Search

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 Pthreshold

Two approaches to achieving long timescale stabilization of the ideal kink mode with a real, finite conductivity wall are considered: plasma rotation and active feedback control. DIII-D experiments have demonstrated stabilization of the resistive wall mode (RWM) by sustaining ? greater than the no-wall limit for up to 200?ms, much longer than the wall penetration time of a few milliseconds. These plasmas are typically terminated by an m = 3, n = 1 mode as the plasma rotation slows below a few kilohertz. Recent temperature profile data show an ideal MHD mode structure, as expected for the RWM at ? above the no-wall limit. The critical rotation rate for stabilization is in qualitative agreement with recent theories for dissipative stabilization in the absence of magnetic islands. However, drag by small amplitude RWMs or damping of stable RWMs may contribute to an observed slowing of rotation at high ?, rendering rotational stabilization more difficult. An initial open loop active control experiment, using non-axisymmetric external coils and a new array of saddle loop detectors, has yielded encouraging results indicating a delayed onset of the RWM.

Magnetohydrodynamic stability calculations of the n = 1 kink mode for equilibria with increasing β and values of the axis safety factor q0 > 1 and q0 1. This provides justification for the usual computational procedure of optimizing β by taking q0 > 1 and applying it to predict the β limit of sawtoothing discharges.

Improving confinement and β limits simultaneously in long pulse ELMy H mode discharges is investigated. The product βN H98y serves as a useful figure of merit for performance, where βN ≡ β/(I/aB) and H98y is the ratio of the thermal confinement time to the most recent ELMy H mode confinement scaling established by the ITER confinement database working group. In discharges with q0 ≈ 1 (no sawteeth) and discharges with qmin > 1.5 and negative central magnetic shear, βN ≈ 2.9 and H98y ≈ 1.4 are sustained for up to 2 s. Although peaked profiles are observed, steep internal transport barriers are not present. Further increases in βN in these discharges are limited by neoclassical tearing modes (NTMs) in the positive shear region. In another recently developed regime, βN ≈ 3.8 and H98y ≈ 2 have been sustained during large infrequent ELMs in non-sawtoothing discharges with q0 ≈ 1. This level of performance is similar to that obtained in ELM free regimes such as VH mode. The limitation on βN and pulse length in these discharges is also the onset of NTMs.

In toroidal magnetic confinement configurations all the charged particles align their magnetic drifts with the flux surfaces if, and only if, the lines of force have zero geodesic curvature (omnigeneous configuration). In this condition, the neoclassical transport is zero; unfortunately, standard tokamak devices are far from meeting such a condition. Nevertheless, a minimization of the geodesic curvature of the lines of force in tokamaks minimizes the neoclassical transport, and could as well reduce any other transport terms depending on the noncoincidence between magnetic and drift surfaces. In particular, the geodesic curvature of the lines of force generates both the neoclassical Pfirsch–Schluter current density j∥PS, as well as Hirshman factor q [Nucl. Fusion 18, 917 (1978)], which increases the moment of inertia of the magnetic configuration. The improved confinement observed in the VH-mode (very high confinement) and in reversed magnetic shear discharges of the DIII-D tokamak [Plasma Physics Contro...

Using newly developed techniques and improved diagnostics, rotating wall-stabilized discharges have been maintained in the DIII-D tokamak for 30 characteristic resistive wall decay times{emdash}significantly longer than was previously achieved. The terminating resistive wall mode has been directly identified using internal fluctuation diagnostics, and its correlation with the slowdown in the plasma rotation is established. {copyright} {ital 1999} {ital The American Physical Society}

One promising approach to maintaining stability of high beta tokamak plasmas is the use of a conducting wall near the plasma to stabilize low-n ideal magnetohydrodynamic instabilities. However, with a resistive wall, either plasma rotation or active feedback control is required to stabilize the more slowly growing resistive wall modes (RWMs). Previous experiments have demonstrated that plasmas with a nearby conducting wall can remain stable to the n=1 ideal external kink above the beta limit predicted with the wall at infinity. Recently, extension of the wall stabilized lifetime τL to more than 30 times the resistive wall time constant τw and detailed, reproducible observation of the n=1 RWM have been possible in DIII-D [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159] plasmas above the no-wall beta limit. The DIII-D measurements confirm characteristics common to several RWM theories. The mode is destabilized as the plasma rotation at the q=3 surfac...

