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Edge localized modes (ELMs) suppression by resonant magnetic perturbations (RMPs) was studied with the non-linear magneto-hydro-dynamic (MHD) code JOREK for the ITER H-mode scenarios at 15 MA, 12.5 MA, 10 MA/5.3 T. The main aim of this work was to demonstrate that ELMs can be suppressed by RMPs while the divertor 3D footprints of heat and particle fluxes remain within divertor material limits. The unstable peeling–ballooning modes responsible for ELMs without RMPs were modelled first for each scenario using numerically accessible parameters for ITER. Then the stabilization of ELMs by RMPs was modelled with the same parameters. RMP spectra, optimized by the linear MHD MARS-F code, with main toroidal harmonics N = 2, N = 3, N = 4 have been used as boundary conditions of the computational domain of JOREK, including realistic RMP coils, main plasma, scrape off layer (SOL) divertor and realistic first wall. The model includes all relevant plasma flows: toroidal rotation, two fluid diamagnetic effects and neoclassical poloidal friction. With RMPs, the main toroidal harmonic and the non-linearly coupled harmonics remain dominant at the plasma edge, producing saturated modes and a continuous MHD turbulent transport thereby avoiding ELM crashes in all scenarios considered here. The threshold for ELM suppression was found at a maximum RMP coils current of 45 kAt–60 kAt compared to the coils maximum capability of 90 kAt. In the high beta poloidal steady-state 10 MA/5.3 T scenario, a rotating QH-mode without ELMs was observed even without RMPs. In this scenario with RMPs N = 3, N = 4 at 20 kAt maximum current in RMP coils, similar QH-mode behaviour was observed however with dominant edge harmonic corresponding to the main toroidal number of RMPs. The present MHD modelling was limited in time by few tens of ms after RMPs were switched on until the magnetic energy of the modes saturates. As a consequence the thermal energy was still evolving on this time scale, far from the ITER confinement time scale and hence only the form of 3D footprints on the divertor targets can be indicated within this set-up. Also note, that the divertor physics was missing in this model, so realistic values of fluxes are out of reach in this modelling. However the stationary 3D divertor and particle fluxes could be simply extrapolated from these results to the stationary situation considering that a large power fraction should be radiated in the core and SOL and only about 50 MW power is going to the divertor, which is an arbitrary, but reasonable number used here. The 3D footprints with RMPs show the characteristic splitting with the main RMP toroidal symmetry. The maximum radial extension of the footprints typically was ∼20 cm in inner divertor and ∼40 cm in outer divertor with stationary heat fluxes decreasing further out from the initial strike point from ∼5 MW m−2 to ∼1 MW m−2 assuming a total power in the divertor and walls is 50 MW. The heat fluxes remain within the divertor target and baffle areas, however with rather small margin in the outer divertor which could be an issue for the first wall especially in transient regimes when part of the plasma thermal energy is released due to switching on the RMP coils. This fact should be considered when RMPs are applied with a more favorable application before or soon after the L–H transition, although optimization is required to avoid increasing the L–H power threshold with RMPs.

Self-consistent modeling using the stability, transport, equilibrium, and pedestal (STEP) workflow in the OMFIT integrated modeling framework (predicting pedestal with EPED, core profiles with TGYRO, current profile with ONETWO, and EFIT for equilibrium) suggests ITER and future devices such as China Fusion Engineering Test Reactor (CFETR) Zhuang et al (2019 Nucl. Fusion 59 112010) will benefit from high-density operation (Greenwald limit fraction f g w ≈ 0.7−1.3). Regimes with an operational density near the Greenwald limit will likely need peaked density profiles so that the pedestal density remains below the Greenwald limit. Peaked density profiles can be achieved with the help of pellet injection. A flexible Pellet Ablation Module (PAM), which predicts the density source based on a comprehensive analytical pellet ablation model, has been developed for predicting pellet fueling for transport studies, and has been incorporated into the STEP workflow for predictive modeling. This workflow is applied to DIII-D and finds good agreement with experiments. On ITER the effect of pellet fueling is examined in an advanced inductive scenario, where a fusion gain of up to Q = 9 is predicted with strong central pellet fueling. On CFETR, with a mid-radius density source, an average of 1.5 × 10 22 electrons s−1 are required to achieve the density and temperature profiles necessary for the 1000 MW advanced scenario with a tritium burn-up fraction of ∼ 3 % .

A coupling between two distinctly different codes—one magnetohydrodynamic (MHD) and another kinetic—is achieved and applied for simulation of runaway electron (RE) production. The 3D initial value MHD code NIMROD simulates a DIII-D pure neon shattered pellet injection plasma quench including the propagation and ablation of the fragments, ionization and recombination of the impurities, and the radiated and transported energies. The field data from NIMROD is then used by the bounce-averaged Fokker–Planck Collisional QuasiLinear 3D (CQL3D) kinetic code to simulate the production of REs and their radial transport. The coupling procedure involves mapping of data between different grids and adjustment of the NIMROD toroidal electric field when REs appear. It is shown that without the radial transport, a large RE current is generated, up to 30% of the pre-pellet ohmic current. However, when the radial transport is included in CQL3D, the RE current is reduced to undetectable level, consistent with experiment. Various forms of the radial diffusion are surveyed to determine conditions when the fast electrons would not have time to be accelerated to relativistic energies before they are lost to chamber wall.

An integrated modeling workflow capable of finding the steady-state plasma solution with self-consistent core transport, pedestal structure, current profile, and plasma equilibrium physics has been developed and tested against a DIII-D discharge. Key features of the achieved core-pedestal coupled workflow are its ability to account for the transport of impurities in the plasma self-consistently, as well as its use of machine learning accelerated models for the pedestal structure and for the turbulent transport physics. Notably, the coupled workflow is implemented within the One Modeling Framework for Integrated Tasks (OMFIT) framework, and makes use of the ITER integrated modeling and analysis suite data structure for exchanging data among the physics codes that are involved in the simulations. Such technical advance has been facilitated by the development of a new numerical library named ordered multidimensional arrays structure.

