high beta poloidal and high bootstrap currents, has been studied in DIII-D tokamak discharges [A. Garofalo et al., Nucl. Fusion 55, 123025 (2015)]. The role of instabilities that can drive the anomalous transport described by MMM7.1 is investigated. The temperature profiles for a high beta poloidal DIII-D discharge are computed using the NCLASS model for the neoclassical transport and the Weiland and Electron Temperature Gradient (ETG) components of the MMM7.1 model for the anomalous transport. The neoclassical transport is found to be the main contributor to the ion thermal transport in the plasma core. The contributions from the ion temperature gradient driven modes are found to be important only outside of the internal transport barrier. The magnitudes of the predicted temperature profiles are found to be in a reason...

A reduced transport model for microtearing modes is developed for use in integrated predictive modeling studies, employing a unified fluid/kinetic approach to derive the nonlinear dispersion relation. This approach advances the kinetic description and allows the inclusion of nonlinear effects due to magnetic fluctuations. In this numerical study, the dependence of the microtearing mode real frequency and growth rate on plasma parameters and on DIII-D like L-mode and H-mode plasma profiles is examined. The magnetic fluctuation strength as well as electron thermal diffusivity due to microtearing modes is computed. The saturated amplitude of the magnetic fluctuations is calculated utilizing numerically determined microtearing mode eigenvalues in the nonlinear microtearing modes envelope equation. It is found that the electron temperature gradient in the presence of moderate collision frequency is required for the microtearing mode to become unstable. The effects of small and large collisionality and small and large wavenumbers on microtearing modes are found to be stabilizing, while the effects of density gradient, plasma beta, low current density, and large magnetic shear are found to be destabilizing. The microtearing mode growth rate, magnetic fluctuation strength, as well as electron thermal diffusivity is found to be larger in the H-mode plasma than in the L-mode plasma.

The guiding-center kinetic neoclassical transport code, XGC0, [C.S. Chang et. al, Phys. Plasmas 11, 2649 (2004)] is used to compute the heat fluxes and the heat-load width in the outer divertor plates of Alcator C-Mod and DIII-D tokamaks. The dependence of the width of heat-load fluxes on neoclassical effects, neutral collisions and anomalous transport is investigated using the XGC0 code. The XGC0 code includes realistic X-point geometry, a neutral source model, the effects of collisions, and a diffusion model for anomalous transport. It is observed that width of the XGC0 neoclassical heat-load is approximately inversely proportional to the total plasma current $I_{\rm p}$. The scaling of the width of the divertor heat-load with plasma current is examined for an Alcator C-Mod discharge and four DIII-D discharges. The scaling of the divertor heat-load width with plasma current is found to be weaker in the Alcator C-Mod discharge compared to scaling found in the DIII-D discharges. The effect of neutral collisions on the $1/I_{\rm p}$ scaling of heat-load width is shown not to be significant. Although inclusion of poloidally uniform anomalous transport results in a deviation from the $1/I_{\rm p}$ scaling, the inclusion of the anomalous transport that is driven by ballooning-type instabilities results in recovering the neoclassical $1/I_{\rm p}$ scaling. The Bohm or Gyro-Bohm scalings of anomalous transport does not strongly affect the dependence of the heat-load width on plasma current. The inclusion of anomalous transport, in general, results in widening the width of neoclassical divertor heat-load and enhances the neoclassical heat-load fluxes on the divertor plates. Understanding heat transport in the tokamak scrape-off layer plasmas is important for strengthening the basis for predicting divertor conditions in ITER., Comment: Submitted to Physics of Plasmas

The linear stability of the ion-temperature-gradient (ITG) driven drift modes is investigated in an International Thermonuclear Experimental Reactor-like geometry using an advanced reactive fluid model and the ballooning mode formalism. The spectrum of stable and unstable modes and their real frequencies, growth rates and eigenfunctions are calculated for two specific magnetic flux surfaces. The effects of density and temperature gradients, temperature ratios, wave vector and geometrical quantities such as local magnetic shear (LMS), normal curvature, geodesic curvature and magnetic field on the ITG mode are discussed. It is found that the most unstable eigenfunction is extended and less unstable at the magnetic surface where global magnetic shear is reversed. Moreover, the role of positive LMS is found to be destabilizing at the reverse shear magnetic surface. However, at a positive global shear magnetic surface, the eigenmode is found to be more localized and more unstable, and its structure and stability are affected by the local behaviour of the geometrical quantities.