The ideal magnetohydrodynamic (MHD) stability of the tokamak edge is analyzed, with particular emphasis on radially localized instabilities; it is proposed that these are responsible for edge pressure gradient limits and edge localized modes (ELMS). Data and stability calculations from DIII-D [to appear in Proceedings of the 16th International Conference on Fusion Energy, Yokohama (International Atomic Energy Agency, Vienna, 1998), Paper No. IAEA-F1-CN-69/EX8/1] tokamak equilibria indicate that two types of instability are important: the ballooning mode (driven by pressure gradient) and the peeling mode (driven by current density). The characteristics of these instabilities, and their coupling, are described based on a circular cross-section, large aspect ratio model of the tokamak equilibrium. In addition, preliminary results are presented from an edge MHD stability code which is being developed to analyze general geometry tokamak equilibria; an interpretation of the density threshold to access the high-...

Characteristics of the H-mode pedestal are studied in Type I ELM discharges with ITER cross-sectional shape and aspect ratio. The scaling of the width of the edge steep gradient region, δ , which is most consistent with the data are with the normalized edge pressure, ( β PED POL ) 0.4 . Fits of δ to a function of temperature, such as ρ POL , are ruled out in divertor pumping experiments. The edge pressure gradient is found to scale as would be expected from infinite n ballooning mode theory; however, the value of the pressure gradient exceeds the calculated first stable limit by more than a factor of 2 in some discharges. This high edge pressure gradient is consistent with access to the second stable regime for ideal ballooning for surfaces near the edge. In lower q discharges, including discharges at the ITER value of q , edge second stability requires significant edge current density. Transport simulations give edge bootstrap current of sufficient magnitude to open second stable access in these discharges. Ideal kink analysis using current density profiles including edge bootstrap current indicate that before the ELM these discharges may be unstable to low n , edge localized modes.

The motional Stark effect (MSE) diagnostic was developed to provide a measurement of the magnetic pitch angle or q profile in tokamaks. The technique relies upon polarization measurements of Stark broadened Dα emission to determine the pitch angle of the Lorentz vb×B electric field, where vb is the injected neutral beam particle velocity and B is the total magnetic field. However, in many advanced confinement regimes, large values of the plasma radial electric field, Er, are observed and can affect the interpretation of MSE measurements. Viewing fixed locations in the plasma from two different viewing angles allows one to separate the Er field from the vb×B field, thus providing simultaneous measurement of the Er and q profiles. To achieve this measurement, the DIII–D MSE diagnostic was recently upgraded from 16 to 35 channels with three independent viewing angles. The new instrument provides an Er resolution of 5–10 kV/m with a time response of 1 ms. Measurement results from the VH mode, reverse shear, a...

Recent advances in tokamak physics indicate that a spherical tokamak may offer a magnetic fusion development path that can be started with a small size pilot plant and progress smoothly to larger power plants. Full calculations of stability to kink and ballooning modes show the possibility of greater than 50% β-toroidal with the normalized β [βN=βT/(I/aβ)] as high as 10 and fully aligned 100% bootstrap current. Such β-values coupled with 2–3 T toroidal fields imply a pilot plant about the size of the present DIII-D tokamak could produce ∼800 MW thermal, 160 MW net electric, and would have a ratio of gross electric power over recirculating power (QPLANT) of 1.9. The high β values in the ST mean that E×B shear stabilization of turbulence should be ten times more effective in the ST than in present tokamaks, implying that the required high quality of confinement needed to support such high beta values will be obtained. The anticipated β values are so high that the allowable neutron flux at the blanket sets the device size, not the physics constraints. The ST has a favorable size scaling so that at 2–3 times the pilot plant size the QPLANT rises to 4–5, an economic range and 4 GW thermal power plants result. Current drive power requirements for 10% of the plasma current are consistent with the plant efficiencies quoted. The unshielded copper centerpost should have an adequate lifetime against nuclear transmutation-induced resistance change and the low voltage, high current power supplies needed for the 12-turn TF coil appear reasonable. The favorable size scaling of the ST and the high β mean that in large sizes, if the copper TF coil is replaced with a superconducting TF coil and a shield, the advanced fuel D-He3 could be burned in a device with QPLANT∼4. If the anticipated physics of the ST regime can be proven in near-term experiments and engineering challenges (such as the high power density to be exhausted and centerpost neutronics issues) can be met, then the ST offers the possibility of a magnetic fusion development path with a minimal cost initial step and exciting further possibilities.