We report the numerical analyses of the linear magnetohydrodynamics (MHD) plasma response to applied three-dimensional magnetic perturbations (MPs) in a joint DIII-D/EAST collaboration on high-β P (poloidal beta) plasmas, utilizing the extended-MHD code M3D-C1, with the purpose of gaining a better understanding of the existing experiment in which n = 3 MPs were applied to such high-β P plasmas attempting to control large-amplitude type-I edge-localized modes (ELMs). These high-β P plasmas obtained at the DIII-D tokamak feature an upper-biased double-null configuration, a high edge safety factor q 95 ∼ 6.4, and a stable internal transport barrier (ITB), leading to relatively high core pressures. Single-fluid simulations show that the plasma response to n = 3 MPs, including both non-resonant/kinking and resonant components, is significantly weaker than that to n = 1 or 2 MPs. To survey the impact of q 95 on the plasma response to applied MPs, the self-consistent equilibrium-generating workflow for analysis module, developed in the OMFIT integrated modeling framework, is employed to generate a series of equilibria with a wide range of q 95, while other key parameters, including the normalized beta, electron density at the pedestal top, and plasma shape, are kept fixed. Compared to the vacuum response, single-fluid M3D-C1 simulations predict a much more significant decrease in resonant plasma response to the applied n = 3 MPs at the maximum penetration radii as q 95 increases. In contrast to single-fluid simulation results, showing that resonant penetration occurs only near the pedestal top where the E × B toroidal rotation frequency is zero, two-fluid simulations show two comparable resonant penetrations located near the pedestal top and the ITB foot, where the perpendicular electron rotation frequency is zero. Such resonant field penetration near the ITB foot may be responsible for the observed formation of a staircase structure in both the electron density and temperature profiles, and thereby a considerable deterioration in the global plasma performance, when MPs are applied in high-β P plasmas. Motivated by this numerical work, we provide some ideas for future research, with the purpose of realizing effective ELM control in such high-β P plasmas in the DIII-D and EAST devices.

Direct interactions between the n=1 (n is the toroidal mode number) resistive internal kink instability and relativistic runaway electrons (REs) in a post thermal quench toroidal plasma are numerically investigated. A recently developed hybrid model, where the runaway current is treated as a fluid component, is adopted to study how REs affect the internal kink stability and the associated eigenmode structure. The RE-modified internal kink perturbation is in turn superposed with the equilibrium field, in order to study the effects of 3D fields on the drift orbits of REs and consequently on the RE confinement and loss. Results are compared with that assuming the single fluid model for the runaway beam. It is found that REs destabilize the resistive internal kink mode, leading to a better recovery (compared to the standard single fluid model) of the mode growth rate scaling of gamma~S^(-1/3) at lower values of Lundquist number S. Furthermore, REs significantly modify the internal kink eigenfunction inside or near the q=1 surface. In particular, a new narrow layer forms within the resistive layer, where a strong peaking of the perturbed parallel current develops. The RE contribution is also found to substantially enhance the coupling among poloidal harmonics, in particular between m=1 and its nearest sidebands. All these changes to the perturbation structure consequently affect the RE drift orbits in the presence of the internal kink instability. Compared to the fluid model, 3D perturbations computed with the more consistent hybrid model lead to less loss of relativistic electrons in the RE beam, when the perturbation level reaches that of the equilibrium field. At lower (but still large) perturbation amplitude (~10% of the equilibrium field), the internal kink mode has little effect on the RE loss. Runaway electrons launched within the q=1 surface always stay confined within the plasma, independent of the field perturbation amplitude (up to the level of the equilibrium field), the beam model adopted (fluid versus hybrid), or the particle traveling direction. On the other hand, the individual drift orbit trajectory is qualitatively sensitive to these factors.

A new small angle slot (SAS) divertor concept has been developed to enhance neutral cooling across the divertor target by coupling a closed slot structure with appropriate target shaping. Initial tests on DIII-D find a strong interplay between such anticipated 'SAS' effects and cross-field drifts, favouring operation with the ion B × ∇B drift away from the X-point, as currently employed for advanced tokamaks. This offers the following key improvements relative to DIII-D's open lower divertor or partially-closed upper divertor: (i) SAS allows for transition to low temperature moderately detached divertor conditions with T e ≲ 10 eV at very low main plasma densities, lower than are usually attainable at all in DIII-D high confinement (H-mode) plasmas as used in these tests; (ii) Pedestal performance and core confinement are significantly improved with SAS. The final confinement collapse associated with the onset of X-point MARFE (multifaceted asymmetric radiation from the edge) following deep detachment occurs at significantly higher pedestal densities, thus widening the window of H-mode operation compatible with a dissipative divertor. For operation with the ion B × ∇B drift toward the X-point, the divertor plasma transitions to a bifurcative detached state at much higher densities, similar to other divertor configurations in DIII-D. These results highlight the strong interplay between divertor closure and drifts, and point to an interesting divertor optimization path to explore that offers potential for future fusion reactors.

A toroidal modeling tool is developed to study the runaway electron (RE) avalanche production process in tokamak plasmas, by coupling the Rosenbluth–Putvinski avalanche model (Rosenbluth and Putvinski 1997 Nucl. Fusion 37 1355) with an n = 0 magneto-hydrodynamic (MHD) solver. Initial value numerical simulations are carried out for two DIII-D discharges with different plasma shapes (one near circular, and the other with high elongation). It is found that, assuming the same level of about 1% seed current level, the Rosenbluth–Putvinski model somewhat underestimates the RE plateau current for the circular-shaped plasma, as compared with that measured in DIII-D experiments. For an elongated, higher current plasma, simulations find strong runaway current avalanche production despite the lack of measured plateau RE current in experiments. A possible reason for this discrepancy is a lack of additional RE dissipation physics in the present two-dimensional model. Systematic scans of the plasma boundary shape, at fixed pre-disruption plasma current, find that the plasma elongation helps to reduce the RE avalanche production, confirming recent results obtained with an analytic model (Fülöp et al 2020 J. Plasma Phys. 86 474860101). The effect of the plasma triangularity (either positive or negative), on the other hand, has a minor effect. On the physics side, the avalanche process involves two competing mechanisms associated with the electric field. On the one hand, a stronger electric field produces a higher instantaneous avalanche growth rate. On the other hand, a fast growing RE current quickly reduces the fraction of the conduction current together with the electric field, and hence a faster dissipation of the poloidal flux. As a final result of these two dynamic processes, the runaway plateau current is not always the largest with the strongest initial electric field. These results lay the foundation for future self-consistent inclusion of the MHD dynamics and the RE amplification process.

