Progress toward fully noninductive, high beta conditions in DIII-D a …

The DIII-D Advanced Tokamak (cid:1) AT (cid:2) program in the DIII-D tokamak (cid:3) J. L. Luxon, Plasma Physics and Controlled Fusion Research, 1986 , Vol. I (cid:1) International Atomic Energy Agency, Vienna, 1987 (cid:2) , p. 159 (cid:4) 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, (cid:1) T =3.6%, normalized beta, (cid:1) N =3.5, and conﬁnement factor, H 89 =2.4 with the plasma current driven completely by bootstrap, neutral beam current drive, and electron cyclotron current drive (cid:1) ECCD (cid:2) . 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 (cid:1) MHD (cid:2) instabilities after about 1 s or half of a current relaxation time (cid:1) (cid:2) CR (cid:2) . Stationary conditions are maintained in similar discharges (cid:1)(cid:5) 90% noninductive (cid:2) , limited only by the 2 s duration (cid:1) 1 (cid:2) CR (cid:2) 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 (cid:1) ITER (cid:2) , Fusion Energy Energy 1987 (cid:2) , paper IAEA-CN-77/OV-1 (cid:4) . 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. © 2006 American Institute of Physics . (cid:3) DOI: 10.1063/1.2173627 (cid:4)

The DIII-D Advanced Tokamak ͑AT͒ program in the DIII-D tokamak ͓J. L. Luxon, Plasma Physics and Controlled Fusion Research, 1986, Vol. I ͑International Atomic Energy Agency, Vienna, 1987͒, p. 159͔ 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, ␤ T = 3.6%, normalized beta, ␤ N = 3.5, and confinement factor, H 89 = 2.4 with the plasma current driven completely by bootstrap, neutral beam current drive, and electron cyclotron current drive ͑ECCD͒. 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 ͑MHD͒ instabilities after about 1 s or half of a current relaxation time ͑ CR ͒. Stationary conditions are maintained in similar discharges ͑ϳ90% noninductive͒, limited only by the 2 s duration ͑1 CR ͒ 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 ͑ITER͒ ͓R. Aymar et al., Fusion Energy Conference on Controlled Fusion and Plasma Physics, Sorrento, Italy ͑International Atomic Energy Agency, Vienna, 1987͒, paper IAEA-CN-77/OV-1͔. 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. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2173627͔

I. INTRODUCTION
The goal of the Advanced Tokamak ͑AT͒ program on DIII-D 1-3 is to develop the scientific basis for steady-state, high-performance operation in future reactors. For steady-state operation, all of the plasma current must be supplied by noninductive ͑NI͒ means, namely, means other than the typical inductively driven current where the plasma current is the secondary of a transformer. A high fraction of bootstrap current, the self-generated current due to plasma density and temperature gradients 4 , f BS = I BS / I p ϰ ␤ N , is desirable to minimize the recirculating power where the normalized beta, plasma pressure to the magnetic pressure, I p is the plasma current, a is the plasma minor radius, B T is the toroidal magnetic field, and q is the safety factor. The remainder of the plasma current is provided by external, noninductive means. High-performance operation is needed to maintain sufficient fusion gain with reduced engineering parameters. High fusion gain ͑ϰ␤ T E ͒ requires high values of normalized ␤ N and high confinement, H 89 , at a modest safety factor, q 95 , where H 89 is the ratio of energy confinement time ͑ E ͒ relative to International Thermonuclear Experimental Reactor ͑ITER͒ L-mode scaling. 5 Combining these parameters, the operation requires high normalized fusion performance, G = ␤ N H 89 / q 95 2 . Toward these goals, AT experiments on DIII-D uniquely strive to integrate the key elements that are required for sustained AT operation: 6,7 high ␤ operation at modest q, high confinement, and efficient current drive. These experiments take advantage of recent improvements on DIII-D, including resistive wall mode ͑RWM͒ stabilization via plasma rotation and active feedback control with external, and more recently additional internal nonaxisymmetric coils, 8 which allows routine operation above the no-wall beta limit. 9 In these experiments, off-axis electron cyclotron current drive ͑ECCD͒ has been shown to be effective for modifying and/or controlling the current profile in high ␤ plasmas. 6,7 Density control of AT discharges 7 with edge localized modes ͑ELMs͒ using divertor cryopumps facilitates high current drive efficiency at reactor relevant collisionality. An advanced plasma control system allows integrated control of these elements. Neoclassical tearing modes ͑NTMs͒ are avoided through current profile control, although active feedback stabilization using localized ECCD [10][11][12][13] has also been demonstrated.
