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New experiments on DIII-D have demonstrated the steady-state potential of the hybrid scenario, with 1 MA of plasma current driven fully non-inductively and βN up to 3.7 sustained for ~3 s (~1.5 current diffusion time, τR, in DIII-D), providing the basis for an attractive option for steady-state operation in ITER and FNSF. Excellent confinement is achieved (H98y2 ~ 1.6) without performance limiting tearing modes. The hybrid regime overcomes the need for off-axis current drive efficiency, taking advantage of poloidal magnetic flux pumping that is believed to be the result of a saturated 3/2 tearing mode. This allows for efficient current drive close to the axis, without deleterious sawtooth instabilities. In these experiments, the edge surface loop voltage is driven down to zero for >1 τR when the poloidal β is increased above 1.9 at a plasma current of 1.0 MA and the ECH power is increased to 3.2 MW. Stationary operation of hybrid plasmas with all on-axis current drive is sustained at pressures slightly above the ideal no-wall limit, while the calculated ideal with-wall MHD limit is βN ~ 4–4.5. Off-axis Neutral Beam Injection (NBI) power has been used to broaden the pressure and current profiles in this scenario, seeking to take advantage of higher predicted kink stability limits and lower values of the tearing stability index Δ′, as calculated by the DCON and PEST3 codes. Results based on measured profiles predict ideal limits at βN > 4.5, 10% higher than the cases with on-axis NBI. A 0-D model, based on the present confinement, βN and shape values of the DIII-D hybrid scenario, shows that these plasmas are consistent with the ITER 9 MA, Q = 5 mission and the FNSF 6.7 MA scenario with Q = 3.5. With collisionality and edge safety factor values comparable to those envisioned for ITER and FNSF, the high-βN hybrid represents an attractive high performance option for the steady-state missions of these devices. [ABSTRACT FROM AUTHOR]

Results from experiments on DIII-D [J. L. Luxon, Fusion Sci. Technol. 48, 828 (2005)] aimed at developing high β steady-state operating scenarios with high-qmin confirm that fast-ion transport is a critical issue for advanced tokamak development using neutral beam injection current drive. In DIII-D, greater than 11 MW of neutral beam heating power is applied with the intent of maximizing βN and the noninductive current drive. However, in scenarios with qmin>2 that target the typical range of q95= 5-7 used in next-step steady-state reactor models, Alfvén eigenmodes cause greater fast-ion transport than classical models predict. This enhanced transport reduces the absorbed neutral beam heating power and current drive and limits the achievable βN. In contrast, similar plasmas except with qmin just above 1 have approximately classical fast-ion transport. Experiments that take qmin>3 plasmas to higher βP with q95= 11-12 for testing long pulse operation exhibit regimes of better than expected thermal confinement. Compared to the standard high-qmin scenario, the high βP cases have shorter slowing-down time and lower ∇βfast, and this reduces the drive for Alfvénic modes, yielding nearly classical fast-ion transport, high values of normalized confinement, βN, and noninductive current fraction. These results suggest DIII-D might obtain better performance in lower-q95, high-qmin plasmas using broader neutral beam heating profiles and increased direct electron heating power to lower the drive for Alfvén eigenmodes. [ABSTRACT FROM AUTHOR]

The initial experiments on off-axis neutral beam injection into high noninductive current fraction (fNI), high normalized pressure (βN) discharges in DIII-D [J. L. Luxon, Fusion Sci. Technol. 48, 828 (2005)] have demonstrated changes in the plasma profiles that increase the limits to plasma pressure from ideal low-n instabilities. The current profile is broadened and the minimum value of the safety factor (qmin) can be maintained above 2 where the profile of the thermal component of the plasma pressure is found to be broader. The off-axis neutral beam injection results in a broadening of the fast-ion pressure profile. Confinement of the thermal component of the plasma is consistent with the IPB98(y,2) scaling, but global confinement with qmin>2 is below the ITER-89P scaling, apparently as a result of enhanced transport of fast ions. A 0-D model is used to examine the parameter space for fNI=1 operation and project the requirements for high performance steady-state discharges. Fully noninductive solutions are found with 4<βN<5 and bootstrap current fraction near 0.5 for a weak shear safety factor profile. A 1-D model is used to show that a fNI=1 discharge at the top of this range of βN that is predicted stable to n=1, 2, and 3 ideal MHD instabilities is accessible through further broadening of the current and pressure profiles with off-axis neutral beam injection and electron cyclotron current drive. [ABSTRACT FROM AUTHOR]

The first real-time profile control experiments integrating magnetic and kinetic variables were performed on DIII-D in view of regulating and extrapolating advanced tokamak scenarios to steady-state devices and burning plasma experiments. Device-specific, control-oriented models were obtained from experimental data using a generic twotime- scale method that was validated on JET, JT-60U and DIII-D under the framework of the International Tokamak Physics Activity for Integrated Operation Scenarios (Moreau et al 2011 Nucl. Fusion 51 063009). On DIII-D, these data-driven models were used to synthesize integrated magnetic and kinetic profile controllers. The neutral beam injection (NBI), electron cyclotron current drive (ECCD) systems and ohmic coil provided the heating and current drive (H&CD) sources. The first control actuator was the plasma surface loop voltage (i.e. the ohmic coil), and the available beamlines and gyrotrons were grouped to form five additional H&CD actuators: co-current on-axis NBI, co-current off-axis NBI, counter-current NBI, balanced NBI and total ECCD power from all gyrotrons (with off-axis current deposition). Successful closed-loop experiments showing the control of (a) the poloidal flux profile, 𝞇(x), (b) the poloidal flux profile together with the normalized pressure parameter, ßN, and (c) the inverse of the safety factor profile, ῑ(x) = 1/q(x), are described. [ABSTRACT FROM AUTHOR]