Experimental and modeling investigations of high βp scenarios on DIII-D and EAST tokamaks show advantages in high energy confinement, avoidance of n = 1 MHD, and core-edge integration with reduced heat flux, making this scenario an attractive option for China Fusion Engineering Test Reactor steady-state operation. Experiments show that plasmas with high confinement and high density can be achieved with neutral beam injection on DIII-D (βp ∼ 2.2, βN ∼ 3.5, fBS ∼ 50%, fGw ∼ 1.0, and H98y2 ∼ 1.5) and pure RF power on EAST (βP ∼ 2.0, βN ∼ 1.6, fBS ∼ 50%, fGw ∼ 0.8, and H98y2 > 1.3). By tailoring the current density profile, a q-profile with local (off-axis) negative shear is achieved, which yields improved confinement and MHD stability. Transport analysis and simulation suggest that the combination of a high density gradient and high Shafranov shift allows turbulence stabilization and higher confinement. Using on-axis Electron Cyclotron Heating injection, tungsten accumulation is avoided on EAST, and this is reproduced in modeling. Reduced heat flux (by > 40%) and maintenance of high core confinement is achieved with active feedback control of the radiated divertor, an important result for long pulse operation in tokamaks. The improved physics understanding and validated modeling tools are used to design a 1 GW steady-state scenario for CFETR.

The 3-D field induced relativistic runaway electron (RE) loss has been simulated for DIII-D and COMPASS plasmas, utilizing the MARS-F code incorporated with the recently developed and updated RE orbit module (REORBIT). Modeling shows effectively 100% loss of a post-disruption, high-current runaway beam in DIII-D due to the 1 kG level of magnetic field perturbation produced by a fast growing n = 1 resistive kink instability. This complete RE loss is shown to be independent of the particle energy or the initial location of particles in the configuration space. Applied resonant magnetic perturbation (RMP) fields from in-vessel coils are not effective for RE beam mitigation in DIII-D but do produce finite (>10%) RE loss in COMPASS post-disruption plasmas, consistent with experimental observations in the above two devices. The major reasons for this difference in RE control by RMP between these two devices are (i) the coil proximity to the RE beam and (ii) the effective coil current scaling vs the machine size and the toroidal magnetic field. In the modeling, the lost REs due to 3-D fields deposit onto the limiting surfaces of the devices. Distributions of the lost REs to the limiting surface show a poloidally peaked profile near the high-field-side in both DIII-D and COMPASS, covering about 100 ° poloidal angle. A higher perturbation field level and/or higher particle energy also result in REs being lost to the low-field-side of the limiting surface of these two devices, increasing the effective wetted area.

On DIII-D, the high βp scenario has an internal transport barrier (ITB), βN~βp~3,q95~10, and very high normalized confinement H98,y2~1.6. Recently, plasmas starting with these conditions have been dynamically driven to q95~6 and βp~3, where we find the ITB and high performance persist for multiple energy confinement times. These conditions are projected to meet the ITER steady-state goal of Q= 5. The ITB is maintained at lower βp with a strong reverse shear, consistent with predictions that negative central shear can lower the βp threshold for the ITB. There are two observed confinement states in the highβp scenario: H-mode confinement state with a high edge pedestal, and an enhanced confinement state with a low pedestal and an ITB. It has been observed in a scan of external resonant magnetic perturbation amplitude that when there are no large type-I ELMs, there is no transition to enhanced confinement. This is consistent with the proposed mechanism for ITB formation being a type-I ELM. Quasilinear gyro-Landau fluid predictive modeling of ITER suggests that only a modest reverse shear is required to achieve the ITB formation necessary for Q=5 when electromagnetic physics including the kinetic ballooning mode (KBM) is incorporated.

The method of plasma current profile reconstruction using the polarimeter/interferometer (POINT) data from a simulated equilibrium is explored and validated. It is shown that the safety factor (q) profile can be generally reconstructed from the external magnetic and POINT data. The reconstructed q profile is found to reasonably agree with the initial equilibriums. Comparisons of reconstructed q and density profiles using the magnetic data and the POINT data with 3%, 5% and 10% random errors are investigated. The result shows that the POINT data could be used to a reasonably accurate determination of the q profile.

Fusion whole device modeling simulations require comprehensive models that are simultaneously physically accurate, fast, robust, and predictive. In this paper we describe the development of two neural-network (NN) based models as a means to perform a snon-linear multivariate regression of theory-based models for the core turbulent transport fluxes, and the pedestal structure. Specifically, we find that a NN-based approach can be used to consistently reproduce the results of the TGLF and EPED1 theory-based models over a broad range of plasma regimes, and with a computational speedup of several orders of magnitudes. These models are then integrated into a predictive workflow that allows prediction with self-consistent core-pedestal coupling of the kinetic profiles within the last closed flux surface of the plasma. The NN paradigm is capable of breaking the speed-accuracy trade-off that is expected of traditional numerical physics models, and can provide the missing link towards self-consistent coupled core-pedestal whole device modeling simulations that are physically accurate and yet take only seconds to run.