Recent progress in this area includes demonstration of fully noninductive conditions using off-axis ECCD. Equilibrium reconstructions indicate that the noninductive current profile is well aligned, with little inductively driven current remaining anywhere in the plasma. These conditions were obtained at high beta: ␤ T = 3.5% and H 89 = 2.4 at q 95 = 5.0, achieving G = 0.3. Therefore these plasmas have demonstrated "in-principle" steady-state conditions with the fusion performance required for ITER steady-state operation.
In these studies, modeling played a key role in interpreting experimental data and guiding the experiments. In particular, understanding the detailed current profile evolution is crucial to extending high-performance plasmas to steady state. Understanding the current profile evolution is very challenging because of the complex interactions amongst the bootstrap current, external current drive, transport and magnetohydrodynamic ͑MHD͒ stability. This requires integrated modeling tools, and these tools need to be validated against experiments. Using both empirical and theory-based models, AT experiments are both planned and interpreted in light of these simulations. By doing so, predictive modeling is validated against the experiment. This modeling projects longer sustainment of 100% noninductive current drive in DIII-D at higher fusion performance with hardware improvements now becoming available. The same modeling has also been applied to ITER steady-state scenario development with favorable results.
In this paper, we discuss progress toward fully noninductive, high beta conditions in DIII-D. In Sec. II, we discuss the characteristic of these discharges: noninductive current balance through measurements, analysis and simulations. Pressure profile evolution to MHD instability and achievement of stationarity consistent with the present hardware limitations are discussed. In Sec. III, optimization for fully noninductive, high beta conditions is discussed by considering choice of operational parameters, choice of plasma density and current drive ͑CD͒ alignment. In Sec. IV, we discuss transport modeling using a theory-based, gyro-Landau fluid ͑GLF-23͒ 14 model. We show validation of this model against plasma profiles of a single discharge as well as trends with parametric variations, in particular, a density scan. We then apply the model to predict DIII-D operation with upgraded capabilities and an ITER steady-state scenario.

II. CHARACTERISTICS OF 100% NONINDUCTIVE, HIGH ␤ DISCHARGES
Fully noninductive conditions at increased beta have been obtained by careful modeling and extension of the discharge obtained in 2002 7 with q min Ͼ 1.5, ␤ N = 3.1, f BS ϳ 60%.
Predictive modeling 15 using both scaled-experimental 16 and theory-based GLF23 14 transport models indicated that increasing the neutral beam power would result in plasmas reaching a noninductive current fraction f NI Ϸ 100% at higher ␤. Experiments in 2003 were carried out to test these predictions. 3 Using 2.5 MW of off-axis ͑normalized minor radius, = 0.4− 0.5͒ ECCD and up to 15 MW neutral beam injection ͑NBI͒ with q 95 = 5.0, nearly 100% of the plasma current was sustained for ϳ0.7 s at high beta ͑␤ Ϸ 3.6%, ␤ N Ϸ 3.5͒. The loop voltage was reduced to near zero and the net noninductive fraction of 100% was achieved. However, internal loop voltage ͑VLOOP͒ analysis 17 indicated that local inductive current was not zero near the plasma center. The negative inductive current there is a reaction to excessive NBCD near the axis which led to neutral beam overdrive near the axis and an increase in the central current density. This resulted in a decrease in the central safety factor q 0 , causing a 3 / 2 NTM, which terminated the high-performance phase. These discharges had somewhat deteriorated confinement ͑H 89 Ϸ 1.9 rather than 2.3-2.4͒ and reduced rotation velocity relative to the original discharges in 2002.