The H-mode confinement enhancement factor, H, is found to be strongly correlated with the height of the edge pressure pedestal in ITER shape discharges. In discharges with type I edge-localized modes (ELMs) the pedestal pressure is set by the maximum pressure gradient before the ELM and the width of the H-mode transport barrier. The pressure gradient before type I ELMs is found to scale as would be expected for a stability limit set by ideal ballooning modes, but with values significantly in excess of that predicted by stability code calculations. The width of the H-mode transport barrier is found to scale equally well with pedestal or . The improved H value in high- discharges may be due to a larger edge pressure gradient and wider H-mode transport barrier consistent with their higher edge ballooning mode limit. Deuterium puffing is found to reduce H, which is consistent with the smaller pedestal pressure which results from the reduced barrier width and critical pressure gradient. Type I ELM energy loss is found to be proportional to the change in the pedestal energy.

The role of E×B flow shear on confinement enhancement in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high internal inductance discharges with high-confinement edge is investigated experimentally using a nonaxisymmetric poloidal magnetic-field perturbation from an external coil to drag down the plasma toroidal rotation. At similar values of internal inductance, discharges which rotate faster and have a stronger E×B flow shear have better confinement. These results indicate that E×B flow shear likely plays an important role in the confinement enhancement of these discharges.

Motional Stark effect polarimetry (MSE) is a well established technique for measuring the magnetic field pitch angle in tokamaks. By viewing the Stark emission spectrum from two different angles, this technique can also provide local measurements of the plasma radial electric field, ${E}_{r}$. Simultaneous measurements of the profiles of magnetic field pitch angle and ${E}_{r}$ are presented for the first time in a high-performance DIII-D tokamak plasma. Direct measurement of ${E}_{r}$ is of great importance in fusion research because the suppression of turbulence through ${\mathbf{E}}_{r}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$ velocity shear provides a mechanism to improve energy confinement.

Discharges with negative central magnetic shear (NCS) hold the promise of enhanced fusion performance in advanced tokamaks. However, stability to long wavelength magnetohydrodynamic modes is needed to take advantage of the improved confinement found in NCS discharges. The stability limits seen in DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] experiments depend on the pressure and current density profiles and are in good agreement with stability calculations. Discharges with a strongly peaked pressure profile reach a disruptive limit at low beta, βN=β(I/aB)−1⩽2.5 (% m T/MA), caused by an n=1 ideal internal kink mode or a global resistive instability close to the ideal stability limit. Discharges with a broad pressure profile reach a soft beta limit at significantly higher beta, βN=4 to 5, usually caused by instabilities with n>1 and usually driven near the edge of the plasma. With broad pressure profiles, the experimental stability limit is independent of the magnitude of negative she...

Discharges exhibiting the highest plasma energy and fusion reactivity yet realized in the DIII-D tokamak have been produced by combining the benefits of a hollow or weakly sheared central current profile with a high confinement (H-mode) edge. In these discharges, low power neutral beam injection heats the electrons during the initial current ramp, and {open_quotes}freezes in{close_quotes} a hollow or flat central current profile. When the neutral beam power is increased, formation of a region of reduced transport and highly peaked profiles in the core often results. Shortly before these plasmas would otherwise disrupt, a transition is triggered from the low (L-mode) to high (H-mode) confinement regimes, thereby broadening the pressure profile and avoiding the disruption. These plasmas continue to evolve until the high performance phase is terminated nondisruptively at much higher {beta}{sub T} (ratio of plasma pressure to toroidal magnetic field pressure) than would be attainable with peaked profiles and an L-mode edge. Transport analysis indicates that in this phase, the ion diffusivity is equivalent to that predicted by Chang-Hinton neoclassical theory over the entire plasma volume. This result is consistent with suppression of turbulence by locally enhanced E x B flow shear, and is supported by observations of reduced fluctuations in the plasma. Calculations of performance in these discharges extrapolated to a deuterium-tritium fuel mixture indicates that such plasmas could produce a DT fusion gain Q{sub DT} = 0.32.