Modern stellarators are designed with neoclassical transport in mind, potentially leading to anomalous transport originating from drift wave turbulence as the primary cause of energy and particle losses. It is therefore of interest to consider the influence of details of geometry on drift wave stability. In this paper the eigenvalue drift wave equation is therefore solved numerically in fully three-dimensional stellarator geometries using the ballooning mode formalism. The correlation between the details of the configurations such as local magnetic shear (LMS), normal curvature, geodesic curvature and magnetic field strength and the drift wave spectrum is discussed for two different stellarator configurations. A detailed discussion of the localization of the most unstable modes is presented and analysed. It is found that the most unstable modes are localized where the stabilizing effect of integrated LMS is minimum or where the coupling between the integrated LMS and geodesic curvature is strong. Since the more the modes are localized the stronger they will be influenced by the local geometrical effects, the most unstable modes are also highly localized.

In this paper, we demonstrate the importance of the details of the equilibria on the stability of electron drift waves. A comparison of electrostatic electron drift waves in numerical and analytical tokamak equilibria is presented in fully three-dimensional circular and non-circular tokamaks. The numerical equilibria are obtained using the variational moments equilibrium code and the analytical equilibria used is the generalized ŝ-α model. An eigenvalue equation for the model is derived using the ballooning mode formalism and solved numerically using a standard shooting technique. The stability and the localization of the electron drift wave is found to be strongly dependent on the local shear of the magnetic field. Large values of the local shear are found to be stabilizing. A disagreement in the results is found between analytical and numerical equilibria at aspect ratios of typical tokamaks, suggesting that the latter approach should be used in the transport calculations. The effects of the local shaping of the magnetic surfaces are complicated and can be both stabilizing and destabilizing, depending on the details of the equilibria.

The linear stability of the ion-temperature-gradient modes (ITG) in the electrostatic limit is examined in the short wavelength region by using a two fluid reactive model in fully three-dimensional Wendelstein 7-X (W7-X) stellarator [G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] geometry. The spectrum of stable and unstable modes and their real frequencies and eigenfunctions are calculated. The effects of density gradients, temperature gradients, temperature ratios, wavevector, ballooning angle, curvature and local magnetic shear on the ITG mode are also investigated. The frequency and growth rate of the most unstable ITG mode is calculated and visualized for a specific magnetic flux surface. For the equilibrium under investigation both localized and extended eigenmodes are found. The effect of small and large temperature ratios, small and large density gradients as well as large local magnetic shear are a...

The influence of plasma geometry on the linear stability of electrostatic ion-temperature-gradient driven drift modes (ITG modes) is investigated. An advanced fluid model is used for the ions together with Boltzmann distributed electrons. The derived eigenvalue equation is solved numerically. A comparison is made between an H – 1NF [Fusion Technol. 17, 123 (1990)] like stellarator equilibrium, a numerical tokamak equilibrium and the analytical s - alpha equilibrium. The numerical and the analytical tokamak are found to be in good agreement in the low inverse aspect ratio limit. The growth rates of the tokamak and stellarator are comparable whereas the modulus of the real frequency is substantially larger in the stellarator. The threshold in Ln/LT for the stellarator is found to be somewhat larger. In addition, a stronger stabilization of the ITG mode growth is found for large L n / R in the stellarator case.