Several more recent improvements led to confinement improvement. Figure 1 shows the time histories of plasma parameters in such a discharge. Beta feedback ͓The plasma control system adjusts NB power in an attempt to keep the ␤ ͑stored energy͒ value in agreement with a prescribed ␤ waveform.͔ was initiated shortly after the L-H transition ͓spontaneous transition from L-mode to H-mode ͑high con-finement͔͒ at t = 0.4 s, resulting in significant improvement in the reproducibility of the q profile prior to the highperformance phase, providing more control over q min and q 0 − q min , where q min is the minimum safety factor and q 0 − q min represents the magnetic shear in the core. Also, feedback control of the nonaxisymmetric magnetic field was improved. The higher rotation associated with the reduced error field led to improved confinement and lower NBI power demand in the high-performance phase, and thus to less current drive near the axis. Good confinement, H 89 = 2.4, was restored, and fusion performance G = 0.3 was achieved in this discharge. Both the axial and surface voltage are nearly zero ͑Ͻ10 mV͒, and both loop voltage analysis and evaluation by a transport code show that 100% noninductive current with good CD alignment is achieved.
In order to show that 100% noninductive conditions are obtained globally and locally across the plasmas, we will discuss three methods used to obtain the inductive current density profile: internal loop voltage analysis, transport analysis, and poloidal field evolution modeling. The VLOOP analysis discussed earlier is derived primarily from experimental data and is shown in Fig. 2͑a͒.The inductive current is the product of the neoclassical conductivity and parallel electric field. 17 The latter is calculated from the time derivative of the poloidal flux based on a series of equilibrium reconstructions using the equilibrium fitting code, EFIT, 18 and is rather insensitive to the parameterization used in EFIT. The total current density profile is sensitive to this parameterization since it is calculated from the spatial derivatives of the poloidal flux. The next method of analyses is carried out by a transport code ͓TRANSP 19 ͔ calculation based on a series of "kinetic" equilibrium reconstructions that are consistent with measured profiles and the equilibrium reconstruction discussed above. The components of the noninductive current are calculated from various current source models as shown in Fig. 2͑b͒. The bootstrap current is estimated to be 59% with the Sauter model 20 and NCLASS model. 21 These models are somewhat sensitive to the input profiles near the axis and edge. The neutral beam current drive fraction is calculated to be 31% from the TRANSP Monte-Carlo beam slowing down calculation, and ECCD calculated by TORAY-GA code 22 is 8%. The difficult part of this analysis is to obtain a reliable estimate of inductive current, the remaining part of the total current. Despite a quest for high-quality kinetic equilibrium reconstruction, the total current derived from the kinetic equilibrium reconstructions lacks spatial resolution, and thus the inductive current derived from it is similarly limited in accuracy. The third FIG. 1. Time histories of parameters for a discharge that is locally and globally fully noninductive: ͑a͒ plasma current, NBI and ECCD power; ͑b͒ normalized beta and four times internal inductance ͑approximate no-wall beta limit͒; ͑c͒ central and minimum safety factor; ͑d͒ line-average electron density and confinement enhancement factor; ͑e͒ ion and electron temperature near the axis; ͑f͒ normalized fusion performance, G = ␤ N H 89 / q 95 2 ; ͑g͒ surface and axial loop voltage; and ͑h͒ noninductive current fractions from the internal loop voltage and transport analysis.
FIG. 2. Three methods of analyses for the current balance: ͑a͒ inductive and total current profile from the internal loop voltage analysis based on a series of equilibrium reconstructions; ͑b͒ total current, bootstrap, neutral beam, and EC current drive profile based on transport analysis; and ͑c͒ profiles of total, bootstrap, NBI, and EC current drive based on the current evolution simulation using TRANSP code; and ͑d͒ toroidal current density profiles as functions of the major radius derived from the MSE measurement, the transport analysis and the current evolution simulation. method, simulation of the poloidal field evolution using a transport code based on the measured time-dependent kinetic profiles, allows us to calculate the total current ͑and thus the inductive current͒ with better spatial resolution. The resultant inductive current is shown in Fig. 2͑c͒. The inductive current inferred from the simulation has more structure than that from the VLOOP analysis ͓Fig. 2͑c͔͒. We consider two possibilities why this might occur: NBCD and bootstrap current models.