The motional Stark effect (MSE) has become the leading diagnostic technique for measurement of the internal poloidal field profile in neutral beam heated tokamak plasmas. The technique relies upon the measurement of the polarization angle of Stark broadened neutral beam Dalpha emission due to the strong E= nu b*B motional electric field. In many recently discovered enhanced confinement regimes in tokamaks, a strong radial electric field Er is also present in the plasma. It is shown that in these cases, the effect of Er on the interpretation of MSE measurements is significant and cannot be neglected. The importance of this effect is illustrated with the analysis of the q profile in a high performance discharge from the DIII-D tokamak

The maximum operational high beta in single-null divertor (SND) long pulse tokamak discharges in the DIII-D tokamak with a cross-sectional shape similar to the proposed International Thermonuclear Experimental Reactor (ITER) device is found to be limited by the onset of resistive instabilities that have the characteristics of neoclassically destabilized tearing modes. There is a soft limit due to the onset of an m/n=3/2 rotating tearing mode that saturates at low amplitude and a hard limit at slightly higher beta due to the onset of an m/n=2/1 rotating tearing mode that grows, slows down and locks. By operating at higher density and thus collisionality, the practical beta limit due to resistive tearing modes approaches the ideal magnetohydrodynamic (MHD) limit

In this paper the authors present measurements of the global power and particle balance in the high-performance phase of negative central magnetic shear (NCS) discharges and compare with reference VH-mode discharges. The principal differences observed are that NCS has a much lower fraction of the total input power flowing into the boundary, less core radiation, and larger rate of stored energy increase as a fraction of total power. Scrape-off layer (SOL) temperature and divertor heat flux profiles, and radiation profiles at the midplane, are similar to VH-mode. Due to the good core particle confinement and efficient fueling by neutral beam injection (NBI), with little gas puffing, the gas load on the walls and the recycling are very low during the NCS discharges. This results in a rate of density rise relative to beam fueling at the L to H transition time which is 1/3 of the value for VH transitions, which is in turn 1/2 that for L-to-ELMing-H-mode transitions.

Strong shaping, favourable for stability and improved energy confinement, together with a significant expansion of the central region of improved confinement in negative central magnetic shear target plasmas, increased the maximum fusion power produced in DIII-D by a factor of 3. Using deuterium plasmas, the highest fusion power gain, the ratio of fusion power to input power, Q, was 0.0015, corresponding to an equivalent Q of 0.32 in a deuterium-tritium plasma, which is similar to values achieved in tokamaks of larger size and magnetic field. A simple transformation relating Q to the stability parameters is presented

Tokamaks with weak to moderate reversed central shear in which the minimum inverse rotational transform (safety factor) qmin is in the neighbourhood of unity can trigger bifurcated magnetohydrodynamic equilibrium states, one of which is similar to a saturated ideal internal kink mode. Peaked prescribed pressure profiles reproduce the ‘snake’ structures observed in many tokamaks which has led to a novel explanation of the snake as a bifurcated equilibrium state. Snake equilibrium structures are computed in simulations of the tokamak `a configuration variable (TCV), DIII-D and mega amp spherical torus (MAST) tokamaks. The internal helical deformations only weakly modulate the plasma–vacuum interface which is more sensitive to ripple and resonant magnetic perturbations. On the other hand, the external perturbations do not alter the helical core deformation in a significant manner. The confinement of fast particles in MAST simulations deteriorate with the amplitude of the helical core distortion. These three-dimensional bifurcated solutions constitute a paradigm shift that motivates the applications of tools developed for stellarator research in tokamak physics investigations.

The low aspect ratio tokamak or spherical torus (ST) approach offers the two key elements needed to enable magnetic confinement fusion to make the transition from a government-funded research program to the commercial marketplace: a low cost, low power, small size market entry vehicle and a strong economy of scale in larger devices. Within the ST concept, a very small device (A = 1.4, major radius about 1 m, similar size to the DIII-D tokamak) could be built that would produce approx.800 MW thermal, 250 MW net electric, and would have a gain, defined as Q{sub PLANT} = (gross electric power/recirculating power), of about 2. Such a device would have all the operating systems and features of a power plant and would therefore be acceptable as a pilot plant, even though the cost of electricity would not be competitive. The ratio of fusion power to copper TF coil dissipation rises quickly with device size (like R{sup 4}) and can lead to 3 GW thermal power plants with Q{sub PLANT} = 4-5 but which remain a factor 3 smaller than superconducting tokamak power plants. Power plants of the scale of ITER might be able to burn the advanced fuel D-He{sup 3}.more » 23 refs., 5 figs., 1 tab.« less

