J.S. deGrassie

Inter-machine comparison of intrinsic toroidal rotation in tokamaks

Parametric scalings of the intrinsic (spontaneous, with no external momentum input) toroidal rotation observed on a large number of tokamaks have been combined with an eye towards revealing the underlying mechanism(s) and extrapolation to future devices. The intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases. Use of dimensionless parameters has led to a roughly unified scaling with M-A alpha beta(N), although a variety of Mach numbers works fairly well; scalings of the intrinsic rotation velocity with normalized gyro-radius or collisionality show no correlation. Whether this suggests the predominant role of MHD phenomena such as ballooning transport over turbulent processes in driving the rotation remains an open question. For an ITER discharge with beta(N) = 2.6, an intrinsic rotation Alfven Mach number of M-A similar or equal to 0.02 may be expected from the above deduced scaling, possibly high enough to stabilize resistive wall modes without external momentum input.

Effect of island overlap on edge localized mode suppression by resonant magnetic perturbations in DIII-D

Recent DIII-D [J. L. Luxon et al., Nucl. Fusion 43, 1813 (2003)] experiments show a correlation between the extent of overlap of magnetic islands induced in the edge plasma by perturbation coils and complete suppression of Type-I edge localized modes (ELMs) in plasmas with ITER-like electron pedestal collisionality νe*∼0.1, flux surface shape and low edge safety factor (q95≈3.6). With fixed amplitude n=3 resonant magnetic perturbation (RMP), ELM suppression is obtained only in a finite window in the edge safety factor (q95) consistent with maximizing the resonant component of the applied helical field. ELM suppression is obtained over an increasing range of q95 by either increasing the n=3 RMP strength, or by adding n=1 perturbations to “fill in” gaps between islands across the edge plasma. The suppression of Type-I ELMs correlates with a minimum width of the edge region having magnetic islands with Chirikov parameter >1.0, based on vacuum calculations of RMP mode components excluding the plasma response ...

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...

Electron heat transport in improved confinement discharges in DIII-D

In DIII-D tokamak plasmas with an internal transport barrier (ITB), the comparison of gyrokinetic linear stability (GKS) predictions with experiments in both low and strong negative magnetic shear plasmas provide improved understanding for ion and electron thermal transport within much of the plasma. As previously reported, the region for improved ion transport seems well characterized by the condition OE~B>Y-, where SERB is the ExB flow shear, calculated from measured quantities, and y,, is the maximum linear growth rate for ion temperature gradient (ITG) modes in the absence of flow shear. Within a limited region just inside the ITB, the electron temperature gradient (ETG) modes appear to control the electron temperature gradient and, consequently, the electron thermal transport. The increase in electron temperature gradient with more strongly negative magnetic shear is consistent with the increase in the ETG mode marginal gradient. Closer to the magnetic axis the Te profile flattens and the ETG modes are predicted to be stable. With additional core electron heating, FIR scattering measurements near the axis show the presence of high k fluctuations (12 cm-l), rotating in the electron diamagnetic drift direction. This turbulence could impact electron transport and possibly also ion transport. Thermal diffusivities for electrons, and to a lesser degree ions, increase. The ETG mode can exist at this wavenumber, but it is computed to be robustly stable near the axis.

Nondimensional transport scaling in DIII‐D: Bohm versus gyro‐Bohm resolved

The scaling of cross‐field heat transport with relative gyroradius ρ* was measured in low (L) and high (H) mode tokamak plasmas using the technique of dimensionally similar discharges. The relative gyroradius scalings of the electron and ion thermal diffusivities were determined separately using a two‐fluid transport analysis. For L‐mode plasmas, the electron diffusivity scaled as χe∝χBρ1.1±0.3* (gyro‐Bohm‐like) while the ion diffusivity scaled as χi∝χBρ−0.5±0.3* (worse than Bohm‐like). The results were independent of the method of auxiliary heating (radio frequency or neutral beam). Since the electron and ion fluids had different gyroradius scalings, the effective diffusivity and global confinement time scalings were found to vary from gyro‐Bohm‐like to Bohm‐like depending upon whether the electron or ion channel dominated the heat flux. This last property can explain the previously disparate results with dimensionally similar discharges on different fusion experiments that have been published. Experimen...