The runaway electron (RE) distributions driven by a large toroidal electric field induced by the drop in the temperature profile due to disruption or pellets are comprehensively simulated by the 3D Fokker–Planck (FP) solver CQL3D (Harvey and McCoy 1992 Proc. of IAEA TCM), recently coupled to the Ampere–Faraday (AF) equations. The evolution of the toroidal current in a plasma occurs on a resistive time scale, τ res = 4πa 2/(c 2 η), which is typically of the order of seconds in present tokamaks. Here, a and η are respectively plasma radius or radial extent of a current density perturbation, and Ohmic resistivity. From the Faraday EM equation, the toroidal electric field is proportional to the time derivative of the poloidal magnetic field, which, from the Ampere equation, is proportional to the toroidal current. Thus, the toroidal electric field rapidly increases due to an abrupt temperature drop decrease in conductivity, to prevent change in the toroidal current faster than τ res. This is a example of Lenz’s law. For example, in simulations with KPRAD (Whyte et al 2003 J. Nucl. Mater. 313–6 1239) of neon pellet injection into a DIII-D shot, T e drops from 2 keV to 10 eV in 0.1 ms and Z eff increases 1–4, giving that the electric field increases 3500× to 0.8 V cm−1. As described in Harvey et al (2000 PoP 7 4590), this places much of the tail electron distribution beyond the Dreicer runaway velocity, giving so-called ‘hot-tail runaways’ which for a time are the dominant source of runaways, more so than the knockon source. In this prior calculation, performed for a single flux surface, the toroidal current density is held constant, on the basis that τ res is large. Most of the initial current can be converted to runaway current, which is then dangerous, particularly for ITER. A more comprehensive A–F model recently implemented in CQL3D, taking into account the time-development of the full-plasma-width toroidal electric field on time-scales of order τ res applies an iterative technique for the toroidal field previously developed for a different application (Kupfer et al 1996 PoP 3 3644), maintaining the implicit-in-time evolution of CQL3D. The degree of runaway current formation is reduced in AF augmented CQL3D, but the basic mechanism of ‘hot-tail runaways’ remains a dominant contribution to the REs at early times after the T e drop in these simulations. On the other hand, a NIMROD (Sovinec et al 2004 J. Comput. Phys. 195 355) simulation of shattered-pellet shutdown of DIII-D plasma (Kim 2018 APS/DPP Meeting), gives a slower thermal quench; when the plasma profiles and electric field are coupled one-way to CQL3D, the ‘hot-tail’ REs are much less, and growth of RE is dominated by the knockon process.

An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor$q$at the 95 % poloidal flux surface,$q_{95}$, is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections (Shafranov,Sov. Phys. Tech. Phys., vol. 15, 1970, p. 175) when$q_{edge}$, the safety factor at the outermost closed flux surface, lies just below a rational value$m/n$. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and$q_{edge}$decreases through successive rational surfaces. For$q_{edge}, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which$q_{edge}$is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when$q_{95}$, reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when$q_{95}, but$q_{edge}\gg 2$. The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the$q=2$surface. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.

To move to a fusion DEMO power plant after ITER, a Fusion Nuclear Science Facility (FNSF) is needed in addition to ITER and research in operating tokamaks and those under construction. The FNSF wil...

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

We report tests of an alternate technique for constraining MHD equilibrium analysis in tokamak plasmas using internal magnetic field measurements based on |B| measurements from the motional Stark splitting of Dα spectral lines emitted by a neutral heating beam (MSE-LS). We compare results using MSE-LS with those of the standard equilibrium analysis technique based on line polarization of the Dα emission (MSE-LP). An alternative to MSE-LP is needed in future devices such as ITER where MSE-LP will be difficult due to a plasma-induced coating of the first optical element. The tests utilized data from 10 DIII-D shots with 7 MSE-LS and 14 MSE-LP views covering a range of radii along the outer midplane of the plasma. Seven MSE-LS measurements can contribute significantly to the equilibrium reconstruction of pressure and q profiles using both synthetic and experimental DIII-D MSE-LS data. For example, 7 MSE-LS plus seven MSE-LP measurements give a fit quality that is as good as the same cases with 14 MSE-LP measurements. Analyzing synthetic data for 14 MSE-LS measurements shows significant improvement in fitting quality over the case with 7 MSE-LS locations.We report tests of an alternate technique for constraining MHD equilibrium analysis in tokamak plasmas using internal magnetic field measurements based on |B| measurements from the motional Stark splitting of Dα spectral lines emitted by a neutral heating beam (MSE-LS). We compare results using MSE-LS with those of the standard equilibrium analysis technique based on line polarization of the Dα emission (MSE-LP). An alternative to MSE-LP is needed in future devices such as ITER where MSE-LP will be difficult due to a plasma-induced coating of the first optical element. The tests utilized data from 10 DIII-D shots with 7 MSE-LS and 14 MSE-LP views covering a range of radii along the outer midplane of the plasma. Seven MSE-LS measurements can contribute significantly to the equilibrium reconstruction of pressure and q profiles using both synthetic and experimental DIII-D MSE-LS data. For example, 7 MSE-LS plus seven MSE-LP measurements give a fit quality that is as good as the same cases with 14 MSE-LP meas...

Experiments have demonstrated improved energy confinement due to the spontaneous formation of an internal transport barrier in high bootstrap fraction discharges. Gyrokinetic analysis, and quasilinear predictive modeling, demonstrates that the observed transport barrier is caused by the suppression of turbulence primarily from the large Shafranov shift. It is shown that the Shafranov shift can produce a bifurcation to improved confinement in regions of positive magnetic shear or a continuous reduction in transport for weak or negative magnetic shear. Operation at high safety factor lowers the pressure gradient threshold for the Shafranov shift-driven barrier formation. Two self-organized states of the internal and edge transport barrier are observed. It is shown that these two states are controlled by the interaction of the bootstrap current with magnetic shear, and the kinetic ballooning mode instability boundary. Election scale energy transport is predicted to be dominant in the inner 60% of the profile. Evidence is presented that energetic particle-driven instabilities could be playing a role in the thermal energy transport in this region.

