W.M. Solomon

Dust measurements in tokamaks (invited)

Dust production and accumulation present potential safety and operational issues for the ITER. Dust diagnostics can be divided into two groups: diagnostics of dust on surfaces and diagnostics of dust in plasma. Diagnostics from both groups are employed in contemporary tokamaks; new diagnostics suitable for ITER are also being developed and tested. Dust accumulation in ITER is likely to occur in hidden areas, e.g., between tiles and under divertor baffles. A novel electrostatic dust detector for monitoring dust in these regions has been developed and tested at PPPL. In the DIII-D tokamak dust diagnostics include Mie scattering from Nd:YAG lasers, visible imaging, and spectroscopy. Laser scattering is able to resolve particles between 0.16 and 1.6 microm in diameter; using these data the total dust content in the edge plasmas and trends in the dust production rates within this size range have been established. Individual dust particles are observed by visible imaging using fast framing cameras, detecting dust particles of a few microns in diameter and larger. Dust velocities and trajectories can be determined in two-dimension with a single camera or three-dimension using multiple cameras, but determination of particle size is challenging. In order to calibrate diagnostics and benchmark dust dynamics modeling, precharacterized carbon dust has been injected into the lower divertor of DIII-D. Injected dust is seen by cameras, and spectroscopic diagnostics observe an increase in carbon line (CI, CII, C(2) dimer) and thermal continuum emissions from the injected dust. The latter observation can be used in the design of novel dust survey diagnostics.

Experimental test of the neoclassical theory of impurity poloidal rotation in tokamaks

Despite the importance of rotation in fusion plasmas, our present understanding of momentum transport is inadequate. The lack of understanding is in part related to the difficulty of performing accurate rotation measurements, especially for poloidal rotation. Recently, measurements of poloidal rotation for impurity ions (Z>1) have been obtained in the core of DIII-D [J. L. Luxon, Nucl. Fusion 42, 6114 (2002)] plasmas using charge exchange recombination spectroscopy. The inferred poloidal rotation is based on careful consideration of the effective energy-dependent cross section and of the gyromotion of the ions. The rotation measurements are found to be consistent with the radial electric field determined independently from multiple impurity species as well as from motional Stark effect spectroscopic measurements. The poloidal rotation measurements have been compared with predictions based on the neoclassical theory of poloidal rotation from the code NCLASS [W. A. Houlberg et al., Phys. Plasmas 4, 3230 (19...

ELM suppression in low edge collisionality H-mode discharges using n = 3 magnetic perturbations

Using resonant magnetic perturbations with toroidal mode number n = 3, we have produced H-mode discharges without edge localized modes (ELMs) which run with constant density and radiated power for periods up to about 2550 ms (17 energy confinement times). These ELM suppression results are achieved at pedestal collisionalities close to those desired for next step burning plasma experiments such as ITER and provide a means of eliminating the rapid erosion of divertor components in such machines which could be caused by giant ELMs. The ELM suppression is due to an enhancement in the edge particle transport which reduces the edge pressure gradient and pedestal current density below the threshold for peeling-ballooning modes. These n = 3 magnetic perturbations provide a means of active control of edge plasma transport.

Intrinsic rotation in DIII-D

In the absence of any auxiliary torque input, the DIII-D plasma consists of nonzero toroidal angular momentum, in other words, it rotates. This effect is commonly observed in tokamaks, being referred to as intrinsic rotation. Measurements of intrinsic rotation profiles have been made in DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] H-mode discharges, with both Ohmic heating (OH) and electron cyclotron heating (ECH) in which there is no auxiliary torque. Recently, the H-mode data set has been extended with the newly configured DIII-D simultaneous co- and counter-directed neutral beam injection (NBI) capability resulting in control of the local torque deposition, where co and counter refer to the direction relative to the toroidal plasma current. Understanding intrinsic rotation is important for projection toward burning plasma performance where any NBI torque will be relatively small. The toroidal velocity is recognizably important regarding issues of stability and confinement. In DIII-D ECH H-modes the r...

Cross-machine comparison of resonant field amplification and resistive wall mode stabilization by plasma rotation

Dedicated experiments in the DIII-D tokamak [J. L. Luxon, Nucl. Fusion, 42, 614 (2002)], the Joint European Torus (JET) [P. H. Rebut, R. J. Bickerton, and B. E. Keen, Nucl. Fusion 25, 1011 (1985)], and the National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)] reveal the commonalities of resistive wall mode (RWM) stabilization by sufficiently fast toroidal plasma rotation in devices of different size and aspect ratio. In each device the weakly damped n=1 RWM manifests itself by resonant field amplification (RFA) of externally applied n=1 magnetic fields, which increases with the plasma pressure. Probing DIII-D and JET plasmas with similar ideal magnetohydrodynamic (MHD) stability properties with externally applied magnetic n=1 fields, shows that the resulting RFA is independent of the machine size. In each device the drag resulting from RFA slows the toroidal plasma rotation and can lead to the onset of an unstable RWM. The critical plasma rotati...