The effects of plasma shaping on the H-mode pedestal structure are investigated. High fidelity kinetic simulations of the neoclassical pedestal dynamics are combined with the magnetohydrodynamic (MHD) stability conditions for triggering edge localized mode (ELM) instabilities that limit the pedestal width and height in H-mode plasmas. The neoclassical kinetic XGC0 code [Chang et al., Phys. Plasmas 11, 2649 (2004)] is used in carrying out a scan over plasma elongation and triangularity. As plasma profiles evolve, the MHD stability limits of these profiles are analyzed with the ideal MHD ELITE code [Snyder et al., Phys. Plasmas 9, 2037 (2002)]. Simulations with the XGC0 code, which includes coupled ion-electron dynamics, yield predictions for both ion and electron pedestal profiles. The differences in the predicted H-mode pedestal width and height for the DIII-D discharges with different elongation and triangularities are discussed. For the discharges with higher elongation, it is found that the gradients o...

A study of the effect of local magnetic shear on the drift wave stability is presented. The eigenvalue problem for the drift wave equation is solved numerically in fully three-dimensional stellarator plasma using the ballooning mode formalism. It is found that negative local magnetic shear has a stabilizing effect on the drift wave instability and positive local shear is destabilizing. This is in agreement with the effect of negative global magnetic shear in tokamaks and also agrees with the simple estimates. As a consequence the highly unstable modes found on a specific magnetic surface are localized in the region of positive local magnetic shear.

The ion-temperature-gradient (ITG)-driven drift mode is studied in three-dimensional stellarator geometry using a two-fluid reactive model in the electrostatic limit. The model includes first-order FLR effect in the presence of parallel ion dynamics and using the Boltzmann distribution for the electrons. The resulting eigenvalue is solved numerically using the ballooning mode theory. The results are contrasted with the corresponding tokamak results with positive shear. In stellarators, the level of the maximum growth rate of the ITG mode is found to be smaller and the threshold (ηi2.2) is somewhat higher. The effects of small and large temperature ratios and density gradients are found to be stabilizing on electrostatic ITG modes in stellarators.

A new set of nonlinear mode coupling equations for finite amplitude low-frequency electromagnetic waves has been derived for nonuniform, resistive, magnetized electron-ion plasma with sheared flows. At equilibrium, the plasma is assumed to have density, ion-temperature, magnetic field, and velocity gradients. The temporal behavior of the nonlinear mode coupling equations is found to be governed by eight coupled equations, which are the generalization of the Lorenz and Stenflo equations, admitting chaotic trajectories. The linear stability of the generalized Lorenz–Stenflo system of equations is also presented under different approximations. The results of the present investigation should be helpful in understanding the wave phenomena in space and tokamak plasmas.

We derive a system of nonlinear equations that govern the dynamics of low-frequency short-wavelength electromagnetic waves in the presence of equilibrium density, temperature, magnetic field and velocity gradients. In the linear limit, a local dispersion relation is obtained and analyzed. New ηe-driven electromagnetic drift modes and instabilities are shown to exist. In the nonlinear case, the temporal behaviour of a nonlinear dissipative system can be written in the form of Lorenz- and Stenflo-type equations that admit chaotic trajectories. On the other hand, the stationary solutions of the nonlinear system can be represented in the form of dipolar and vortex-chain solutions.

By using Braginskii transport equations for ions and Boltzmann distribution for electrons, a new system of nonlinear equations governing the dynamics of low-frequency, short-wavelength electrostatic waves in the presence of equilibrium density, temperature, magnetic field, and electrostatic potential gradients has been derived. New ion-temperature-gradient (ITG) driven drift-dissipative modes are shown to exist. An expression for anomalous ion energy transport caused by nonthermal electrostatic fluctuations is also derived. Furthermore, possible stationary solutions of the nonlinear system are obtained in the form of double vortex. On the other hand, the temporal behavior of newly derived nonlinear dissipative systems can be described by the generalized Lorenz–Stenflo equations which admit chaotic solutions. The results of the present investigation should be helpful for understanding the wave phenomena in space and tokamak plasmas.