An integrated-modeling workflow has been developed for the purpose of performing predict-first analysis of transient-stability experiments. Starting from an existing equilibrium reconstruction from a past experiment, the workflow couples together the EFIT Grad-Shafranov solver [L. Lao et al., Fusion Sci. Technol. 48, 968 (2005)], the EPED model for the pedestal structure [P. B. Snyder et al., Phys. Plasmas 16, 056118 (2009)], and the NEO drift-kinetic-equation solver [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)] (for bootstrap current calculations) in order to generate equilibria with self-consistent pedestal structures as the plasma shape and various scalar parameters (e.g., normalized β, pedestal density, and edge safety factor [q95]) are changed. These equilibria are then analyzed using automated M3D-C1 extended-magnetohydrodynamic modeling [S. C. Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)] to compute the plasma response to three-dimensional magnetic perturbations. This workflow was created in conjunction with a DIII-D experiment examining the effect of triangularity on the 3D plasma response. Several versions of the workflow were developed, and the initial ones were used to help guide experimental planning (e.g., determining the plasma current necessary to maintain the constant edge safety factor in various shapes). Subsequent validation with the experimental results was then used to revise the workflow, ultimately resulting in the complete model presented here. We show that quantitative agreement was achieved between the M3D-C1 plasma response calculated for equilibria generated by the final workflow and equilibria reconstructed from experimental data. A comparison of results from earlier workflows is used to show the importance of properly matching certain experimental parameters in the generated equilibria, including the normalized β, pedestal density, and q95. On the other hand, the details of the pedestal current did not significantly impact the plasma response in these equilibria. A comparison to the experimentally measured plasma response shows mixed agreement, indicating that while the equilibria are predicted well, additional analysis tools may be needed. Finally, we note the implications that these results have for the success of future predict-first studies, particularly the need for scans of uncertain parameters and for close collaboration between experimentalists and theorists.

The objective of the Fusion Development Facility (FDF) under consideration is to carry forward advanced tokamak physics for optimization of fusion reactors and enable development of fusion’s energy...

The Experimental Advanced Superconducting Tokamak (EAST) has a major radius of R0 = 1.75 m and a midplane halfwidth of 0.5 m. It has been operated with a toroidal magnetic field B0 = 2 T and Ip ≤ 500 kA. The evolution of the plasma equilibrium is analysed between discharges by Equilibrium Fitting Code (EFIT). Limiter, single-null and double-null diverted configurations have been produced. A plasma elongation in the range 1.3 ≤ κ ≤ 1.9 and a triangularity in the range 0.1 ≤ δ ≤ 0.55 have been sustained. The operation space of elongated discharges is also presented based on the EAST database.

Reconstruction of experimental axisymmetric equilibria is an important part of tokamak data analysis. Fourier expansion is applied to reconstruct the vessel current distribution in EFIT code. Benchmarking and testing calculations are performed to evaluate and validate this algorithm. Two cases for circular and non-circular plasma discharges are presented. Fourier expansion used to fit the eddy current is a robust method and the real time EFIT can be introduced to the plasma control system in the coming campaign.

Plasmas with vertically elongated cross-sections tend to be unstable to an axis-symmetric instability. This paper studies the magnetohydrodynamic equilibria in elongated plasmas after failure of vertical feedback control by using magnetic data for EAST device. Vertical forces on the vessel due to the induced polodial and toroidal currents are evaluated. The maximum force of the Fzpol in vertical displacement events for EAST designed parameters is given.

Two phases of a DIII-D discharge with and without magnetohydrodynamics (MHD) activity are analysed using ONETWO code. The toroidal momentum flux is extracted from experimental data and compared with the predictions by neoclassical theory, Gyro?Landau fluid transport model (GLF23) and Multi-Mode model (MMM95). It is found that without MHD activities GLF23 and MMM95 provide a reasonable description while with MHD activity no model alone can fully describe the experimental momentum flux. For the phase with MHD activity a simple model of resonant magnetic drag is tested and it cannot fully explain the plasma slowing down observed in experiment.

Experimental observations in a number of tokamaks operated in the hybrid regime revealed that the presence of a rotating neoclassical island substantially reduces the occurrence of sawtooth. This possibility of a rotating mangetic island driving counter currents near the plasma centre in present-day tokamaks is studied. Three mechanisms are investigated with two of them driving sufficient current. They rely on establishing an oscillating parallel electric field by the rotating neoclassical island. First is the excitation of an electrostatic side band through diamagnetic and curvature drifts; second is the excitation of the kinetic Alfven wave at the plasma centre through the polarization drifts. The third mechanism is the 'prompt' modification of the energetic particle distribution function by the neoclassical island and was found to be relatively weak. The effect of the energetic particles on the counter-current drive due to modification of the energetic particle distribution function on the long (energetic particle slowing-down) time scale has been simulated using a particle simulation code. A firm conclusion has not yet been drawn. Transport simulations indicate that present experimental observations could be the effect of either a negative current drive in the background plasma or the anomalous transport of the energetic particles.

Measurements show fast ion losses correlated with applied three-dimensional (3D) fields in a variety of plasmas ranging from L-mode to resonant magnetic perturbation (RMP) edge localized mode (ELM) suppressed H-mode discharges. In DIII-D L-mode discharges with a slowly rotating n = 2 magnetic perturbation, scintillator detector loss signals synchronized with the applied fields are observed to decay within one poloidal transit time after beam turnoff indicating they arise predominantly from prompt loss orbits. Full orbit following using M3D-C1 calculations of the perturbed fields and kinetic profiles reproduce many features of the measured losses and points to the importance of the applied 3D field phase with respect to the beam injection location in determining the overall impact on prompt beam ion loss. Modeling of these results includes a self-consistent calculation of the 3D perturbed beam ion birth profiles and scrape-off-layer ionization, a factor found to be essential to reproducing the experimental measurements. Extension of the simulations to full slowing down timescales, including fueling and the effects of drag and pitch angle scattering, show the applied n = 3 RMPs in ELM suppressed H-mode plasmas can induce a significant loss of energetic particles from the core. With the applied n = 3 fields, up to 8.4% of the injected beam power is predicted to be lost, compared to 2.7% with axisymmetric fields only. These fast ions, originating from minor radii ρ > 0.7, are predicted to be primarily passing particles lost to the divertor region, consistent with wide field-of-view infrared periscope measurements of wall heating in n = 3 RMP ELM suppressed plasmas. Edge fast ion Dα (FIDA) measurements also confirm a large change in edge fast ion profile due to the n = 3 fields, where the effect was isolated by using short 50ms RMP-off periods during which ELM suppression was maintained yet the fast ion profile was allowed to recover. The role of resonances between fast ion drift motion and the applied 3D fields in the context of selectively targeting regions of fast ion phase space is also discussed.