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.

Toroidal rotation in DIII-D in electron cyclotron heating and Ohmic H-mode discharges

Spatially and temporally resolved toroidal rotation measurements have been made in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] discharges with no externally applied torque. The velocity measurements are made using the charge exchange recombination (CER) technique viewing emission from the intrinsic carbon impurity in deuterium discharges. Three cases have been studied: L mode and H mode with Ohmic heating and H mode with electron cyclotron heating (ECH). The ECH H mode has carbon counter-rotation in the center of the plasma, and co-rotation outside, where co- and counter- are relative to the direction of the toroidal plasma current. The Ohmic H mode has carbon rotation everywhere in the co-direction. Neoclassical theory is applied to compute the deuterium toroidal velocity and it is found that the counter-rotation measured for carbon in the core of the ECH H mode is also thus predicted for the bulk deuterium species. Short blips of neutral beams (NB) must be used for the CER technique and these blip...

Dependence of the L- to H-mode Power Threshold on Toroidal Rotation and the Link to Edge Turbulence Dynamics

The injected power required to induce a transition from L-mode to H-mode plasmas is found to depend strongly on the injected neutral beam torque and consequent plasma toroidal rotation. Edge turbulence and flows, measured near the outboard midplane of the plasma (0.85 < r/a < 1.0) on DIII-D with the high-sensitivity 2D beam emission spectroscopy (BES) system, likewise vary with rotation and suggest a causative connection. The L–H power threshold in plasmas with the ion ∇B drift directed away from the X-point decreases from 4–6 MW with co-current beam injection, to 2–3 MW near zero net injected torque and to <2 MW with counter-injection in the discharges examined. Plasmas with the ion ∇B drift directed towards the X-point exhibit a qualitatively similar though less pronounced power threshold dependence on rotation. 2D edge turbulence measurements with BES show an increasing poloidal flow shear as the L–H transition is approached in all conditions. As toroidal rotation is varied from co-current to balanced in L-mode plasmas, the edge turbulence changes from a uni-modal character to a bi-modal structure, with the appearance of a low-frequency (f = 10–50 kHz) mode propagating in the electron diamagnetic direction, similar to what is observed as the ion ∇B drift is directed towards the X-point in co-rotating plasmas. At low rotation, the poloidal turbulence flow near the edge reverses prior to the L–H transition, generating a significant poloidal flow shear that exceeds the measured turbulence decorrelation rate. This increased poloidal turbulence velocity shear appears to facilitate the L–H transition. No such reversal is observed in high rotation plasmas. The high-frequency poloidal turbulence velocity spectrum exhibits a transition from a geodesic acoustic mode zonal flow to a higher-power, lower frequency zero-mean-frequency zonal flow as rotation varies from co-current to balanced during a torque scan at constant injected neutral beam power, perhaps also facilitating the L–H transition. This reduced power threshold at lower toroidal rotation may benefit inherently low-rotation plasmas such as ITER.

High‐power soliton generation at microwave frequencies

We point out that the creation of a soliton pulse train in a nonlinear‐dispersive system can be used for the generation of high‐power microwave bursts. A modulated transmission line with an appropriate nonlinear dielectric is proposed. The nonlinear wave evolution is analyzed and requirements for the dielectric material are found. Problems associated with the material are discussed. Low‐power experimental demonstrations of these concepts are presented.

Particle transport studies with applied resonant fields on TEXT

Externally applied resonant magnetic fields have been used on TEXT to modify the particle flux and the radial electric field near the plasma edge. Magnetic fields with primary mode numbers m/n = 7/3 and 7/2, and an average radial field amplitude |br|/B ? 0.1% have been employed. This perturbation produces mixed islands and stochastic regions at the plasma edge (r/a ? 0.8) without affecting the interior. Working particle transport is shown to be increased by typically 30% only in the presence of (computed) magnetic islands. The effect is diminished at high perturbing field strength when the islands become stochastic. A novel transport mechanism due to ? convection is proposed to explain this. Outward impurity transport is increased as well.