By employing the two-fluid model, a system of nonlinear equations for low-frequency electromagnetic waves in nonuniform collisional magnetoplasmas has been derived. The plasma contains both the equilibrium density gradient and sheared flows. In the linear limit, a local dispersion relation has been obtained and analyzed in several interesting limiting cases. It is found that equilibrium sheared plasma flows cause instabilities of Alfven-type waves even in the absence of the density gradient. The numerical results also show a large growth rate of electromagnetic parallel velocity shear (PVS) mode compared to the electrostatic mode for some ionospheric parameters. For this case, the temporal nonlinear behavior of the relevant governing mode coupling equations is governed by six coupled equations, which are a generalization of the Lorenz–Stenflo equations and which admit chaotic trajectories. The results of this investigation should be useful for understanding the linear and nonlinear properties of electromagnetic waves that are generated by sheared plasma flows in magnetized plasmas.

Anomalous transport in the H-mode pedestal region of five Alcator C-Mod discharges, representing a collisionality scan is analyzed. The understanding of anomalous transport in the pedestal region is important for the development of a comprehensive model for the H-mode pedestal slope. In this research, a possible role of the drift resistive inertial ballooning modes (Rafiq et al 2010 Phys. Plasmas 17 082511) in the edge of Alcator C-Mod discharges is analyzed. The stability analysis, carried out using the TRANSP code, indicates that the DRIBM modes are strongly unstable in Alcator C-Mod discharges with large electron collisionality. An improved interpretive analysis of H-mode pedestal experimental data is carried out utilizing the additive flux minimization technique (Pankin et al 2013 Phys. Plasmas 20 102501) together with the guiding-center neoclassical kinetic XGC0 code. The neoclassical and neutral physics are simulated in the XGC0 code and the anomalous fluxes are computed using the additive flux minimization technique. The anomalous fluxes are reconstructed and compared with each other for the collisionality scan Alcator C-Mod discharges. It is found that the electron thermal anomalous diffusivities at the pedestal top increase with the electron collisionality. This dependence can also point to the drift resistive inertial ballooning modes as the modes that drive the anomalous transport in the plasma edge of highly collisional discharges.

Microtearing modes (MTMs) have been identified as a source of significant electron thermal transport in tokamak discharges. In order to describe the evolution of these discharges, it is necessary to improve the prediction of electron thermal transport. This can be accomplished by utilizing a model for transport driven by MTMs in whole device predictive modeling codes. The objective of this paper is to develop the dispersion relation that governs the MTM driven transport. A unified fluid/kinetic approach is used in the development of a nonlinear dispersion relation for MTMs. The derivation includes the effects of electrostatic and magnetic fluctuations, arbitrary electron-ion collisionality, electron temperature and density gradients, magnetic curvature, and the effects associated with the parallel propagation vector. An iterative nonlinear approach is used to calculate the distribution function employed in obtaining the nonlinear parallel current and the nonlinear dispersion relation. The third order nonlinear effects in magnetic fluctuations are included, and the influence of third order effects on a multi-wave system is considered. An envelope equation for the nonlinear microtearing modes in the collision dominant limit is introduced in order to obtain the saturation level. In the limit that the mode amplitude does not vary along the field line, slab geometry, and strong collisionality, the fluid dispersion relation for nonlinear microtearing modes is found to agree with the kinetic dispersion relation.

Self-consistent simulations of 15 MA ITER H-mode DT scenarios, from ramp-up through flat-top, are carried out. Electron and ion temperatures, toroidal angular frequency, and currents are evolved, in simulations carried out using the predictive TRANSPort and integrated modeling code starting with initial profiles and equilibria obtained from tokamak simulation code studies. Studies are carried out examining the dependence and sensitivity of fusion power production on electron density, argon impurity concentration, choice of radio frequency heating, pedestal temperature without and with E × B flow shear effects included, and the degree of plasma rotation. The goal of these whole-device ITER simulations is to identify dependencies that might impact ITER fusion performance.

The mixed gradient method [Zhong et al. Phys. Rev. Lett. 111, 265001 (2013)] is adopted and effects of collisions and finite beta are included in the Weiland 9-equation fluid model. The particle flux and particle pinch, obtained using the Weiland anomalous transport fluid model, are compared with Tore Supra experimental results. Particle transport is also studied using predictive simulation data for an experimental advanced superconducting tokamak discharge in which neutral beam heating is utilized. The effects of collisions on particle transport are studied by turning collisions on and off in the Weiland model. It is found that the particle pinch region is related to the mode structure. The particle pinch region coincides with the region where the strong ballooning modes are present due to large gradients. The general properties of the fluid model are examined by finding regions where collisions can enhance the particle pinch.