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.

The effect of plasma shape on sawtooth oscillations in the DIII-D tokamak plasmas is investigated by comparing discharges with cross-sections shaped like a bean and an oval. The two shapes are designed so that the Mercier instability threshold is reached when the axial safety factor is below unity for the bean and above unity for the oval cross-sections. This allows the role of interchange modes to be differentiated from that of the kink-tearing mode. The differences in the nature of the sawtooth oscillations in the bean and oval discharges are found to be determined primarily by extreme differences in the electron heat transport during the reheat. In both cases, the axial safety factor is found to be near unity following the crash. (Some figures in this article are in colour only in the electronic version)

The National Spherical Torus Experiment (NSTX) has demonstrated the advantages of low aspect ratio geometry in accessing high toroidal and normalized plasma beta, and βN ≡ 10 8〈βt〉 aB0/Ip. Experiments have reached βt = 39% and βN = 7.2 through boundary and profile optimization. High βN plasmas can exceed the ideal no-wall stability limit, βNno-wall, for periods much greater than the wall eddy current decay time. Resistive wall mode (RWM) physics is studied to understand mode stabilization in these plasmas. The toroidal mode spectrum of unstable RWMs has been measured with mode number n up to 3. The critical rotation frequency of Bondeson-Chu, Ωcrit = ωA/(4q2), describes well the RWM stability of NSTX plasmas when applied over the entire rotation profile and in conjunction with the ideal stability criterion. Rotation damping and global rotation collapse observed in plasmas exceeding βNno-wall differs from the damping observed during tearing mode activity and can be described qualitatively by drag due to neoclassical toroidal viscosity in the helically perturbed field of an ideal displacement. Resonant field amplification of an applied n = 1 field perturbation has been measured and increases with increasing βN. Equilibria are reconstructed including measured ion and electron pressure, toroidal rotation and flux isotherm constraint in plasmas with core rotation ω/ωA up to 0.48. Peak pressure shifts of 18% of the minor radius from the magnetic axis have been reconstructed.

The quiescent H (QH) mode, an edge localized mode (ELM)-free and high-confinement mode, combines well with an internal transport barrier to form quiescent double barrier stationary state, high performance plasmas. The QH-mode edge pedestal pressure is similar to that seen in ELMing phases of the same discharge, with similar global energy confinement. The pedestal density in early ELMing phases of strongly pumped counter injection discharges drops, and a transition to QH-mode occurs, leading to lower calculated edge bootstrap current. The plasmas current ramp experiment and ELITE code modelling of edge stability suggest that QH-modes lie near an edge current stability boundary. At high triangularity, QH-mode discharges operate at higher pedestal density and pressure and have achieved ITER level values of βPED and ν*.

The major objective of the National Spherical Torus Experiment (NSTX) is to understand basic toroidal confinement physics at low aspect ratio and high βT in order to advance the spherical torus (ST) concept. In order to do this, NSTX utilizes up to 7.5 MW of neutral beam injection, up to 6 MW of high harmonic fast waves (HHFWs), and it operates with plasma currents up to 1.5 MA and elongations of up to 2.6 at a toroidal field up to 0.45 T. New facility, and diagnostic and modelling capabilities developed over the past two years have enabled the NSTX research team to make significant progress towards establishing this physics basis for future ST devices. Improvements in plasma control have led to more routine operation at high elongation and high βT (up to ~40%) lasting for many energy confinement times. βT can be limited by either internal or external modes. The installation of an active error field (EF) correction coil pair has expanded the operating regime at low density and has allowed for initial resonant EF amplification experiments. The determination of the confinement and transport properties of NSTX plasmas has benefitted greatly from the implementation of higher spatial resolution kinetic diagnostics. The parametric variation of confinement is similar to that at conventional aspect ratio but with values enhanced relative to those determined from conventional aspect ratio scalings and with a BT dependence. The transport is highly dependent on details of both the flow and magnetic shear. Core turbulence was measured for the first time in an ST through correlation reflectometry. Non-inductive start-up has been explored using PF-only and transient co-axial helicity injection techniques, resulting in up to 140 kA of toroidal current generated by the latter technique. Calculated bootstrap and beam-driven currents have sustained up to 60% of the flat-top plasma current in NBI discharges. Studies of HHFW absorption have indicated parametric decay of the wave and associated edge thermal ion heating. Energetic particle modes, most notably toroidal Alfven eigenmodes and fishbone-like modes result in fast particle losses, and these instabilities may affect fast ion confinement on devices such as ITER. Finally, a variety of techniques has been developed for fuelling and power and particle control.

The measurement of the plasma current profile is crucial to many operating regimes and investigations on the DIII-D tokamak. The measurement is required to obtain accurate equilibria and to accurately calculate stability and transport characteristics of the plasma. The measurement of the profile is also required to obtain the different components of the current to guide efforts on the control of the current profile and experiments toward obtaining steady-state operating regimes. The edge current profile measurement is necessary to understand the formation of edge pedestal and edge-localized modes. The DIII-D tokamak has a three-array, 45-channel motional Stark effect (MSE) diagnostic to measure the plasma current density and radial electric field. A 32-channel lithium-beam (Li-beam) diagnostic has recently been installed on the DIII-D tokamak for the measurement of edge current density. Both diagnostics measure the current profile from the measurement of the pitch angle of the magnetic field that, in turn, is derived from the orientation angle of polarization of the appropriate neutral beam spectral line. The MSE and the Li-beam diagnostics are described, and some examples of measurements are shown.

Theory and simulation have provided one of the critical foundations for many of the significant achievements in magnetohydrodynamic (MHD) stability in DIII-D over the past two decades. Early signature achievements included the validation of tokamak MHD stability limits, beta and performance optimization through cross-section shaping and profiles, and the development of new operational regimes. More recent accomplishments encompass the realization and sustainment of wall stabilization using plasma rotation and active feedback, a new understanding of edge stability and its relation to edge-localized modes, and recent successes in predicting resistive tearing and interchange instabilities. The key to success has been the synergistic tie between the theory effort and the experiment made possible by the detailed equilibrium reconstruction data available in DIII-D and the corresponding attention to the measured details in the modeling. This interaction fosters an emphasis on the important phenomena and leads to testable theoretical predictions. Also important is the application of a range of analytic and simulation techniques, coupled with a program of numerical tool development. The result is a comprehensive integrated approach to fusion science and improving the tokamak approach to burning plasmas.