An analysis of the dependence of transport on the safety factor profile in high-performance, steady-state scenario discharges is presented. This is based on experimental scans of q95 and qmin taken with fixed βN, toroidal field, double-null plasma shape, divertor pumping, and electron cyclotron current drive input. The temperature and thermal diffusivity profiles were found to vary considerably with the q-profile, and these variations were significantly different for electrons and ions. With fixed q95, both temperature profiles increase and broaden as qmin is increased and the magnetic shear becomes low or negative in the inner half radius, but these temperature profile changes are stronger for the electrons. Power balance calculations show the peak in the ion thermal diffusivity (χi) at ρ=0.6-0.8 increases with q95 or qmin. In contrast, the peak in the electron diffusivity (χe) decreases as qmin is raised from ∼1 to 1.5, and it is insensitive to q95. This is important for fully non-inductive scenario development because it demonstrates that elevated qmin and weak or reversed shear allow larger electron temperature gradients and, therefore, increased bootstrap current density to exist at ρ=0.6-0.8. Chord-averaged measurements of long wavelength density fluctuation amplitudes (ñ) are shown, and these have roughly the same dependence on q-profile as χi. This data set provides an opportunity for testing whether theory based transport models can provide insight into the underlying transport physics of high performance scenarios and if they can reproduce observed experimental trends. To this end, we applied the trapped gyro-Landau fluid (TGLF) code to calculate the linear stability of drift waves and found that the resulting variation of growth rates with q-profile are mostly inconsistent with the observed trends of χi, χe, and ñ with q-profile. TGLF simulations of the temperature profiles consistent with heating sources also have mixed agreement with the measured profiles, such that the simulated electron and ion heat flux in low qmin discharges are too low and heat fluxes in high qmin discharges are too high. [ABSTRACT FROM AUTHOR]

Setting up a suitable current spatial profile in tokamak plasmas has been demonstrated to be a key condition for one possible advanced scenario with improved confinement and possible steady-state operation. Experiments at the DIII-D tokamak focus on creating the desired current profile during the plasma current ramp-up and early flattop phases with the aim of maintaining this target profile during the subsequent phases of the discharge. The evolution in time of the current profile is related to the evolution of the poloidal magnetic flux, which is modeled in normalized cylindrical coordinates using a parabolic partial differential equation usually referred to as the magnetic diffusion equation. We propose a framework to solve a finite-time, optimal tracking control problem for the current profile evolution via diffusivity, interior, and boundary actuation during the ramp-up and early flattop phases of the discharge. The proposed approach is based on reduced order modeling via proper orthogonal decomposition and successive optimal control computation for a bilinear system. Simulation results illustrate the performance of the proposed controller. [ABSTRACT FROM PUBLISHER]

The DIII-D device began operation in 1986, and a fully digital plasma control system (PCS) was implemented in 1993. Over time, the success of the PCS to exploit the inherent versatility of the DIII-D device led to a philosophy of using the PCS to control all available plasma system actuators. This made the PCS a very powerful physics tool that is at the core of Physics Operations at DIII-D. The complexity of the DIII-D device and all the systems the PCS must control makes the proper setup of the PCS for new experiments a daunting task. A cadre of physicists specially trained in PCS operation forms the bulk of the Physics Operations staff at DIII-D. They are the interface between experimental plans and successful execution and, as such, are a critical component of each experiment. Physics Operations is also a set of tools and procedures. We will briefly examine some of those tools, such as the TokSys control design and modeling environment and the "smart" PCS setup checklist, that greatly reduce human error in reconfiguring the PCS for a new experiment. We will examine the procedures that allow efficient use of those tools and some of the human factors that can affect productivity. [ABSTRACT FROM AUTHOR]

Recent commissioning of two major fully superconducting (SC)-shaped tokamaks, Experimental Advanced Superconducting Tokamak (EAST) and Korean Superconducting Tokamak Advanced Research (KSTAR), represents a significant advance in magnetic fusion research. The key to commissioning success in these complex and unique tokamaks was as follows: 1) use of a robust, flexible plasma control system (PCS) based on the validated DIII-D design; 2) use of the TokSys design and modeling environment, which is tightly coupled with the DIII-D PCS architecture for first-plasma scenario development and plasma diagnosis; and 3) collaborations with experienced internationally recognized teams of tokamak operations and control experts. We provide an overview of the generic modeling environment and plasma control tools developed and validated within the DIII-D experimental program and applied through an international collaborative program to successfully address the unique constraints associated with the startup of these next-generation tokamaks. The unique characteristics of each tokamak and the machine constraints that must be included in device modeling and simulation, such as SC coil current slew rate limits and the presence of nonlinear magnetic materials, are discussed, along with commissioning and initial operational results. Lessons learned from the startup experience in these devices are summarized, with special emphasis on ramifications for International Thermonuclear Experimental Reactor (ITER). [ABSTRACT FROM AUTHOR]