Three numerical techniques employing differentiation matrices are used to investigate the linear stability of drift-resistive-inertial ballooning mode for conditions that occur in tokamak edge plasmas. Hermite and Sinc spectral methods are applied to compute the ballooning mode eigenvalues and eigenvectors. In addition, a finite difference method is utilized to construct a differentiation matrix in order to verify results obtained using the spectral methods. It is shown that the spectral methods converge more rapidly than the finite difference method. Ballooning and strongly ballooning approximations are used to calculate the eigen-spectrum. The techniques that are utilized in this paper for calculating eigenvalues are quite general and are relevant to investigate other modes that use the ballooning mode formalism.

A new additive flux minimization technique is proposed for carrying out the verification and validation (V&V) of anomalous transport models. In this approach, the plasma profiles are computed in time dependent predictive simulations in which an additional effective diffusivity is varied. The goal is to obtain an optimal match between the computed and experimental profile. This new technique has several advantages over traditional V&V methods for transport models in tokamaks and takes advantage of uncertainty quantification methods developed by the applied math community. As a demonstration of its efficiency, the technique is applied to the hypothesis that the paleoclassical density transport dominates in the plasma edge region in DIII-D tokamak discharges. A simplified version of the paleoclassical model that utilizes the Spitzer resistivity for the parallel neoclassical resistivity and neglects the trapped particle effects is tested in this paper. It is shown that a contribution to density transport, in ...

The derivation of Multi-Mode anomalous transport module version 8.1 (MMM8.1) is presented. The MMM8.1 module is advanced, relative to MMM7.1, by the inclusion of peeling modes, dependence of turbulence correlation length on flow shear, electromagnetic effects in the toroidal momentum diffusivity, and the option to compute poloidal momentum diffusivity. The MMM8.1 model includes a model for ion temperature gradient, trapped electron, kinetic ballooning, peeling, collisionless and collision dominated magnetohydrodynamics modes as well as model for electron temperature gradient modes, and a model for drift resistive inertial ballooning modes. In the derivation of the MMM8.1 module, effects of collisions, fast ion and impurity dilution, non-circular flux surfaces, finite beta, and Shafranov shift are included. The MMM8.1 is used to compute thermal, particle, toroidal, and poloidal angular momentum transports. The fluid approach which underlies the derivation of MMM8.1 is expected to reliably predict, on an energy transport time scale, the evolution of temperature, density, and momentum profiles in plasma discharges for a wide range of plasma conditions.

ITER hybrid and target steady-state fusion burn scenarios are simulated using the PTRANSP integrated modelling code together with input from the TSC code. In the hybrid scenarios, the majority of the current is driven inductively; whereas, for the target steady-state scenarios, approximately 22% of the current (at 1000 s) is driven inductively with the remaining current driven by the bootstrap, neutral beam and radio frequency sources. Predictive simulations are carried out using either the new Multi-Mode or the GLF23 anomalous transport model. Momentum transport is used to compute the toroidal angular frequency profile which, in turn, is used to compute the self-consistent flow shear suppression of anomalous transport. The simulations of the hybrid scenario indicate that the fusion power production at 1000 s will be approximately 500 MW corresponding to a fusion Q = 9.4. The fusion power predicted in the simulations of the target steady-state scenarios is found to depend on the time dependence of the input heating and associated current drive. It is found that turning off some components of auxiliary heating causes the fusion power production to increase. The fusion power obtained in the target steady-state scenarios, depending on the transport model and input injected power, ranges from 168 MW up to 226 MW, corresponding to a fusion Q ranging from 2.0 to 6.8.