Recent fast ion diagnostic data verify that beam ions are redistributed in the core during these discharges. The diagnostic uses spatially resolved charge exchange recombination ͑CER͒ spectroscopy of Doppler-shifted D ␣ light from beam ions in the energy band between 40 and 80 keV ͑beam injection energy͒. 23 Figure 3 shows time histories of measured beam ion densities along two different vertical chords 24 together with neutron rate and MHD activity for a more recent, but similar f NI Ϸ 100% discharge. Also shown are classical slowing down calculations of beam ion densities and neutron rate. Although the beam ion density at the outer radius is in rough agreement throughout the discharge, the beam ion density at the inner radius does not increase as the neutral beam power increases, suggesting anomalous spatial redistribution of beam ions from the core. When we apply an anomalous diffusion ͓with an ad hoc beam ion diffusivity shown in Fig. 4͑a͔͒ in the TRANSP Monte-Carlo slowing down calculations, the calculated beam density profile is significantly reduced in the core compared to the case with classical slowing down. This results in a significant flattening of the NBCD profile in the core region. Applying the same model to the discharge that we are discussing, a flatter NBCD would reduce the structure in the inductive current profile as shown in Fig. 4. In addition, the calculated neutron rates and stored energy using the anomalous diffusion agree better with the measurements.
The other possible explanation is inaccuracy in the bootstrap current calculation which is rather sensitive to input profiles ͑particularly electron density͒ near the center. Despite our best efforts to obtain electron density profiles consistent among measurements from Thomson scattering, reflectometer, and electron cyclotron emission ͑ECE͒ radiometer cutoff conditions, ±10% uncertainty in the bootstrap current in the inner half of the plasma remains. Together with uncertainties in the bootstrap current models, the accuracy of the inductive current calculations are estimated to be limited to ±10% in local and ±5% in the integrated values. Nevertheless all of these methods of analysis indicate that, to within the uncertainty, fully noninductive conditions have been obtained.
In this discharge, sustainment of the 100% noninductive condition was limited by the plasma pressure evolution rather than the current evolution. As shown in Fig. 5, pressure peaking ͑primarily due to density peaking͒ increased as ␤ N increased. At ␤ N = 3.3, the calculated wall position for n = 1 marginal stability reached the DIII-D conformal wall po-  4. Studies of impacts of the measurements on NBCD modeling; ͑a͒ the anomalous fast ion diffusivity assumed. and beam ion densities calculated for classical and anomalous beam slowing down; ͑b͒ calculated NB CD profiles for classical and anomalous slowing down calculation. Inductive current profile ͑bold dash͒ derived from neutral beam current drive model taken into account of anomalous beam ion diffusion assumed in ͑b͒ compared with inductive current profile ͑fine dash͒ with more conventional anomalous diffusion assumption and that derived from the equilibrium measurement ͑solid with error bars͒. sition ͑1.45a͒. 9 At that point, we observed an n = 1 fast growing mode that triggered n = 1 neoclassical tearing modes. Even at ␤ N near the ideal wall limit, the high-performance phase almost always ends as a result of a tearing mode rather than a kink mode.
In a separate discharge, a nearly full noninductive, stationary discharge was obtained, which was limited only by the ECCD source. Time histories of pitch angles of individual motional Stark effect ͑MSE͒ diagnostic channels 25 are very stationary, indicating that the total current profile stopped evolving. 26 In this discharge f NI Ͼ 90% lasted for 1.8 s, about one current relaxation time ͑ CR ͒, at ␤ T = 3.7%, ␤ N = 3.5, and q 95 = 5.1. This current relaxation time 27 is defined as the time constant of the lowest order spatial eigenmode of the current evolution equation with the constraint of constant current, CR = 0.17R / R, where R is the plasma major radius in meters and R is the plasma resistance in ⍀. The normalized fusion performance ͑G͒ for this discharge is 0.3 with bootstrap current fraction of 60%. Therefore the performance level required for the ITER steady-state scenario was achieved. However, we have to point out that there are substantial differences in plasma conditions between the present experiments and ITER ͑for example, T i / T e , rotation, etc.͒. This motivates us to continue to work on using im-proved hardware that will allow us to access to the more ITER-relevant regime.