The achievement of suitable toroidal-current-density profiles in tokamak plasmas plays an important role in enabling high fusion gain and noninductive sustainment of the plasma current for steady-state operation with improved magnetohydrodynamic stability. The evolution in time of the current profile is related to the evolution of the poloidal magnetic flux, which is modeled in normalized cylindrical coordinates using a partial differential equation (PDE) usually referred to as themagnetic flux diffusion equation. The dynamics of the plasma current density profile can be modified by the total plasma current and the power of the noninductive current drive. These two actuators, which are constrained not only in value and rate but also in their initial and final values, are used to drive the current profile as close as possible to a desired target profile at a specific final time. To solve this constrained finite-time open-loop PDE optimal control problem, model reduction based on proper orthogonal decomposition is combined with sequential quadratic programming in an iterative fashion. The use of a low-dimensional dynamical model dramatically reduces the computational effort and, therefore, the time required to solve the optimization problem, which is critical for a potential implementation of a real-time receding-horizon control strategy. [ABSTRACT FROM AUTHOR]

Neutral beam current drive (NBCD) experiments in DIII-D using vertically shifted plasmas to move the current drive away from the axis have clearly demonstrated robust off-axis NBCD. Time-dependent measurements of magnetic field pitch angles by the motional Stark effect diagnostic are used to obtain the evolution of the poloidal magnetic flux, which indicates a broad off-axis NBCD profile with a peak at about half the plasma minor radius. In most cases, the measured off-axis NBCD profile is consistent with calculations using an orbit-following Monte Carlo code for the beam ion slowing down including finite-orbit effects provided there is no large-scale magnetohydrodynamic activity such as Alfvén eigenmodes modes or sawteeth. An alternative analysis method shows good agreement between the measured pitch angles and those from simulations using transport-equilibrium codes. Two-dimensional image of Doppler-shifted fast ion Dα light emitted by neutralized energetic ions shows clear evidence for a hollow profile of beam ion density, consistent with classical beam ion slowing down. The magnitude of off-axis NBCD is sensitive to the alignment of the beam injection relative to the helical pitch of the magnetic field lines. If the signs of toroidal magnetic field and plasma current yield the proper helicity, both measurement and calculation indicate that the efficiency is as good as on-axis NBCD because the increased fraction of trapped electrons reduces the electron shielding of the injected ion current, in contrast with electron current drive schemes where the trapping of electrons degrades the efficiency. The measured off-axis NBCD increases approximately linearly with the injection power, although a modest amount of fast ion diffusion is needed to explain an observed difference in the NBCD profile between the measurement and the calculation at high injection power. [ABSTRACT FROM AUTHOR]

Recent studies on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] have elucidated key aspects of the dependence of stability, confinement, and density control on the plasma magnetic configuration, leading to the demonstration of nearly noninductive operation for >1 s with pressure 30% above the ideal no-wall stability limit. Achieving fully noninductive tokamak operation requires high pressure, good confinement, and density control through divertor pumping. Plasma geometry affects all of these. Ideal magnetohydrodynamics modeling of external kink stability suggests that it may be optimized by adjusting the shape parameter known as squareness (ζ). Optimizing kink stability leads to an increase in the maximum stable pressure. Experiments confirm that stability varies strongly with ζ, in agreement with the modeling. Optimization of kink stability via ζ is concurrent with an increase in the H-mode edge pressure pedestal stability. Global energy confinement is optimized at the lowest ζ tested, with increased pedestal pressure and lower core transport. Adjusting the magnetic divertor balance about a double-null configuration optimizes density control for improved noninductive auxiliary current drive. The best density control is obtained with a slight imbalance toward the divertor opposite the ion grad(B) drift direction, consistent with modeling of these effects. These optimizations have been combined to achieve noninductive current fractions near unity for over 1 s with normalized pressure of 3.5<βN<3.9, bootstrap current fraction of >65%, and a normalized confinement factor of H98(y,2)≈1.5. [ABSTRACT FROM AUTHOR]

The role of interchange and internal kink modes in the sawtooth oscillations is explored by comparing bean- and oval-shaped plasmas. The n=1 instability that results in the collapse of the sawtooth has been identified as a quasi-interchange in the oval cases and the internal kink in the bean shape. The ion and electron temperature profiles are followed in detail through the sawtooth ramp. It is found that electron energy transport rates are very high in the oval and quite low in the bean shape. Ion energy confinement in the oval is excellent and the sawtooth amplitude (δT/T) in the ion temperature is much larger than that of the electrons. The sawtooth amplitudes for ions and electrons are comparable in the bean shape. The measured q profiles in the bean and oval shapes are found to be consistent with neoclassical current diffusion of the toroidal current, and the observed differences in q largely result from the severe differences in electron energy transport. For both shapes the collapse flattens the q profile and after the collapse return to q0>=1. Recent results on intermediate shapes are reported. These shapes show that the electron energy transport improves gradually as the plasma triangularity is increased. [ABSTRACT FROM AUTHOR]