Plasma discharges with negative central magnetic shear (NCS) and access to the ballooning second stability regime have been produced on DIII-D with edge plasma conditions similar to those in the standard L mode confinement regime. Confinement enhancement factors up to H identical to tau E/ tau ITER-89P~2.5 are obtained while maintaining the L mode edge. Compared with discharges with monotonic q profiles, highly peaked toroidal rotation (fphi (0) approximately=30-70 kHz), ion temperature (Ti(0) approximately=15-22 keV) and density (ne(0)/ne approximately=2.2) profiles are observed. This regime has yielded the highest DD neutron rates observed to date on DIII-D. Steep pressure gradients drive a large bootstrap current, with up to ~75% total non-inductive current drive. These features make this an attractive advanced tokamak operating regime for further study

Resistive interchange modes can be driven unstable by large pressure gradients in the negative central magnetic shear (NCS) region of advanced tokamaks. Localized stability analysis reveals that the resistive interchange stability criterion (D-R less than or equal to 0) is violated in this region, and unstable n = 1 localized resistive magnetohydrodynamic (MHD) modes are computed using the resistive MHD code MARS. In DIII-D NCS plasmas, these instabilities appear as bursting MHD activities, constituting the first identification of resistive interchange in a high temperature tokamak experiment. These bursts also appear to play a role in triggering disruptions.

Using the combination of early neutral beam injection, ramping of the plasma current, low electron density and controlled L - H transitions, robust discharges with negative central magnetic shear are reproducibly obtained on the DIII-D tokamak. The effects of these factors on the formation and evolution of the q profile during the initial phase of these discharges are documented. Details of the evolution of the inverted q profile are obtained from measurements of the internal field pitch using a 16-channel motional Stark effect (MSE) system. Time-dependent MSE data are used to directly construct the profile of the toroidal electric field and allow a straightforward calculation of the non-inductive current density profile.

The confinement and the stability properties of the DIII-D tokamak high performance discharges are evaluated in terms of rotational and magnetic shear with emphasis on the recent experimental results obtained from the negative central magnetic shear (NCS) experiments. In NCS discharges, a core transport barrier is often observed to form inside the NCS region accompanied by a reduction in core fluctuation amplitudes. Increasing negative magnetic shear contributes to the formation of this core transport barrier, but by itself is not sufficient to fully stabilize the toroidal drift mode (trapped- electron-{eta}{sub i}mode) to explain this formation. Comparison of the Doppler shift shear rate to the growth rate of the {eta}{sub i} mode suggests that the large core {bold E x B} flow shear can stabilize this mode and broaden the region of reduced core transport . Ideal and resistive stability analysis indicates the performance of NCS discharges with strongly peaked pressure profiles is limited by the resistive interchange mode to low {Beta}{sub N} {lt} 2.3. This mode is insensitive to the details of the rotational and the magnetic shear profiles. A new class of discharges which has a broad region of weak or slightly negative magnetic shear (WNS) is described. The WNS discharges have broader pressure profiles and higher values than the NCS discharges together with high confinement and high fusion reactivity.

Reliable operation of discharges with negative central magnetic shear has led to significant increases in plasma performance and reactivity in both low confinement, L‐mode, and high confinement, H‐mode, regimes in the DIII‐D tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159]. Using neutral beam injection early in the initial current ramp, a large range of negative shear discharges have been produced with durations lasting up to 3.2 s. The total noninductive current (beam plus bootstrap) ranges from 50% to 80% in these discharges. In the region of shear reversal, significant peaking of the toroidal rotation [fφ(0)∼30–60 kHz] and ion temperature [Ti(0)∼15–22 keV] profiles are observed. In high‐power discharges with an L‐mode edge, peaked density profiles are also observed. Confinement enhancement factors up to H≡τE/τITER‐89P∼2.5 with an L‐mode edge, and H∼3.3 in an edge localized mode (ELM)‐free H mode, are obtained. Transp...