The Tokamak simulation code (TSC) is used to provide initial conditions for predictive TRANSPort and integrated modeling code (PTRANSP) simulations of ITER target steady state scenarios. The PTRANSP simulations are carried out using the new multi-mode (MMM7.1) and the gyro-Landau-fluid (GLF23) transport models. It is found that there are circumstances under which the total fusion power decreases with increasing pedestal temperature height. When the total current (from magnetic axis to plasma edge) is fixed, an increased fraction of the current is concentrated in the pedestal region as the pedestal height is increased. As a consequence of the fixed total current, this results a smaller fraction of the current in the core plasma and, consequently, lower energy confinement. In previous simulations of ITER, in which the fusion power increased with increasing pedestal temperature height, the plasma current from the top of the pedestal to the magnetic axis was held fixed independent of the pedestal temperature. Simulations presented in this paper also indicate that improvement in fusion power production occurs when the lower hybrid current drive is replaced with electron cyclotron current drive. Again, the improvement results from the redistribution of plasma current since the lower hybrid power generally drives current closer to the plasma edge than does the electron cyclotron power. ITER simulation results obtained using the MMM7.1 transport model are compared with those using the GLF23 model. It is found that, in simulations of target steady state scenarios, momentum transport and flow-shear suppression features of the new MMM7.1 model can lead to predictions of internal transport barriers in temperature and rotation frequency.

A new model is developed for transport driven by drift-resistive-inertial ballooning modes (DRIBMs) in axisymmetric tokamak plasmas. The model is derived using two-fluid reduced Braginskii equations in a generalized s−α geometry. The unified theory includes diamagnetic effects, parallel electron and ion dynamics, electron inertia, magnetic perturbations, transverse particle diffusion, gyroviscous stress terms, electron and ion equilibrium temperature gradients, and temperature perturbations. A mixing length approximation is used to compute electron and ion thermal transport as well as particle fluxes from eigenvalues and eigenvectors of the linearized equations. The prediction for the saturation level is obtained by balancing the DRIBM growth rate against the nonlinear E×B convection. The parametric dependence of DRIBMs is investigated in systematic scans over density gradient, electron and ion temperature gradients, magnetic-q, collision frequency, magnetic shear, and Larmor radius. The DRIBM threshold is determined as a function of the collision frequency and the density and temperature gradients. The transition from DRIBM to the toroidal ion temperature gradient (ITG) mode is observed for small density gradients. For steep density gradients, the effect of ITG on DRIBM is found to be stabilizing. The transport seen in the DRIBM is of a scale that is consistent with the observed experimental anomalous transport, suggesting that the DRIBM mode could be the principle agent responsible for edge transport in Ohmic and L-mode discharges.

An H-mode edge pedestal plasma transport benchmarking exercise was undertaken for a single DIII-D pedestal. Transport modelling codes used include 1.5D interpretive (ONETWO, GTEDGE), 1.5D predictive (ASTRA) and 2D ones (SOLPS, UEDGE). The particular DIII-D discharge considered is 98889, which has a typical low density pedestal. Profiles for the edge plasma are obtained from Thomson and charge-exchange recombination data averaged over the last 20% of the average 33.53 ms repetition time between type I edge localized modes. The modelled density of recycled neutrals is largest in the divertor X-point region and causes the edge plasma source rate to vary by a factor ∼102 on the separatrix. Modelled poloidal variations in the densities and temperatures on flux surfaces are small on all flux surfaces up to within about 2.6 mm (ρN > 0.99) of the mid-plane separatrix. For the assumed Fick's-diffusion-type laws, the radial heat and density fluxes vary poloidally by factors of 2–3 in the pedestal region; they are largest on the outboard mid-plane where flux surfaces are compressed and local radial gradients are largest. Convective heat flows are found to be small fractions of the electron (≲10%) and ion (≲25%) heat flows in this pedestal. Appropriately averaging the transport fluxes yields interpretive 1.5D effective diffusivities that are smallest near the mid-point of the pedestal. Their ‘transport barrier’ minima are about 0.3 (electron heat), 0.15 (ion heat) and 0.035 (density) m2 s−1. Electron heat transport is found to be best characterized by electron-temperature-gradient-induced transport at the pedestal top and paleoclassical transport throughout the pedestal. The effective ion heat diffusivity in the pedestal has a different profile from the neoclassical prediction and may be smaller than it. The very small effective density diffusivity may be the result of an inward pinch flow nearly balancing a diffusive outward radial density flux. The inward ion pinch velocity and density diffusion coefficient are determined by a new interpretive analysis technique that uses information from the force balance (momentum conservation) equations; the paleoclassical transport model provides a plausible explanation of these new results. Finally, the measurements and additional modelling needed to facilitate better pedestal plasma transport modelling are discussed.