This work describes active control algorithms used by DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] to stabilize and maintain suppression of 3/2 or 2/1 neoclassical tearing modes (NTMs) by application of electron cyclotron current drive (ECCD) at the rational q surface. The DIII-D NTM control system can determine the correct q-surface/ECCD alignment and stabilize existing modes within 100–500 ms of activation, or prevent mode growth with preemptive application of ECCD, in both cases enabling stable operation at normalized beta values above 3.5. Because NTMs can limit performance or cause plasma-terminating disruptions in tokamaks, their stabilization is essential to the high performance operation of ITER [R. Aymar et al., ITER Joint Central Team, ITER Home Teams, Nucl. Fusion 41, 1301 (2001)]. The DIII-D NTM control system has demonstrated many elements of an eventual ITER solution, including general algorithms for robust detection of q-surface/ECCD alignment and for real-time maintenance of alignment following the disappearance of the mode. This latter capability, unique to DIII-D, is based on real-time reconstruction of q-surface geometry by a Grad-Shafranov solver using external magnetics and internal motional Stark effect measurements. Alignment is achieved by varying either the plasma major radius (and the rational q surface) or the toroidal field (and the deposition location). The requirement to achieve and maintain q-surface/ECCD alignment with accuracy on the order of 1 cm is routinely met by the DIII-D Plasma Control System and these algorithms. We discuss the integrated plasma control design process used for developing these and other general control algorithms, which includes physics-based modeling and testing of the algorithm implementation against simulations of actuator and plasma responses. This systematic design/test method and modeling environment enabled successful mode suppression by the NTM control system upon first-time use in an experimental discharge. [ABSTRACT FROM AUTHOR]

High values of normalized β (βN∼4) and safety factor (qmin∼2) have been sustained simultaneously for ∼2 s in DIII-D [J.L. Luxon, Nucl. Fusion 42, 64 (2002)], suggesting a possible path to high fusion performance, steady-state tokamak scenarios with a large fraction of bootstrap current. The combination of internal transport barrier and negative central magnetic shear at high β results in high confinement (H89P>2.5) and large bootstrap current fraction (fBS>60%) with good alignment. Previously, stability limits in plasmas with core transport barriers have been observed at moderate values of βN (<3) because of the pressure peaking which normally develops from improved core confinement. In recent DIII-D experiments, the internal transport barrier is clearly observed in the electron density and in the ion temperature and rotation profiles at ρ∼0.5 but not in the electron temperature profile, which is very broad. The misalignment of Ti and Te gradients may help to avoid a large local pressure gradient. Furthermore, at low internal inductance ∼0.6, the current density gradients are close to the vessel and the ideal kink modes are strongly wall-coupled. Simultaneous feedback control of both external and internal sets of n=1 magnetic coils was used to maintain optimal error field correction and resistive wall mode stabilization, allowing operation above the free-boundary β limit. Large particle orbits at high safety factor in the core help to broaden both the pressure and the beam-driven current profiles, favorable for steady-state operation. At plasma current flat top and β∼5%, a noninductive current fraction of ∼100% has been observed. Stability modeling shows the possibility for operation up to the ideal-wall limit at β∼6%. [ABSTRACT FROM AUTHOR]

The DIII-D Advanced Tokamak (AT) program in the DIII-D tokamak [J. L. Luxon, Plasma Physics and Controlled Fusion Research, 1986, Vol. I (International Atomic Energy Agency, Vienna, 1987), p. 159] is aimed at developing a scientific basis for steady-state, high-performance operation in future devices. This requires simultaneously achieving 100% noninductive operation with high self-driven bootstrap current fraction and toroidal beta. Recent progress in this area includes demonstration of 100% noninductive conditions with toroidal beta, βT=3.6%, normalized beta, βN=3.5, and confinement factor, H89=2.4 with the plasma current driven completely by bootstrap, neutral beam current drive, and electron cyclotron current drive (ECCD). The equilibrium reconstructions indicate that the noninductive current profile is well aligned, with little inductively driven current remaining anywhere in the plasma. The current balance calculation improved with beam ion redistribution that was supported by recent fast ion diagnostic measurements. The duration of this state is limited by pressure profile evolution, leading to magnetohydrodynamic (MHD) instabilities after about 1 s or half of a current relaxation time (τCR). Stationary conditions are maintained in similar discharges (∼90% noninductive), limited only by the 2 s duration (1τCR) of the present ECCD systems. By discussing parametric scans in a global parameter and profile databases, the need for low density and high beta are identified to achieve full noninductive operation and good current drive alignment. These experiments achieve the necessary fusion performance and bootstrap fraction to extrapolate to the fusion gain, Q=5 steady-state scenario in the International Thermonuclear Experimental Reactor (ITER) [R. Aymar et al., Fusion Energy Conference on Controlled Fusion and Plasma Physics, Sorrento, Italy (International Atomic Energy Agency, Vienna, 1987), paper IAEA-CN-77/OV-1]. The modeling tools that have been successfully employed to both plan and interpret the experiment are used to plan future DIII-D experiments with higher power and longer pulse ECCD and fast wave and co- and counterneutral beam injection in a pumped double-null configuration. The models predict our ability to control the current and pressure profiles to reach full noninductivity with increased beta, bootstrap fraction, and duration. The same modeling tools are applied to ITER, predicting favorable prospects for the success of the ITER steady-state scenario. [ABSTRACT FROM AUTHOR]