III. OPTIMIZATION FOR FULL NONINDUCTIVE, HIGH ␤ OPERATION
Optimization of fully noninductive, high beta operation can be explored by studying the detailed characteristics of a few discharges and also by studying trends with various plasma parameters in a database containing a large number of such discharges. We have assembled two databases from these experiments: a profile database and a global parameter database. The profile database stores the detailed parameters for about 15 discharges whose characteristics have been studied in detail using time-dependent TRANSP analysis. Figure 6 shows results of the profile database indicating noninductive conditions with ϳ60% bootstrap fraction have been sustained up to one current relaxation time ͑ CR ͒. A typical value of CR is 2 s in these discharges.
The global parameter database contains about 160 shots whose primary selection criteria are: 28,29 the duration of ␤ N above 85% of the maximum ␤ N is longer than five energy confinement times or 0.7 s, whichever is longer; ␤ N Ͼ 2; and H 89 Ͼ 2. All parameters are time averaged over the period of ␤ N Ͼ 85% of the maximum ␤ N . One of the most useful parameters in this database is the average noninductive current fraction, ͗f NI ͘, which is equal to 1 − ͗V surf ͘ / ͗R͘ / I p , where ͗V surf ͘ is the average surface voltage, and ͗R͘ is the average plasma resistance. Note that different averaging processes result in slightly different estimates of noninductive fraction in the two different databases. Comparing the noninductive fractions indicates that the global noninduction fraction underestimates by ϳ6% relative to that in the profile database. Figure 7 shows a large number of discharges have attained the conditions required for the ITER steady-state conditions ͑G = 0.3 and ͗f NI ͘ =1͒. Figure 8 shows the average noninductive fraction as a function of ␤ N for two different values of q 95 ͑5.0 and 5.5͒ in this database. These data show that the noninductive fraction increases strongly with ␤ N for a given q 95 . Although ͗f NI ͘ also increases strongly with increasing q 95 , operating with a higher q 95 substantially compromises the fusion performance, G = ␤ N H 89 / q 95 2 . Studies 2,7 have shown q 95 must stay close to 5 to maintain adequate G. 2 The choice of the plasma density is important for optimization of the noninductive operation. Figure 9 shows the dependencies of the noninductive current components as a function of line average density based on a set of density scan discharges in the profile database. The overlaid curves are results of simulations using the GLF23 model ͑discussed later͒ for a fixed density shape of one of the shots ͑111221͒. The curves represent well the trend of the fractions of noninductive current components, validating CD source models. The bootstrap current is observed to increase with density, but more slowly than NBCD and ECCD decrease. The net result is that the noninductive current fraction decreases with density, and thus noninductive current is maximized at lower density. A measure of the current drive alignment can be estimated using a CD alignment figure of merit: 7 tot = 1 − ͵ ͑n e /T e ͉͒J ind ͉dA ͵ ͑n e /T e ͉͒J tot ͉dA .
This figure of merit measures the relative amount of additional current drive power that will be required to achieve full CD alignment. Both f NI and the CD figure of merit are reduced at high density, which indicates the CD alignment is poor in a region where it is difficult to drive current, i.e., at larger radii. Low density discharges are much better in this regard.