The energy loss for grassy edge localized modes (ELMs) has been studied to investigate the applicability of the grassy ELM regime to ITER. The grassy ELM regime is characterized by high frequency periodic collapses of 800–1500 Hz, which is ~15 times faster than that for type I ELMs. The divertor peak heat flux due to grassy ELMs is less than 10% of that for type I ELMs. This smaller heat flux is caused by a narrower radial extent of the collapse of the temperature pedestal. The different radial extent between type I ELMs and grassy ELMs agrees qualitatively with the different radial distribution of the eigenfunctions as determined from ideal MHD stability analysis. The dominant ELM energy loss for grassy ELMs appears to be caused by temperature reduction, and its ratio to the pedestal stored energy was 0.4–1%. This ratio is lower by a factor of about 10 than that for type I ELMs, which typically have between 2–10% fractional loss of the pedestal energy. A systematic study of the effects of counter (CTR) plasma rotation on the ELM characteristics has been performed using a combination of tangential and perpendicular neutral beam injections (NBIs) in JT-60U. In the high plasma triangularity (δ) regime, ELM characteristics (e.g. amplitude, frequency and type) can be changed from type I ELMs to high frequency grassy ELMs as the CTR plasma rotation is increased. On the other hand, in the low δ regime, complete ELM suppression (QH-mode) can be sustained for long periods up to 3.4 s (~18τE or energy confinement times), when the plasma position in terms of the clearance between the first wall and the plasma separatrix is optimized during the application of CTR-NBIs. In JT-60U, a transient QH phase was also observed during the CO-NBI phase with almost no net toroidal rotation at the plasma edge.

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

This work investigates the potential roles played by the scrape-off-layer current (SOLC) in MHD activity of tokamak plasmas, including effects on stability. SOLCs are found to be an integral part of the MHD activity, with a propensity to flow in a non-axisymmetric pattern and with magnitude potentially large enough to play a role in the MHD stability. Candidate mechanisms that can drive these SOLCs are identified: (a) non-axisymmetric thermoelectric potential, (b) electromotive force from MHD activity, and (c) flux swing, both toroidal and poloidal, of the plasma column. Other potential magnetic consequences of the SOLC are identified: (a) its error field can introduce complications in feedback control schemes for stabilizing MHD activity, and (b) its non-axisymmetric field can be falsely identified as an axisymmetric field by the tokamak control logic and in equilibrium reconstruction. The radial profile of an SOLC observed during a quiescent discharge period is determined, and found to possess polarity reversals as a function of radial distance.

A set of twelve coils for stability control has recently been installed inside the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] vacuum vessel, offering faster time response and a wider range of applied mode spectra than the previous external coils. Stabilization of the n=1 ideal kink mode is crucial to many high beta, steady-state tokamak scenarios. A resistive wall converts the kink to a slowly growing resistive wall mode (RWM). With feedback-controlled error field correction, rotational stabilization of the RWM has been sustained for more than 2.5 s. Using the internal coils, the required correction field is smaller than with the external coils, consistent with a better match to the mode spectrum of the error field. Initial experiments in direct feedback control have stabilized the RWMs at higher beta and lower rotation than could be achieved by the external coils in similar plasmas, in qualitative agreement with numerical modeling. The new coils have also allowed wall stabilization in plasmas with...

Steady-state operation of the advanced tokamak reactor relies on maintaining plasma stability with respect to the resistive wall mode ~RWM!. Active magnetic feedback and plasma rotation are the two methods proposed and demonstrated for this purpose. A comprehensive modeling effort including both magnetic feedback and plasma rotation is needed for understanding the physical mechanisms of the stabilization and to project to future devices. For plasma with low rotation, a complete solution for the feedback issue is obtained by assuming the plasma obeys ideal magnetohydrodynamics ~MHDs! and utilizing a normal mode approach ~NMA! @M. S. Chu et al., Nucl. Fusion 43, 441 ~2003!#. It is found that poloidal sensors are more effective than radial sensors and coils inside of the vacuum vessel more effective than outside. For plasmas with non-negligible rotation, a comprehensive linear nonideal MHD code, the MARS-F has been found to be suitable. MARS-F @Y. Q. Liu et al., Phys. Plasmas 7, 3681 ~2000!# has been benchmarked in the ideal MHD limit against the NMA. The effect of rotation stabilization of the plasma depends on the plasma dissipation model. Broad qualitative features of the experiment are reproduced. Rotation reduces the feedback gain required for RWM stabilization. Reduction is significant when rotation is near the critical rotation speed needed for stabilization. The International Thermonuclear Experimental Reactor ~ITER! @R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 ~2002!# ~scenario IV for advanced tokamak operation! may be feedback stabilized with babove the no wall limit and up to an increment of ;50% towards the ideal limit. Rotation further improves the stability.

H-mode operation is the choice for next step tokamak devices based on either conventional or advanced tokamak physics. This choice, however, comes at a significant cost for both the conventional and advanced tokamaks because of the effects of edge localized modes (ELMs). ELMs can produce significant erosion in the divertor and can affect the ? limit and reduced core transport regions needed for advanced tokamak operation. Experimental results from DIII-D over the past four years have demonstrated a new operating regime, the quiescent H-mode (QH-mode) regime, that solves these problems. QH-mode plasmas have now been run for over 4?s (>30 energy confinement times). Utilizing the steady-state nature of the QH-mode edge allows us to obtain unprecedented spatial resolution of the edge ion profiles and the edge radial electric field, Er, by sweeping the edge plasma slowly past the view points of the charge exchange spectroscopy system. We have investigated the effects of direct edge ion orbit loss on the creation and sustainment of the QH-mode. Direct loss of ions injected into the velocity-space loss cone at the plasma edge is not necessary for creation or sustainment of the QH-mode. The direct ion orbit loss has little effect on the edge Er well. The Er at the bottom of the well in these cases is about ?100?kV?m?1 compared with ?20 to ?30?kV?m?1 in the standard H-mode. The well is about 1?cm wide, which is close to the diameter of the deuteron gyro-orbit. We also have investigated the effect of changing edge triangularity by changing the plasma shape from upwardly biased single null to magnetically balanced double null. We have now achieved the QH-mode in these double-null plasmas. The increased triangularity allows us to increase pedestal density in QH-mode plasmas by a factor of about 2.5 and overall pedestal pressure by a factor of 2. Pedestal ? and ?* values matching the values desired for ITER have been achieved. In these higher density plasmas, the Er well is significantly shallower and broader.