Results are presented from comparisons of modeling and experiment in studies to assess the best choices of safety factor q profile, pressure profile, and discharge shape for high β, steady-state, noninductive advanced tokamak operation in the DIII-D device [J. L. Luxon, Nucl. Fusion 42, 614 (2002)]. These studies are motivated by the need for high qminβN to maximize the self-driven bootstrap current while maintaining high toroidal β to increase fusion gain. Modeling shows that increases in the normalized beta βN stable to ideal, low toroidal mode number (n=1,2), instabilities can be obtained through broadening of the pressure profile and use of a symmetric double-null divertor shape. Experimental results are in agreement with this prediction. The general trend is for qminβN to increase with the minimum q value (qmin) although βN decreases as qmin increases. By broadening the pressure profile, βN≈4 is obtained with qmin≈2. Modeling of equilibria with near 100% bootstrap current indicates that operation with βN≈5 should be possible with a sufficiently broad pressure profile. [ABSTRACT FROM AUTHOR]

Determining the scaling of transport with beta (β), the ratio of the plasma kinetic pressure to the magnetic pressure, helps to differentiate between various proposed theories of turbulent transport since mechanisms that are primarily electrostatic show little change in transport with increasing β, while primarily electromagnetic mechanisms generally have a strong unfavorable β scaling. Experiments on the DIII-D tokamak [J.L. Luxon, Nucl. Fusion 42, 614 (2002)] have measured the β scaling of heat transport with all of the other dimensionless parameters held constant in high confinement mode (H-mode) plasmas with edge localized modes. A four point scan varied β from 30% to 85% of the ideal ballooning stability limit (normalized beta from 1.0 to 2.8) and found no change in the normalized confinement time, i.e., B τth∞ β0.01-0.09. The measured thermal diffusivities, normalized to the Bohm diffusion coefficient, also did not vary during the bscan to within the experimental uncertainties, whereas the normalized helium particle transport decreased with increasing β. The H-mode pedestal β varied in concert with the core band showed no signs of saturation. This weak, possibly nonexistent, β scaling of transport favors primarily electrostatic mechanisms such as E×B transport, and is in marked disagreement with the strong unfavorable β dependence contained in empirical scaling relations derived from multimachine H-mode confinement databases. [ABSTRACT FROM AUTHOR]

Advanced Tokamak (AT) research in DIII-D [K. H. Burrell for the DIII-D Team, in Proceedings of the 19th Fusion Energy Conference, Lyon, France, 2002 (International Atomic Energy Agency, Vienna, 2002) published on CD-ROM] seeks to provide a scientific basis for steady-state high performance operation in future devices. These regimes require high toroidal beta to maximize fusion output and poloidal beta to maximize the self-driven bootstrap current. Achieving these conditions requires integrated, simultaneous control of the current and pressure profiles, and active magnetohydrodynamic stability control. The building blocks for AT operation are in hand. Resistive wall mode stabilization via plasma rotation and active feedback with nonaxisymmetric coils allows routine operation above the no-wall beta limit. Neoclassical tearing modes are stabilized by active feedback control of localized electron cyclotron current drive (ECCD). Plasma shaping and profile control provide further improvements. Under these conditions, bootstrap supplies most of the current. Steady-state operation requires replacing the remaining Ohmic current, mostly located near the half radius, with noninductive external sources. In DIII-D this current is provided by ECCD, and nearly stationary AT discharges have been sustained with little remaining Ohmic current. Fast wave current drive is being developed to control the central magnetic shear. Density control, with divertor cryopumps, of AT discharges with edge localized moding H-mode edges facilitates high current drive efficiency at reactor relevant collisionalities. A sophisticated plasma control system allows integrated control of these elements. Close coupling between modeling and experiment is key to understanding the separate elements, their complex nonlinear interactions, and their integration into self-consistent high performance scenarios. [ABSTRACT FROM AUTHOR]

Recent experiments in the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] have demonstrated high β with good confinement quality under stationary conditions. Two classes of stationary discharges are observed-low q95 discharges with sawteeth and higher q95 without sawteeth. The discharges are deemed stationary when the plasma conditions are maintained for times greater than the current profile relaxation time. In both cases the normalized fusion performance ( βNH89P/q95² ) reaches or exceeds the value of this parameter projected for Qfus=10 in the International Thermonuclear Experimental Reactor (ITER) design [R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 (2002)]. The presence of sawteeth reduces the maximum achievable normalized β, while confinement quality (confinement time relative to scalings) is largely independent of q95 . Even with the reduced β limit, the normalized fusion performance maximizes at the lowest q95. Projections to burning plasma conditions are discussed, including the methodology of the projection and the key physics issues which still require investigation. [ABSTRACT FROM AUTHOR]

Using off-axis electron cyclotron current drive (ECCD), self-consistent integrated advanced tokamak operation has been demonstrated on DIII-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159], combining high beta; (>3%) at high q (q[SUBmin] > 2.0) with good energy confinement (H[SUB89] ∼ 2.5) and high noninductive current fraction (f[SUBBS] ∼55%,f[SUBNI] ∼ 90%). Modification of the current profile by ECCD led to internal transport barrier formation even in the presence of type I edge localized modes. Improvements were observed in all transport channels, and increased peaking of profiles led to higher bootstrap current in the core. Separate experiments have shown the ability to maintain a nearly steady-state current profile for up to 1 s with q[SUBmin] > 1.5. Modeling indicates that this favorable current profile can be maintained indefinitely at a higher β[SUBN] using tools available to the near-term DIII-D program. Modeling and simulation have become essential tools for the experimental program in interpreting the data and developing detail plans for new experiments. [ABSTRACT FROM AUTHOR]

