D.R. Baker

Sustained rotational stabilization of DIII-D plasmas above the no-wall beta limit

Sustained stabilization of the n=1 kink mode by plasma rotation at beta approaching twice the stability limit calculated without a wall has been achieved in DIII-D by a combination of error field reduction and sufficient rotation drive. Previous experiments have transiently exceeded the no-wall beta limit. However, demonstration of sustained rotational stabilization has remained elusive because the rotation has been found to decay whenever the plasma is wall stabilized. Recent theory [Boozer, Phys. Rev. Lett. 86, 5059 (2001)] predicts a resonant response to error fields in a plasma approaching marginal stability to a low-n kink mode. Enhancement of magnetic nonaxisymmetry in the plasma leads to strong damping of the toroidal rotation, precisely in the high-beta regime where it is needed for stabilization. This resonant response, or “error field amplification” is demonstrated in DIII-D experiments: applied n=1 radial fields cause enhanced plasma response and strong rotation damping at beta above the no wal...

Density profile consistency and its relation to the transport of trapped versus passing electrons in tokamaks

A formal expression for the canonical steady-state density profile in a tokamak can be obtained from the Fokker–Planck-type diffusion equation derived from the Vlasov equation in the limit of anomalous diffusion due to strong turbulence. Here we derive an explicit expression for this canonical profile for a tokamak with arbitrary cross section and aspect ratio. The resulting profile is independent of the spatial dependence of the diffusion coefficient, but does depend on the relative diffusion of trapped versus passing particles. Under conditions where only the trapped particles transport due to interactions with the turbulence the profiles are considerably flatter than if both the trapped and passing transport the same. The steepness of the calculated profile depends on the ratio of the diffusion coefficients for passing and trapped particles. The calculated profiles are compared with measured profiles from the tokamak known as DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Rese...

Non-dimensional scaling of turbulence characteristics and turbulent diffusivity

Plasma turbulence characteristics, including radial correlation lengths, decorrelation times, amplitude profile and flow velocity, have been measured during a ρ* scan on DIII-D while all other transport relevant dimensionless quantities (e.g., β, ν*, κ, q, Te/Ti) are held nearly constant. The turbulence is measured by examining the correlation properties of the local long wavelength (k⊥ρi ≤ 1) density fluctuations, measured with beam emission spectroscopy. The radial correlation length of the turbulence Lc,r is shown to scale with the local ion gyroradius, Lc,r ≈ 5ρi, while the decorrelation times scale with the local acoustic velocity as τc~a/cs. The turbulent diffusivity parameter, D~(Lc,r2/τc), scales in a roughly gyro-Bohm-like fashion, as predicted by the gyrokinetic equations governing turbulent transport. The experimental one fluid power balance heat diffusivity scaling and that from GLF23 modelling compare reasonably well.

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.

Progress in quantifying the edge physics of the H mode regime in DIII-D

Edge conditions in DIII-D are being quantified in order to provide insight into the physics of the H?mode regime. Several studies show that electron temperature is not the key parameter that controls the L-H transition. Gradients of edge temperature and pressure are much more promising candidates for elements of such parameters. They systematically increase during the L phases of discharges which make a transition to H?mode, and these increases are typically larger than the increases in the underlying quantities. The quality of H?mode confinement is strongly correlated with the height of the H?mode pedestal for the pressure. The gradient of the pressure is limited by MHD modes, in particular by ideal kink ballooning modes with finite mode number n. For a wide variety of discharges, the width of the barrier for electron pressure is well described by a relationship that is proportional to (?pedp)1/2. A new regime of confinement, called the quiescent H?mode, which provides steady state operation with no ELMs, low radiated power and normal H?mode confinement, has been discovered. A coherent edge MHD mode provides adequate particle transport to control the plasma density while permitting the pressure pedestal to remain almost identical to that observed in ELMing discharges.

Toroidal rotation in neutral beam heated discharges in DIII-D

It is known that the toroidal angular momentum and the ion thermal energy are correlated in tokamak discharges heated by neutral beam injection. Here, data from ten years of measurements on DIII-D are considered, for representative discharges from all types and all conditions. The ratio of simple replacement times for momentum and energy is found to order this correlation indicating that these times are approximately equal, across the minor radius. Representative discharges of several types are discussed in more detail, as well as transport analysis results for the momentum and thermal ion diffusivities.