A technique for tokamak equilibrium reconstructions is used for multiple DIII-D discharges, including L-mode and H-mode cases when weakly 3D fields ( δ B / B ∼ 10 − 3 ) are applied. The technique couples diagnostics to the non-linear, ideal MHD equilibrium solver VMEC, using the V3FIT code, to find the most likely 3D equilibrium based on a suite of measurements. It is demonstrated that V3FIT can be used to find non-linear 3D equilibria that are consistent with experimental measurements of the plasma response to very weak 3D perturbations, as well as with 2D profile measurements. Observations at DIII-D show that plasma rotation larger than 20 krad s−1 changes the relative phase between the applied 3D fields and the measured plasma response. Discharges with low averaged rotation (10 krad s−1) and peaked rotation profiles (40 krad s−1) are reconstructed. Similarities and differences to forward modeled VMEC equilibria, which do not include rotational effects, are shown. Toroidal phase shifts of up to 30 ° are found between the measured and forward modeled plasma responses at the highest values of rotation. The plasma response phases of reconstructed equilibra on the other hand match the measured ones. This is the first time V3FIT has been used to reconstruct weakly 3D tokamak equilibria.

Detailed analysis of recent high beta discharges in the DIII-D tokamak demonstrates that the resistive vacuum vessel can provide stabilization of low n magnetohydrodynamic (MHD) modes. The experimental beta values reaching up to {beta}{sub T} = 12.6% are more than 30% larger than the maximum stable beta calculated with no wall stabilization. Plasma rotation is essential for stabilization. When the plasma rotation slows sufficiently, unstable modes with the characteristics of the predicted {open_quotes}resistive wall{close_quotes} mode are observed. Through slowing of the plasma rotation between the q = 2 and q = 3 surfaces with the application of a non-axisymmetric field, the authors have determined that the rotation at the outer rational surfaces is most important, and that the critical rotation frequency is of the order of {Omega}/2{pi} = 1 kHz.

In previous analysis of edge localized modes (ELMs), three different types (types I, II and III) of ELM were observed in DIII-D, whereas only one type of ELM has been found in ASDEX. The type III ELMs observed on DIII-D are similar to the ELMs observed on ASDEX, whereas the type I ELMs did not occur on ASDEX. ELMs are found to be MHD events of short duration (1 to 2 ms), which, on DIII-D, may be followed by a transient L mode phase. This compound event was not observed on ASDEX. A stability analysis of DIII-D discharges indicates that in the standard DIII-D configuration, type III ELMs occur well below the ideal ballooning limit, whereas Type I ELMs generally occur close to this limit. In DIII-D discharges where the plasma parameters are close to the ASDEX values, type I ELMs are not observed, even at the beta limit. This suggests that the ELM behaviour in DIII-D is not uniquely governed by ballooning stability

Recent DIII-D experiments have increased the normalized fusion performance of the high bootstrap current fraction tokamak regime toward reactor-relevant steady state operation. The experiments, conducted by a joint team of researchers from the DIII-D and EAST tokamaks, developed a fully noninductive scenario that could be extended on EAST to a demonstration of long pulse steady-state tokamak operation. Improved understanding of scenario stability has led to the achievement of very high values of βp and βN, despite strong internal transport barriers. Good confinement has been achieved with reduced toroidal rotation. These high βp plasmas challenge the energy transport understanding, especially in the electron energy channel. A new turbulent transport model, named TGLF-SAT1, has been developed which improves the transport prediction. Experiments extending results to long pulse on EAST, based on the physics basis developed at DIII-D, have been conducted. More investigations will be carried out on EAST with m...

Free-boundary 3D tokamak equilibria and resistive wall instabilities are calculated using a new resistive wall model in the two-fluid M3D-C1 code. In this model, the resistive wall and surrounding vacuum region are included within the computational domain. This implementation contrasts with the method typically used in fluid codes in which the resistive wall is treated as a boundary condition on the computational domain boundary and has the advantage of maintaining purely local coupling of mesh elements. This new capability is used to simulate perturbed, free-boundary non-axisymmetric equilibria; the linear evolution of resistive wall modes; and the linear and nonlinear evolution of axisymmetric vertical displacement events (VDEs). Calculated growth rates for a resistive wall mode with arbitrary wall thickness are shown to agree well with the analytic theory. Equilibrium and VDE calculations are performed in diverted tokamak geometry, at physically realistic values of dissipation, and with resistive walls of finite width. Simulations of a VDE disruption extend into the current-quench phase, in which the plasma becomes limited by the first wall, and strong currents are observed to flow in the wall, in the SOL, and from the plasma to the wall.