Sustained stabilization of the n=1 kink mode by plasma rotation at beta approaching twice the stability limit calculated without a wall has been achieved in DIII-D by a combination of error field reduction and sufficient rotation drive. Previous experiments have transiently exceeded the no-wall beta limit. However, demonstration of sustained rotational stabilization has remained elusive because the rotation has been found to decay whenever the plasma is wall stabilized. Recent theory [Boozer, Phys. Rev. Lett. 86, 5059 (2001)] predicts a resonant response to error fields in a plasma approaching marginal stability to a low-n kink mode. Enhancement of magnetic nonaxisymmetry in the plasma leads to strong damping of the toroidal rotation, precisely in the high-beta regime where it is needed for stabilization. This resonant response, or “error field amplification” is demonstrated in DIII-D experiments: applied n=1 radial fields cause enhanced plasma response and strong rotation damping at beta above the no wall limit but have little effect at lower beta. The discovery of an error field amplification has led to sustained operation above the no-wall limit through improved magnetic field symmetrization using an external coil set. The required symmetrization is determined both by optimizing the external currents with respect to the plasma rotation and by use of feedback to detect and minimize the plasma response to nonaxisymmetric fields as beta increases. Ideal stability analysis and rotation braking experiments at different beta values show that beta is maintained 50% higher than the no wall stability limit for durations greater than 1 s, and approaches beta twice the no-wall limit in several cases, with steady-state rotation levels. The results suggest that improved magnetic-field symmetry could allow plasmas to be maintained well above no-wall beta limit for as long as sufficient torque is provided. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A model based on magnetohydrodynamic (MHD) stability of the tokamak plasma edge region is presented, which describes characteristics of edge localized modes (ELMs) and the pedestal. The model emphasizes the dual role played by large bootstrap currents driven by the sharp pressure gradients in the pedestal region. Pedestal currents reduce the edge magnetic shear, stabilizing high toroidal mode number (n) ballooning modes, while at the same time providing drive for intermediate to low n peeling modes. The result is that coupled peeling–ballooning modes at intermediate n (3

Significant progress has been made in obtaining high-performance discharges for many energy confinement times in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159]. Normalized performance (measured by the product of β[sub N]H[sub 89] and indicative of the proximity to both conventional β limits and energy confinement quality, respectively) ∼10 has been sustained for >5 τ[sub E] with q[sub min] > 1.5. These edge localized modes (ELMing) H-mode discharges have &beta∼5%, which is limited by the onset of resistive wall modes slightly above the ideal no-wall n = 1 limit, with approximately 75% of the current driven noninductively. The remaining Ohmic current is localized near the half-radius. The DIII-D electron cyclotron heating system is being upgraded to replace this inductively driven current with localized electron cyclotron current drive (ECCD). Density control, which is required for effective ECCD, has been successfully demonstrated in long-pulse high-performance ELMing H-mode discharges with &beta[sub N]H[sub 89]∼ 7 for up to 6.3 s. In plasma shapes compatible with good density control in the present divertor configuration, the achieved β[sub N] is somewhat less than that in the high β[sub N]H[sub 89] = 10 discharges. © 2001 American Institute of Physics. [DOI: 10.1063/1. [ABSTRACT FROM AUTHOR]

The amplitude and frequency of modes driven in the edge region of tokamak high mode (H-mode) discharges [type I edge-localized modes (ELMs)] are shown to depend on the discharge shape. The measured pressure gradient threshold for instability and its scaling with discharge shape are compared with predictions from ideal magnetohydrodynamic theory for low toroidal mode number (n) instabilities driven by pressure gradient and current density and good agreement is found. Reductions in mode amplitude are observed in discharge shapes with either high squareness or low triangularity where the stability threshold in the edge pressure gradient is predicted to be reduced and the most unstable mode is expected to have higher values of n. The importance of access to the ballooning mode second stability regime is demonstrated through the changes in the ELM character that occur when second regime access is not available. An edge stability model is presented that predicts that there is a threshold value of n for second regime access and that the most unstable mode has n near this threshold. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Transport phenomena are studied in Advanced Tokamak (AT) regimes in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomics Energy Agency, Vienna, 1987), Vol. I, p. 159], with the goal of developing understanding and control during each of three phases: Formation of the internal transport barrier (ITB) with counter neutral beam injection taking place when the heating power exceeds a threshold value of about 9 MW, contrasting to co-NBI injection, where P[sub threshold]<2.5 MW. Expansion of the ITB is enhanced compared to similar co-injected discharges. Both differences are believed to arise from modification of the ExB shear dynamics when the sign of the rotation contribution is reversed. Sustainment of an AT regime with β[sub N]H[sub 89]=9 for 16 confinement times has been accomplished in a discharge combining an ELMing H-mode (edge localized, high confinement mode) edge and an ITB, and exhibiting ion thermal transport down to 2-3 times neoclassical. The microinstabilities usually associated with ion thermal transport are predicted stable, implying that another mechanism limits performance. High frequency magnetohydrodynamic (MHD) activity is identified as the probable cause. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Improvement in both the energy confinement time and the achievable value of normalized beta is obtained by modifying the current density profile from the relatively broad shape obtained in standard tokamak discharges to a more peaked shape. The peaked current profile is produced with either a rapid negative ramp in the total plasma current or a rapid increase in the discharge elongation. Discharges have been obtained with β[sub N]=β/(I/aB)=6% mT/MA simultaneously with total energy confinement time two times the value predicted by L-mode scaling relations. Up to a factor of 1.8 improvement in the normalized thermal energy confinement time, τ[sub th]/I[sub p], has been obtained in both L-mode and H-mode discharges. It is shown that the increase in confinement can be attributed to a local decrease in the thermal diffusivity that is correlated with a local increase in the poloidal magnetic field and the magnetic shear. [ABSTRACT FROM AUTHOR]