Progress toward long-pulse high-performance Advanced Tokamak discharges on the DIII-D tokamak

Significant progress has been made in obtaining high-performance discharges for many energy confinement times in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159]. Normalized performance (measured by the product of βNH89 and indicative of the proximity to both conventional β limits and energy confinement quality, respectively) ∼10 has been sustained for >5 τE with qmin>1.5. These edge localized modes (ELMing) H-mode discharges have β∼5%, which is limited by the onset of resistive wall modes slightly above the ideal no-wall n=1 limit, with approximately 75% of the current driven noninductively. The remaining Ohmic current is localized near the half-radius. The DIII-D electron cyclotron heating system is being upgraded to replace this inductively driven current with localized electron cyclotron current drive (ECCD). Density control, which is required for effective ECCD, has been successfully demonstrated ...

Long pulse high performance discharges in the DIII-D tokamak

Significant progress in obtaining high performance discharges for many energy confinement times in the DIII-D tokamak has been realized since the previous IAEA meeting. In relation to previous discharges, normalized performance {approx}10 has been sustained for >5 {tau}{sub E} with q{sub min} >1.5. (The normalized performance is measured by the product {beta}{sub N} H{sub 89} indicating the proximity to the conventional {beta} limits and energy confinement quality, respectively.) These H-mode discharges have an ELMing edge and {beta} {approx}{le} 5%. The limit to increasing {beta} is a resistive wall mode, rather than the tearing modes previously observed. Confinement remains good despite the increase in q. The global parameters were chosen to optimize the potential for fully non-inductive current sustainment at high performance, which is a key program goal for the DIII-D facility in the next two years. Measurement of the current density and loop voltage profiles indicate {approx}75% of the current in the present discharges is sustained non-inductively. The remaining ohmic current is localized near the half radius. The electron cyclotron heating system is being upgraded to replace this remaining current with ECCD. Density and {beta} control, which are essential for operating advanced tokamak discharges, were demonstrated in ELMing H-mode discharges with {beta}{sub N}H{sub 89} {approx} 7 for up to 6.3 s or {approx} 34 {tau}{sub E}. These discharges appear to be in resistive equilibrium with q{sub min} {approx} 1.05, in agreement with the current profile relaxation time of 1.8 s.

Particle transport phenomena in the DIII-D tokamak

Many theoretical models show a direct connection between energy transport and particle transport. For a complete understanding of transport processes both energy and particle transport must be understood. A discussion is presented of how energy and particle transport should be related in terms of the relative importance of the diagonal and off-diagonal terms in the equation for the fluxes. A model for particle transport is discussed and it is shown that this model can describe measured density profiles in the DIII-D tokamak under a wide range of DIII-D parameters. This model is obtained from a Lagrangian formulation of the kinetic equation and utilizes the assumption that transport takes place while approximately conserving the first and second adiabatic invariants. The measured results utilize the improved diagnostic capability of DIII-D with an improved capability of measuring current density profiles and particle density profiles. This model is then extended to include energy transport. It is experimentally observed that the particle diffusivity and the thermal diffusivity do not differ greatly and have roughly the same radial dependence. This is discussed and compared with the model. A brief discussion of the effect of internal transport barriers is included.

Thermal diffusivities in DIII-D show evidence of critical gradients

The ion thermal diffusivities (χi) in DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] discharges exhibit a strong nonlinear dependence on the measured temperature gradients. In low confinement mode (L-mode) discharges with low toroidal rotation, the ion thermal diffusivity, χi, has an approximately Heaviside function dependence on the major radius divided by the radial scale length of the ion temperature, R/LTi. When R/LTi is less than a critical value, the χi’s are very small. When R/LTi is about equal to the critical value, χi increases rapidly. Although the gradient profiles for high confinement (H-mode) have a different shape, they still show a critical gradient type of behavior. This type of dependence is consistent with the predictions for transport, which is dominated by ion temperature gradient modes and is a strong indicator that these modes are the main contributors toward L-mode transport in DIII-D and a major contributor to transport in a certain region of DIII-D H-mode dis...