An overview of intrinsic torque and momentum transport bifurcations in toroidal plasmas

An overview of the physics of intrinsic torque is presented, with special emphasis on the phenomenology of intrinsic toroidal rotation in tokamaks, its theoretical understanding, and the variety of momentum transport bifurcation dynamics. Ohmic reversals and electron cyclotron heating-driven counter torque are discussed in some detail. Symmetry breaking by lower single null versus upper single null asymmetry is related to the origin of intrinsic torque at the separatrix. (Some figures may appear in colour only in the online journal)

Advances towards QH-mode viability for ELM-stable operation in ITER

The application of static, non-axisymmetric, nonresonant magnetic fields (NRMFs) to high beta DIII-D plasmas has allowed sustained operation with a quiescent H-mode (QH-mode) edge and both toroidal rotation and neutral beam injected torque near zero. Previous studies have shown that QH-mode operation can be accessed only if sufficient radial shear in the plasma flow is produced near the plasma edge. In past experiments, this flow shear was produced using neutral beam injection (NBI) to provide toroidal torque. In recent experiments, this torque was nearly completely replaced by the torque from applied NRMFs. The application of the NRMFs does not degrade the global energy confinement of the plasma. Conversely, the experiments show that the energy confinement quality increases with lower plasma rotation. Furthermore, the NRMF torque increases plasma resilience to locked modes at low rotation. These results open a path towards QH-mode utilization as an edge-localized mode (ELM)-stable H-mode in the self-heated burning plasma scenario, where toroidal momentum input from NBI may be small or absent.

Intrinsic toroidal velocity near the edge of DIII-D H-mode plasmas

The intrinsic toroidal velocity, V, in DIII-D (Luxon 2002 Nucl. Fusion 42 614) H-modes is measured to be nonzero in the pedestal region, in the direction of the plasma current, co-Ip. Intrinsic, or spontaneous, velocity is that which arises with no known external momentum injection. This intrinsic velocity is measured to scale roughly linearly with the local ion temperature, Ti, V ~ Ti, in the pedestal and in the edge region just inside the pedestal. With either co-Ip, or counter-Ip neutral beam injected torque, the pedestal velocity is accelerated in the direction of the torque; it is not a fixed boundary condition. A simple model of thermal ion orbit loss predicts the sign of V, a relevant magnitude for V, and the approximate scaling V ~ Ti. This model for a boundary condition on the intrinsic toroidal velocity gives a result of approximate diamagnetic form, V ~ epTi/LBθ, where L is a scale length, Bθ the poloidal magnetic field and ep a small numerical parameter. This model is a local calculation of velocity, an approximation to the inherently nonlocal region of the pedestal where the thermal ion banana width is comparable to the pedestal width. In this model we also assume that the loss cone in velocity space is empty; no collisions are considered. A recent particle simulation of the pedestal region of a DIII-D NBI-driven H-mode discharge that includes collisions indicates that thermal ion orbit loss results in a co-Ip velocity just inside the last closed flux surface (Chang and Ku 2008 Phys. Plasmas 15 062510-1). Thus, we do not expect that nonlocality nor finite collisionality wash out the effect. Inside the pedestal our model shows that thermal ion orbit loss is negligible. In this region of the edge we also measure a similar scaling for the intrinsic velocity several pedestal widths inside the pedestal location, V ~ Ti. One mechanism that could maintain the Ti scaling inwards from the pedestal is the model of an inward momentum pinch velocity proportional to the gradient of Ti.

Stability and control of resistive wall modes in high beta, low rotation DIII-D plasmas

Recent high-β DIII-D (Luxon J.L. 2002 Nucl. Fusion 42 64) experiments with the new capability of balanced neutral beam injection show that the resistive wall mode (RWM) remains stable when the plasma rotation is lowered to a fraction of a per cent of the Alfven frequency by reducing the injection of angular momentum in discharges with minimized magnetic field errors. Previous DIII-D experiments yielded a high plasma rotation threshold (of order a few per cent of the Alfven frequency) for RWM stabilization when resonant magnetic braking was applied to lower the plasma rotation. We propose that the previously observed rotation threshold can be explained as the entrance into a forbidden band of rotation that results from torque balance including the resonant field amplification by the stable RWM. Resonant braking can also occur naturally in a plasma subject to magnetic instabilities with a zero frequency component, such as edge localized modes. In DIII-D, robust RWM stabilization can be achieved using simultaneous feedback control of the two sets of non-axisymmetric coils. Slow feedback control of the external coils is used for dynamic error field correction; fast feedback control of the internal non-axisymmetric coils provides RWM stabilization during transient periods of low rotation. This method of active control of the n = 1 RWM has opened access to new regimes of high performance in DIII-D. Very high plasma pressure combined with elevated qmin for high bootstrap current fraction, and internal transport barriers for high energy confinement, are sustained for almost 2 s, or 10 energy confinement times, suggesting a possible path to high fusion performance, steady-state tokamak scenarios.

Edge pedestal control in quiescent H-mode discharges in DIII-D using co-plus counter-neutral beam injection

We have made two significant discoveries in our recent studies of quiescent H-mode (QH-mode) plasmas in DIII-D. First, we have found that we can control the edge pedestal density and pressure by altering the edge particle transport through changes in the edge toroidal rotation. This allows us to adjust the edge operating point to be close to, but below the ELM stability boundary, maintaining the ELM-free state while allowing up to a factor of two increase in edge pressure. The ELM boundary is significantly higher in more strongly shaped plasmas, which broadens the operating space available for QH-mode and leads to improved core performance. Second, for the first time on any tokamak, we have created QH-mode plasmas with strong edge co-rotation; previous QH-modes in all tokamaks had edge counter-rotation. This result demonstrates that counter-NBI and edge-counter rotation are not essential conditions for QH-mode. Both these investigations benefited from the edge stability predictions based on peeling–ballooning mode theory. The broadening of the ELM-stable region with plasma shaping is predicted by that theory. The theory has also been extended to provide a model for the edge harmonic oscillation that enhances edge transport in the QH-mode. Many of the features of that theory agree with the experimental results reported either previously or in this paper. One notable example is the prediction that co-rotating QH-mode is possible provided sufficient shear in the edge rotation can be created.