Low-q (q[sub 95] < 3) double-null divertor discharges with values of the volume-average toroidal beta as high as 9.3% have been operated in the DIII-D tokamak [Fusion Technol. 8, 441 ( 1985 ) ]. In discharges with q[sub 95] ≈ 5, values of β[sub T]/(I/aB) as high as 5 have been obtained. These discharges are shown to be at or below the stability limit to the value of beta for infiniten, ideal ballooning modes. The discharges are significantly below the beta limit for ideal,low toroidal mode number kink modes. The kink mode beta limit is shown to be strongly dependent on the radial profiles of plasma pressure and current. The theoretical beta limit in DIII-D is shown to be in the range β[sub T]/(I/aB) = 4-5 depending on the value of I/aB, and this is consistent with the experiment. High-beta discharges have been operated with ion temperature up to 17 keV. Steady-state, high-beta, low-q operation is demonstrated by a discharge with I/aB = 2.6, q[sub 95] = 2.7, in which β[sub T] > 7% is maintained for 1.5 sec. [ABSTRACT FROM AUTHOR]

Electrostatic end plugging is observed in a completely axisymmetric, three cell tandem mirror under conditions where the central-cell plasma density is always larger than the end-cell density. A factor of 4 increase in the central-cell density, to a maximum of 1.2×1013 cm-3 with simultaneous plasma beta of 13%, occurs upon application of the end plugging potential. Ion confining potentials of 25 V and 80 V at the two ends of the device, respectively, result in a factor of 2.5 increase in the axial confinement time for Tic =40 eV in agreement with the collisional flow model for ion confinement. The non-Boltzmann ion confining potential is caused by electron heating in the end cells by rf near the ion-cyclotron frequency. The initial central-cell density rise is caused by an increase in the ionization rate that occurs because of an increase in the electron temperature. The density remains high throughout the end-cell heating pulse as a result of increased particle confinement time. There is no nonambipolar radial ion loss in the core plasma (r≤16 cm) but inward radial transport of ions is observed at a rate consistent with ion–neutral collisions and a radial electric field in the negative radial direction. Steady-state thermal-barrier-like potential dips that are in agreement with the Boltzmann model for potentials are observed in the transitions between the central cell and the end cells. [ABSTRACT FROM AUTHOR]

Stabilization of interchange instabilities in the Phaedrus tandem mirror [Phys. Rev. Lett. 51, 1955 (1983)] through the use of externally applied rf at a single frequency is demonstrated over a wide range of frequency (1.03Ωi <ω<4.1Ωi). Here rf stabilized plasmas are reported with ion temperature up to 550 eV and beta up to 8%. Calculations of the rf electric fields show that the dominant mode is the m=+1 fast wave. When the rf frequency is near Ωi the calculated ponderomotive forces on ions and electrons are shown to be comparable. For ω>1.3Ωi it is shown that the force acts primarily on electrons. Stable plasmas are only achieved when the net radial ponderomotive force is calculated to be stabilizing and comparable to the curvature force. Results are also reported for rf applied simultaneously at two frequencies, one which is stabilizing and one which is destabilizing. Abrupt changes in stability are observed as the rf power is increased whenever one of the rf frequencies is effective at plasma heating. [ABSTRACT FROM AUTHOR]

A high speed data acquisition system which is closely coupled with a high speed digital processor is described. Data acquisition at a rate of 40 million 14 bit data values per second is possible simultaneously with data processing at a rate of 80 million floating point operations per second. This is achieved by coupling a commercially available VME format single board computer based on the Intel i860 microprocessor with a custom designed first-in, first-out memory circuit that transfers data at high speed to the processor board memory. Parallel processing to achieve increased computation speed is easily implemented because the data can be transferred simultaneously to multiple processor boards. Possible applications include high speed process control and real time data reduction. A specific example is described in which this hardware is used to implement a feedback control system for 18 parameters which uses 100 input signals and achieves a 100 μs cycle time. [ABSTRACT FROM AUTHOR]

The techniques used in implementing two applications of real time digital analysis of data from the DIII-D tokamak are described. These tasks, which are demanding in both the speed of data acquisition and the speed of computation, execute on hardware capable of acquiring 40 million data samples per second and executing 80 million floating point operations per second. In the first case, a feedback control algorithm executing at a 10 kHz cycle frequency is used to specify the current in the poloidal field coils in order to control the discharge shape. In the second, fast Fourier transforms of Mirnov probe data are used to find the amplitude and frequency of each of eight toroidal mode numbers as a function of time during the discharge. Data sampled continuously at 500 kHz are used to produce results at 2 ms intervals. [ABSTRACT FROM AUTHOR]