A. Validation
Close coupling between modeling and experiment is key to understanding complex interactions between bootstrap current, external current drive, transport and MHD stability and their integration into self-consistent high-performance scenarios in the experiments. Both empirical and theorybased transport models are used to plan and interpret these experiments. These comparisons validate the models to allow their use in planning future DIII-D experiments. The gyro-Landau-fluid ͑GLF23͒ model 14 implemented in the ONETWO transport code 30 is the primary tool in this experiment. Validation of this model was carried out against one of the fully noninductive, high ␤ discharges. The experimental data in Fig. 10 were chosen to be at the same phase ͑60%-80%͒ in the ELM cycles in a stationary part of the discharge using the tools developed for pedestal studies. 31 The GLF23 model 14,32 uses drift-wave eigenmodes to compute the quasilinear energy, toroidal momentum fluxes due to ion/electron temperature gradient ͑ITG/ETG͒ and trapped electron modes ͑TEM͒. The model includes E ϫ B shear and alpha stabilization using the predicted profiles. The electron and ion turbulent diffusivities from GLF23 are added to the neoclassical diffusivities, while the toroidal momentum transport is added to an ad hoc enhancement, taken in this case to be twice the neoclas- sical ion thermal diffusivity. 32 In this simulation, the electron temperature ͑T e ͒, ion temperature ͑T i ͒, poloidal magnetic field ͑current density͒, toroidal momentum, and equilibrium evolution are solved with self-consistent source and sink calculations by time stepping from initial profiles for about 0.5 CR . The GLF23 model reproduces experimental profiles reasonably well, as seen in Fig. 10. An exception is an overestimate of the toroidal rotation in the core. An empirical multiplier larger than two on the ion thermal neoclassical diffusivity in the toroidal momentum equation would improve the agreement with the experimental toroidal rotation data. Simulation without E ϫ B shear stabilization leads to a substantially lower ion temperature ͓Fig. 10͑a͔͒, indicating the importance of the rotation, while the alpha ͑Shafranov shift͒ stabilization plays a minor role.

B. DIII-D simulation
Predictive simulations with the GLF23 model indicate that 100% noninductive operation at higher ␤ will be possible using hardware improvements being made on DIII-D. 33 As presented in Fig. 9, the GLF23 model reproduced well the trends of the noninductive current components in the density scan data based on density profiles scaled from that of a single-null discharge, serving a validation test of the model against the density scan data. Figure 11extracts the results of the modeling. Similar dependencies were found for existing higher-density double-null divertor ͑DND͒ discharges without pumping. Replacing the flat density profile with a peaked density profile, expected from DND operation with pumping, would increase the noninductive fraction. The DN pumped divertor configuration will allow operation with density control in an optimized shape for improved stability at high ␤. 9 A GLF23 simulation indicates that 100% noninductive, high ␤ conditions can be obtained with 4.5 MW of ECCD deposited around Ϸ 0.6 and 3.5 MW of fast wave ͑FW͒ heating and current drive. 26 Higher FW power, allow-ing lower NB heating and current drive power, should facilitate operation with T e Ϸ T i , a more relevant regime for nextstep burning plasmas. Finally, two ͑out of seven͒ NBI sources have been reaimed in the counter direction. This will give added flexibility by allowing us to vary the co/counter mix of NBI sources, thereby modifying both NB H/CD and rotation. Higher NB heating power will be available without beam overdrive in the core with the appropriate co/counter beam mix, allowing exploration of the stability boundaries of full noninductive operation at high beta.

C. ITER simulation
The modeling tools that were successfully employed to devise experiments in DIII-D, when applied to ITER, indicate fully noninductive operation is plausible for an ITER steady-state scenario with Q Ϸ 5 with Day-1 hardware capabilities. 34 Previously we showed an "existence proof" of full noninductive operation at Q Ϸ 5 at high density ͑N GW = 1.25͒ using the GLF23 model 26,34 with the ITER Day-1 hardware capabilities. 34 Here we evaluate how the noninductive operation would change when the plasma density is varied as in DIII-D. Each simulation was evolved for 100 s, which is about 1 CR for ITER, to follow the evolutions of T e , T i , toroidal rotation, current density and equilibrium with a fixed density profile using the theory-based ͑GLF23͒ model with self-consistent sources and sinks. Fractions of the noninductive current components and fusion gain, Q, are plotted as a function of Greenwald number ͑Fig. 12͒. The trend of the noninductive current fractions are reminiscent of those for the DIII-D density scan. Increased noninductive fraction above 100% is attained at N GW Ϸ 1 with Q ͑nearly equal͒ 5. Table I tabulates a self-consistent set of the parameters corresponding to the N GW = 1 case, attaining f NI = 100%. This suggests that a steady-state solution exists with Q =5.
This work is still in progress. Some important advanced tokamak physics issues that have to be addressed include consistency of the pedestal temperature, the density profiles, FIG. 10. Comparison of profiles of ͑a͒ ion temperature, ͑b͒ electron temperature, and ͑c͒ toroidal angular velocity from experimental measurements and predictions of the GLF23 model based on ͑d͒ the density profiles and the respective profiles as initial conditions and boundary conditions imposed at = 0.9. The experimental data were chosen to be the same phase ͑60%-80%͒ in the ELM cycles in a stationary part of a fully inductive discharge.