High performance discharges under steady-state condition in the Hefei Tokamak-7 (HT-7) have been investigated. Lower hybrid current drive (LHCD) was used both for sustaining plasma current and current density profile control. The experiments demonstrated that features of ion Bernstein wave heating in controlling the electron pressure profile can be integrated into LHCD plasmas and the assist localization of LHCD. This local synergy effect was used to tailor the current density profile in a negative shear configuration and to control the internal transport barrier (ITB) under steady-state conditions. The high performance with a stationary ITB at the footprint of the minimum q and β N H 89 >2 was sustained for >220 τ E or >20 τ CR . The fraction of noninductive plasma current was larger than 80% in such discharges with considerable bootstrap current. The duration at H 89 >1.2 and β N ∼1 has been extended to nearly 8 s, longer than 400 τ E . More than 90% of the plasma current was sustained by LHCD and boots...

One of the goals of the National Spherical Torus Experiment (NSTX) is to investigate the physics of global mode stabilization in a low aspect ratio device. NSTX has a major radius R0 = 0.86 m, a midplane half-width of 0.7 m, and an on-axis vacuum toroidal field B0 0.6 T and has reached a plasma current Ip = 1.5 MA. Experiments have established the wall-stabilized MHD operating space of the machine. The maximum βt and βN have reached 35% and 6.5%, respectively, with βN reaching 9.5li. Collapses in plasma toroidal rotation and βt have been correlated with violation of the n = 1 ideal MHD beta limit, β Nn o-wall, computed by the DCON stability code using timeevolving EFIT reconstructions of experimental discharges. The resistive wall mode (RWM) was observed over a wide range of βN when β Nn o-wall was exceeded. Plasma toroidal rotation damping during the RWM was rapid and global. Damping rates were more than five times larger than caused by low toroidal mode number rotating modes alone, which displayed a slower, diffusive rotation damping away from the rational surface. The rotation damping rate and dynamics depend on the applied toroidal field and the computed minimum value of the safety factor. The computed RWM perturbed field structure from experimental plasma reconstructions has been input to the VALEN feedback analysis code for quantitative comparison of experimental and theoretical RWM growth rates and to analyse the effectiveness of various active feedback stabilization designs. The computed RWM n = 1 mode growth rate, which depends on plasma equilibrium parameters such as βN and pressure profile peaking, agrees well with experimental growth rates in different operating regimes. Increasing βN in the ST initially improves mode coupling to the stabilizing wall; however, at the highest βN values reached, the ideal with-wall beta limit, βN wall, is approached, the effectiveness of the passive stabilizing plates is reduced, and the computed RWM growth rate approaches ideal MHD growth rates. Several active mode control designs were considered and evaluated. The most effective configuration is computed to provide stabilization at βN up to 94% of the ideal with-wall limit.

Recent progress in the development of electron cyclotron heating⁄current drive systems in regard to power and pulse duration have allowed the extension of two normalized parameters (toroidal electric field Eφ and wave power density p). In the extended regime, the conventional theory requires consideration of a distorted electron distribution function. The first validation of the ECCD theory in the extended regime having large Eφ and p is presented. Linear calculation has a tendency to overestimate the EC driven current, as normalized parameters for Eφ and p increase. While the EC driven current IEC obtained by a linearized Fokker-Planck calculation (1.1 MA) did not agree with the measured EC driven current (0.74 ± 0.06MA), non-linear calculation of the Fokker-Planck equation considering the effect of Eφ (0.76 MA) shows close agreement with the experimental result. Calculations show that the decreasing effect of Eφ on IEC was stronger than the increasing effect of p on IEC in the experiment.

A major research goal of the national spherical torus experiment is establishing long-pulse, high beta, high confinement operation and its physics basis. This research has been enabled by facility capabilities developed during 2001 and 2002, including neutral beam (up to 7?MW) and high harmonic fast wave (HHFW) heating (up to 6?MW), toroidal fields up to 6?kG, plasma currents up to 1.5?MA, flexible shape control, and wall preparation techniques. These capabilities have enabled the generation of plasmas with of up to 35%. Normalized beta values often exceed the no-wall limit, and studies suggest that passive wall mode stabilization enables this for H mode plasmas with broad pressure profiles. The viability of long, high bootstrap current fraction operations has been established for ELMing H mode plasmas with toroidal beta values in excess of 15% and sustained for several current relaxation times. Improvements in wall conditioning and fuelling are likely contributing to a reduction in H mode power thresholds. Electron thermal conduction is the dominant thermal loss channel in auxiliary heated plasmas examined thus far. HHFW effectively heats electrons, and its acceleration of fast beam ions has been observed. Evidence for HHFW current drive is obtained by comparision of the loop voltage evolution in plasmas with matched density and temperature profiles but varying phases of launched HHFW waves. Studies of emissions from electron Bernstein waves indicate a density scale length dependence of their transmission across the upper hybrid resonance near the plasma edge that is consistent with theoretical predictions. A peak heat flux to the divertor targets of 10?MW?m?2 has been measured in the H mode, with large asymmetries being observed in the power deposition between the inner and outer strike points. Non-inductive plasma startup studies have focused on coaxial helicity injection. With this technique, toroidal currents up to 400?kA have been driven, and studies to assess flux closure and coupling to other current drive techniques have begun.