Accurate equilibrium reconstruction and detailed stability analysis of a strongly shaped, double-null, βT=11% discharge shows that the plasma core is in the second stable regime to ideal ballooning modes. The equilibrium reconstruction using all the available data (coil currents, poloidal magnetic loops, motional Stark effect data, the kinetic pressure profile, the magnetic axis location, and the location of the two q=1 surfaces) shows a region of negative magnetic shear near the magnetic axis, an outer positive shear region, and a low shear region connecting the two. The inner negative shear region allows a large positive shear region near the boundary, even at low q (q95=2.6), permitting a large outer region pressure gradient to be first regime stable. The inner region is in the second stable regime, consistent with the observed axial beta [βT(0)=44%]. In the low shear region p’ vanishes, consistent with Mercier stability. This is one way to extend the ballooning limit in shaped plasmas while maintaining stability against external kinks. The n=1 analysis shows that the plasma is unstable to an ideal internal mode, consistent with the experimental observations of a saturated internal m/n=1/1 mode. The core plasma pressure, not being limited by ballooning stability, appears to be reaching a local equilibrium limit at the magnetic axis. [ABSTRACT FROM AUTHOR]

The stability of the n=1 ideal kink in DIII-D-like [Fusion Technol. 8, 441 (1985)] configurations is found to depend critically on the details of the current density and pressure profiles. The maximum stable normalized β, β[sub N]=β/(I/aB) (I in MA, a in meters, and B[sub 0] in tesla), is found to increase dramatically as the peak in the pressure gradient is shifted from the central region toward the plasma boundary. Further, for peaked pressure profiles, the β limit is insensitive to the internal inductance, l[sub i], whereas for broad pressure profiles, the β limit depends more strongly on l[sub i] and can increase with l[sub i] almost up to the point where the q profile becomes hollow. With broad pressure profiles and a conducting wall at 1.5 minor plasma radii, kink-stable β[sub N] values of 5.8—significantly above both the Troyon limit and the ballooning limit—have been found. [ABSTRACT FROM AUTHOR]

The effects of current profile on the ideal ballooning mode for circular and shaped poloidal cross-section plasmas in tokamaks are studied analytically and numerically. The results show that for moderately shaped plasmas the critical normalized beta, βNC, against the ballooning mode increases approximately linearly with the plasma internal inductance li. As the plasma becomes more strongly shaped, this dependence on li becomes weaker, and for a divertor plasma βNC shows a very weak dependence on li for the range of moderate li values considered. [ABSTRACT FROM AUTHOR]

A theoretical and experimental evaluation of axisymmetric stability and axisymmetric control has led to a modification of the vertical position control in the DIII-D tokamak, which now allows operation to within a few percent of the ideal magnetohydrodynamic (MHD) n = 0 limit. It is found that the onset the departure from rigid shift behavior in D-shaped plasmas limits plasma elongation to 2.5 in DIII-D. The possibility of avoiding the vertical instability in future tokamaks with highly elongated plasmas is discussed. Recent experiments have focused on utilizing this capability for axisymmetric control to construct plasma shapes optimized to increase the achievable beta. Operation near the axisymmetric stability limit allows an increase in the achieved normalized current I[sub p]/aB[sub T], where I[sub p], is the total plasma current, a is the minor radius, and B[sub T] is the toroidal field. Based on stability calculations, an equilibrium was developed to achieve marginal stability simultaneously to axisymmetric, kink, and ballooning instabilities. In the experiment, the shape was altered to higher elongation during the high-beta phase as the current profile broadened. A record high beta for DIII-D of t 1% was achieved. The high-beta phase of the discharge lasted 40 msec, approximately one confinement time. [ABSTRACT FROM AUTHOR]

It is demonstrated that the radial electric field in the Phaedrus Tandem Mirror [Plasma Physics and Controlled Nuclear Fusion Research 1984 (IAEA, Vienna, 1985), Vol. 2, p. 265] can be altered using plasma potential control rings (PPC rings) situated at each end of the device, and the azimuthal plasma rotational velocity may thus be varied. Low-frequency (ω<ωci), low azimuthal mode number (m=-1 and m=-2) instabilities driven by E×B rotation are observed and shown to be in qualitative agreement with the theory of Freidberg and D’Ippolito [Phys. Fluids 26, 2657 (1983)], and Phillips [Phys. Fluids 27, 1783 (1984)] for the case when Phaedrus is operated as a conventional tandem mirror with minimum-|B| end cells. [ABSTRACT FROM AUTHOR]

Fueling and heating of tandem mirror end cells by rf at the ion-cyclotron frequency have been studied experimentally in the Phaedrus Tandem Mirror. The end cell density is found to increase linearly with rf voltage. The total plasma energy is observed to increase with rf power with no evidence of saturation at high power. The plasma axial length decreases with increasing rf power down to a length of approximately the distance between the two resonance locations in the end cell. The highest density and average ion energy are achieved with the resonance closest to the midplane. It is necessary to assume that the rf electric field at the resonance decreases with increasing density and with distance from the antenna in order to model the ion particle and power balance. The particle and power balance model predicts that dense, hot end cells may be maintained with E[sub +] ∼ 1 V/cm and a fueling efficiency of a few percent when the resonance is close to the midplane because of better ion confinement and small plasma volume. Monte Carlo simulation of the trapping process shows that E²[sub +] ∞ T[sup 1.5, sub ic] is required to maintain a given rf trapping efficiency. [ABSTRACT FROM AUTHOR]