FIG. 11. Density dependence of the noninductive current fractions predicted for double-null diverter ͑DND͒ discharge by the GLF23 model based on existing profiles of unpumped DND discharge. The noninductive fraction for DND discharge with peaked density profile with pump is predicted to be higher. The overlaid curves for the noninductive current fractions and their components are those for single null discharges shown in Fig. 9.
MHD stability, and the divertor heat load and stability. We would like to point out some of the caveats regarding the present modeling: 1. The edge temperature used in the above modeling is based on the edge temperature required for generating the Q = 5 ITER steady-state scenario using the specific theory-based model. 36 As such it is not based on any edge physics model. Therefore the validity of the edge temperature needs to be investigated. The temperature fixed at = 0.9 seems high ͑T Ͼ 7.2 keV͒, but the value of ␤ where the boundary conditions were imposed in the simulation is only slightly above the DIII-D case ͑1.3% vs 1.0%͒. 2. The density profile used in the present modeling originates from the one used in an earlier ITER simulation study as a density profile similar to that of a DIII-D AT discharge. 37 The large density "pedestal" width assumed in the simulation, and observed in the experiment, gives a larger stability margin for peeling-ballooning modes. 37 It is our plan to include the density equation in the GLF23 model. 3. The target ␤ N Ϸ 2.8 calculated is above the beta limit against the n = 1 mode without conducting wall ͑␤ N no−wall Ϸ 2.4− 2.5͒. 37,38 Although the predicted central plasma rotation frequency is about 2.5% of the Alfvén frequency, uncertainties in the simulation ͑e.g., empirical addition of the neoclassical ion thermal diffusivity in the momentum diffusivity͒ make it unclear whether it is sufficient to provide RWM stabilization without an active feedback system. The forthcoming DIII-D experiments with the external and internal control coils and capability to produce nonrotating high beta plasmas using co-and counter NBI will provide opportunities to study effectiveness of feedback stabilization under more ITER-relevant conditions.

V. CONCLUSIONS
One hundred percent noninductively driven plasmas were obtained with good CD alignment at ␤ T ഛ 3.6%, ␤ N ഛ 3.5 and H 89 = 2.4. The duration was limited to ϳ0.5 CR by pressure profile evolution to unstable MHD. The current balance calculation improved with beam ion redistribution that was supported by the recent fast ion diagnostic measurements. Nearly ͑ϳ90% ͒ noninductive, stationary discharges were sustained for 1 CR and were only limited by present hardware limits. These experiments have achieved normalized fusion performance G = 0.3 and f BS = 60%, which is consistent with requirements for the ITER Q = 5 steady-state scenario. With good coupling between experiment and modeling, progress has been made in identifying the need for low density and other optimizations for noninductive operation and current drive alignment. Future plans of DIII-D include exploring stability boundaries using more EC and FW power with longer duration, double-null divertor with pumping and co + counter NBI. Modeling tools that were successfully employed to devise experiments in DIII-D, when applied to ITER, indicate full noninductive operation is conceivable for steady-state operation with Q Ϸ 5. The scientific basis being developed on DIII-D is leading to increased confidence in establishing steady-state scenarios for ITER and beyond. We would like to thank the DIII-D Team. We also wish to acknowledge useful discussions with Dr. C. Gormezano, Dr. W. A. Houlberg, and Dr. J. M. Park. Some of the modeling was carried out using Grid-enabled TRANSP on the National Fusion Grid, and we would like to thank the members of the National Fusion Collaboratory Project ͑www.fusiongrid.org͒ at PPPL and GA sponsored by the U.S. DOE SciDAC Program. FIG. 12. Density dependences of the noninductive current fraction and its components, bootstrap current, neutral beam and rf ͑ion cyclotron and electron cyclotron current drive combined͒, and fusion gain predicted by the GLF23 model using the ITER Day-1 hardware capabilities. The electron density is expressed by the Greenwald density number.