Accurate prediction of fusion performance in present and future tokamaks requires taking into account the strong interplay between core transport, pedestal structure, current profile, and plasma equilibrium. An integrated modeling workflow capable of calculating the steady-state self-consistent solution to this strongly coupled problem has been developed. The workflow leverages state-of-the-art components for collisional and turbulent core transport, equilibrium and pedestal stability. Testing against a DIII-D discharge shows that the workflow is capable of robustly predicting the kinetic profiles (electron and ion temperature and electron density) from the axis to the separatrix in a good agreement with the experiments. An example application is presented, showing self-consistent optimization for the fusion performance of the 15 MA D-T ITER baseline scenario as functions of the pedestal density and ion effective charge Zeff.

Axisymmetric equilibrium reconstruction using MHD equilibrium solutions to the Grad-Shafranov equation has long been an important tool for interpreting tokamak experiments. This paper describes recent results in applying non-axisymmetric (3D) equilibrium reconstruction codes to nominally axisymmetric plasmas (tokamaks and reversed field pinches), and fully non-axisymmetric plasmas (stellarators). Results from applyingthe V3FIT code to CTH and HSX stellarator plasmas, RFX-mod reversed field pinch plasmas and DIII-D tokamak plasmas and the STELLOPT code to LHD stellarator plasmas and DIII-D tokamak plasmas are presented.

Simultaneous achievement of high energy confinement, tau E, and high plasma beta, beta , leads to an economically attractive compact tokamak fusion reactor. High confinement enhancement, H= tau E/ tau E-ITER89P=4, and high normalized beta beta N beta /(I/aB)=6%-m-T/MA have been obtained in DIII-D experimental discharges. These improved confinement and/or improved stability limits are observed in several DIII-D high performance operational regimes: VH-mode, high li H-mode, second stable core, and high beta poloidal. We have identified several important features of the improved performance in these discharges: details of the plasma shape, toroidal rotation or E*B flow profile, q profile and current density profile, and pressure profile. From our improved physics understanding of these enhanced performance regimes, we have developed operational scenarios which maintain the essential features of the improved confinement and which increase the stability limits using localized current profile control. The stability limit is increased by modifying the interior safety factor profile to be nonmonotonic with high central q, while maintaining the edge current density consistent with the improved transport regimes and the high edge bootstrap current. We have calculated high beta equilibria with beta N=6.5, stable to ideal n=1 kinks and stable to ideal ballooning modes. The safety factor at the 95% flux surface is 6, the central q value is 3.9 and the minimum in q is 2.6.

A regime of improved H-mode energy confinement, VH-mode, is obtained in the DIII-D tokamak with adequate vessel conditioning. The improved confinement in VH-mode is consistent with the extension of the region of high E*B velocity shear turbulence suppression zone further in from the plasma boundary. The energy confinement enhancement in VH-mode can be limited by ELMs, localized momentum transfer events, or operation at high heating power or low q. Energy confinement enhancement improves with increasing triangularity of the plasma cross section and is independent of elongation. The termination of VH-mode is associated with an edge localized kink mode which is destabilized by both the large edge pressure gradient and edge current density.

Experiments to explore the long‐time evolution of noninductive, high βp plasmas in the DIII‐D tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159], have identified a new, quiescent, high performance regime. The experiments were carried out at low current (400–800 kA) with medium power neutral beam injection (3–10 MW). This regime is characterized by high q0 (≳2) and moderate li(∼1.3). It is reached by slow relaxation of the current profile, on the resistive time scale. As the profiles relax, q0 rises and li falls. When q0 goes above 2 (approximately), magnetohydrodynamic (MHD) activity disappears, and the stored energy rises. Most dramatic is the strong peaking of the central density, which increases by as much as a factor of 2. The improved central confinement appears similar to the PEP/reversed central shear/second stable core modes seen in tokamak experiments, but in this case without external intervention or transient ...

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 βN=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, τth/Ip, 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.

High confinement mode (H-mode) discharges with peaked toroidal current density profile (high internal inductance, ${\mathit{l}}_{\mathit{i}}$) and improved confinement are obtained in the DIII-D tokamak by dynamically varying the current profile using a rapid elongation ramp technique. The confinement improvement increases with ${\mathit{l}}_{\mathit{i}}$ and persists in the presence of edge-localized modes. The plasma toroidal rotation and the corresponding radial electric field component also increase with the peakedness of the current density profile.

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 maintainin...