A linear stability theory of nonideal magnetohydrodynamic (MHD) ballooning modes is investigated using a two fluid model for electron-ion plasmas. Drift-resistive-inertial ballooning mode eigenvalues and eigenfunctions are calculated for a variety of equilibria including axisymmetric shifted circular geometry (s−α model) as well as for three dimensional configurations relevant for the Helically Symmetric Stellarator (HSX) [F. S. B. Anderson, A. F. Almagri, D. T. Anderson, et al., Fusion Technology 27, 273 (1995)]. For typical HSX parameters, characteristic ballooning mode growth rates exceed the electron collision frequency. In this regime, electron inertial effects dominate plasma resistivity and produce an instability whose growth rate scales with the electromagnetic skin depth. However, as plasma β is increased, the resistive and inertial effects become unimportant. Under these conditions, the mode is completely stabilized by drift frequency effects, which dominate resistivity and inertia. Numerical r...

Analytic results for the stability of resistive ballooning modes (RBMs) and electron inertial ballooning modes are obtained using a two-scale analysis. This work generalizes previous calculations used for axisymmetric s−α geometry [R. H. Hastie, J. J. Ramos, and F. Porcelli, Phys. Plasmas 10, 4405 (2003)] to general three-dimensional geometry. A unified theory is developed for RBMs and inertial ballooning modes, in which the effects of both ideal magnetohydrodynamic free energy (as measured by the asymptotic matching parameter Δ′) and geodesic curvature drives in the nonideal layer are included in the dispersion relation. This unified theory can be applied to determine the stability of drift-resistive-inertial ballooning modes in the low temperature edge regions of tokamak and stellarator plasmas where steep density gradients exist.

Electron thermal transport in DIII-D H-mode tokamak plasmas [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] is investigated by comparing predictive simulation results for the evolution of electron temperature profiles with experimental data. The comparison includes the entire profile from the magnetic axis to the bottom of the pedestal. In the simulations, carried out using the automated system for transport analysis (ASTRA) integrated modeling code, different combinations of electron thermal transport models are considered. The combinations include models for electron temperature gradient (ETG) anomalous transport and trapped electron mode (TEM) anomalous transport, as well as a model for paleoclassical transport [J. D. Callen, Nucl. Fusion 45, 1120 (2005)]. It is found that the electromagnetic limit of the Horton ETG model [W. Horton et al., Phys. Fluids 31, 2971 (1988)] provides an important contribution near the magnetic axis, which is a region where the ETG mode in the GLF23 model [R. E. Waltz et al., Phy...

The linear stability of coupled collisionless trapped electron (TE) and ion temperature gradient (ITG) modes is investigated in an International Thermonuclear Experimental Reactor [C. Gormezano , Nucl. Fusion 47, S285 (2007)]-like magnetic field configuration. An advanced fluid model in the electrostatic limit and the ballooning mode formalism are used to derive an eigenvalue equation. The growth rates and real frequencies of the most unstable modes and their eigenfunctions are calculated. The coexistence of unstable ITG and TE modes and their relative strengths with respect to the fraction of trapped electrons, wave vector, and local plasma parameters, such as density gradient, electron/ion temperature gradient, and ion to electron temperature ratio are analyzed. The influence of geometrical factors, such as local/global magnetic shear and magnetic field curvature on both ITG and TE modes is also discussed.