It is evaluated how the upper limit to plasma elongation kappa , caused by vertical stability, varies with the ratio A=R/a of the tokamak. Equilibria were generated with EFITD and the vertical stability was assessed by GATO. For a 'generic' tokamak with a superconducting wall conformal to the plasma shape and a distance 0.5 a away from the plasma edge and a constant current profile (q0=1.0, li 1.0, q95 = 3.2) it is found that the maximum stable kappa decreased only slowly from 2.65 at A = 2.0 to 2.4 at A=6.0. To first order, a reasonable assumption in tradeoff studies of new machine designs is no dependence of κmax on A

An efficient full domain method for plasma equilibrium construction in iron core tokamaks is described. Illustrative calculations and comparison with results obtained from a finite domain method using JET data are given. The results show that the two methods are in agreement with respect to global plasma parameters such as stored energy, internal inductance, volume, and edge safety factor. However, when there is an uncertainty in the magnetic flux loop measurement, the full domain method yields a more accurate separatrix location

A regime of very high confinement (VH mode) has recently been observed in DIII‐D with global energy confinement times up to a factor of 3.5 above the ITER89‐P L‐mode scaling [Nucl. Fusion 30, 1999 (1990)] and 1.5 to 2 times greater than the DIII‐D/JET edge‐localized‐mode‐free H‐mode scaling relation [Nucl. Fusion 31, 73 (1991)]. These discharges were obtained after boronization in DIII‐D and are characterized by low radiated power and Zeff, increasing confinement time during the VH phase of the discharge and low Ohmic target density. The low radiated power and Zeff are a consequence of the boronization. During the VH phase these discharges exhibit an inward shift in the region of highest electric field shear and a large calculated edge bootstrap current. The outer region (ρ≳0.85) is calculated to be in the second stable regime to ideal ballooning modes.

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, βN=β/(I/aB) (I in MA, a in meters, and B0 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, li, whereas for broad pressure profiles, the β limit depends more strongly on li and can increase with li 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 βN values of 5.8−significantly above both the Troyon limit and the ballooning limit−have been found.

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.

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 Ip/aBT, where Ip is the total plasma current, a is the minor radius, and BT is the toroidal field. Based on stability calculations, an equilibrium was developed to achieve marginal stability simultaneously to axisymmetric, kink, and balloon...

An attached poloidal current, which flows in a circuit lying partly in the vacuum vessel wall and partly in the scrape-off layer of the plasma, is observed during vertical instabilities in the DIII-D tokamak. A direct measurement of the current, using Rogowski loops on several protective tiles at locations where the plasma contacts the wall, is in good agreement with the value determined from MHD equilibrium reconstructions using measured values of magnetic field and flux. This attached current, which can reach transient peaks of several hundred kiloamperes, interacts with the toroidal magnetic field to create a large vertical force on the vacuum vessel. The predicted motion of the vessel resulting from the measured currents agrees well with the observed displacement of the vacuum vessel.

Motional Stark effect produces large net linear polarization of Hα emission from neutral beams in tokamaks. Measurement of the polarization direction permits determination of the local magnetic field pitch angle. Design of a single point, spatially scannable, high‐sensitivity polarimeter installed on DIII‐D is described. Excellent signal‐to‐noise ratio with good temporal and spatial resolution was obtained in preliminary measurements of magnetic field pitch angle.

On DIII-D, periods of improved particle and energy confinement have been observed in low q, low BT divertor discharges with Ohmic heating alone. The Ohmic H-mode has characteristics similar to those of the H-mode produced by auxiliary heating. In the Ohmic H-mode the energy confinement time can have values near those predicted by Neo-ALCATOR scaling and a factor of two above those of non-H-mode Ohmic discharges at similar densities. These observations indicate that the H-mode is not limited to an improvement in confinement over that of the L-mode in auxiliary heating discharges.

The occurrence of giant edge localized modes (ELMs) in DIII-D has previously been correlated with the violation of the ballooning stability criterion at the plasma edge. These results are extended in the paper. It is demonstrated theoretically that flux surfaces near the separatrix of properly elongated and triangulated plasmas may be moved into the connection region between the first and second stability regions for ideal MHD ballooning modes, when q is high and the shear is low near the plasma surface. The edge flux surfaces are then predicted to have no limit to the sustainable pressure gradient. Experimentally, giant ELMs disappear in these highly shaped plasmas. However, the edge pressure gradient does not increase and 'grassy' ELM behaviour appears instead. These results lend further support to the hypothesis that giant ELMs in DIII-D are triggered by ideal ballooning mode instabilities, but they indicate that giant ELM and grassy ELM behaviour may arise from somewhat different mechanisms.