Geometrical effects on linear stability of electrostatic resistive edge modes are investigated in the three-dimensional Wendelstein 7-X stellarator [G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] and the International Thermonuclear Experimental Reactor [Progress in the ITER Physics Basis, Nucl. Fusion 7, S1, S285 (2007)]-like equilibria. An advanced fluid model is used for the ions together with the reduced Braghinskii equations for the electrons. Using the ballooning mode representation, the drift wave problem is set as an eigenvalue equation along a field line and is solved numerically using a standard shooting technique. A significantly larger magnetic shear and a less unfavorable normal curvature in the tokamak equilibrium are found to give a stronger finite-Larmor radius stabilization and a more narrow mode spectrum than in the stellarator. The effect of negative global magnetic shear in the tokamak is ...

The linear electrostatic dissipative trapped-electron mode is investigated in a quasihelically symmetric (QHS) stellarator and a configuration whose symmetry is spoiled by the addition of a mirror contribution to the magnetic spectrum. The effect of the trapped electrons is accounted for using the drift kinetic equation with an energy-dependent Krook collision operator and an effective collision frequency giving the rate of detrapping. The ballooning mode formalism and Wentzel-Kramers-Brillouin type boundary conditions are used to solve an eigenvalue problem for a drift wave equation with nearly adiabatic electrons in a fully three-dimensional magnetohydrodynamic equilibria. The trapped-electron growth rate is calulated using a perturbative approach. Multiple classes of helically localized and toroidally localized eigenfunctions in the ballooning space are calculated. The results of the QHS configuration is compared and contrasted with the results of the mirror configuration. The helically trapped modes a...

The local linear stability of electron drift waves and ion temperature gradient modes (ITG) is investigated in a quasihelically symmetric (QHS) stellarator and a conventional asymmetric (Mirror) stellarator. The geometric details of the different equilibria are emphasized. Eigenvalue equations for the models are derived using the ballooning mode formalism and solved numerically using a standard shooting technique in a fully three-dimensional stellarator configuration. While the eigenfunctions have a similar shape in both magnetic geometries, they are slightly more localized along the field line in the QHS case. The most unstable electron drift modes are strongly localized at the symmetry points (where stellarator symmetry is present) and in the regions where normal curvature is unfavorable and magnitude of the local magnetic shear and magnetic field is minimum. The presence of a large positive local magnetic shear in the bad curvature region is found to be destabilizing. Electron drift modes are found to ...

A set of coupled nonlinear differential equations governing the dynamics of low-frequency electromagnetic waves in the presence of equilibrium sheared flow for inhomogeneous collisional magnetized plasma has been derived. In the linear limit of a uniform density plasma, it is shown that equilibrium sheared plasma flows can cause an instability of resistive Alfven-like waves. Furthermore, a quasi-stationary solution of the mode coupling equations can be represented in the form of localized vortex structures. On the other hand, the temporal behavior of the mode coupling equations is governed by six coupled equations, which are a generalization of the Lorenz-Stenflo equations and which admit chaotic trajectories.

Simulations of doublet III-D, the joint European tokamak, and the tokamak fusion test reactor L-mode tokamak plasmas are carried out using the PTRANSP predictive integrated modeling code. The simulation and experimental temperature profiles are compared. The time evolved temperature profiles are computed utilizing the Multi-Mode anomalous transport model version 7.1 (MMM7.1) which includes transport associated with drift-resistive-inertial ballooning modes (the DRIBM model [T. Rafiq et al., Phys. Plasmas 17, 082511 (2010)]). The tokamak discharges considered involved a broad range of conditions including scans over gyroradius, ITER like current ramp-up, with and without neon impurity injection, collisionality, and low and high plasma current. The comparison of simulation and experimental temperature profiles for the discharges considered is shown for the radial range from the magnetic axis to the last closed flux surface. The regions where various modes in the Multi-Mode model contribute to transport are illustrated. In the simulations carried out using the MMM7.1 model it is found that: The drift-resistive-inertial ballooning modes contribute to the anomalous transport primarily near the edge of the plasma; transport associated with the ion temperature gradient and trapped electron modes contribute in the core region but decrease in the region of the plasma boundary; and neoclassical ion thermal transport contributes mainly near the center of the discharge.