M. S. Chu

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...

STABILITY AND DYNAMICS OF THE EDGE PEDESTAL IN THE LOW COLLISIONALITY REGIME: PHYSICS MECHANISMS FOR STEADY-STATE ELM-FREE OPERATION

Understanding the physics of the edge pedestal and edge localized modes (ELMs) is of great importance for ITER and the optimization of the tokamak concept. The peeling–ballooning model has quantitatively explained many observations, including ELM onset and pedestal constraints, in the standard H-mode regime. The ELITE code has been developed to efficiently evaluate peeling–ballooning stability for comparison with observation and predictions for future devices. We briefly review recent progress in the peeling–ballooning model, including experimental validation of ELM onset and pedestal height predictions, and nonlinear 3D simulations of ELM dynamics, which together lead to an emerging understanding of the physics of the onset and dynamics of ELMs in the standard intermediate to high collisionality regime. We also discuss new studies of the apparent power dependence of the pedestal, and studies of the impact of sheared toroidal flow. Recently, highly promising low collisionality regimes without ELMs have been discovered, including the quiescent H-mode (QH) and resonant magnetic perturbation (RMP) regimes. We present recent observations from the DIII-D tokamak of the density, shape and rotation dependence of QH discharges, and studies of the peeling–ballooning stability in this regime. We propose a model of the QH-mode in which the observed edge harmonic oscillation (EHO) is a saturated kink/peeling mode which is destabilized by current and rotation, and drives significant transport, allowing a near steady-state edge plasma. The model quantitatively predicts the observed density dependence and qualitatively predicts observed mode structure, rotation dependence and outer gap dependence. Low density RMP discharges are found to operate in a similar regime, but with the EHO replaced by an applied magnetic perturbation.

Confinement physics of H-mode discharges in DIII-D

The authors data indicate that the L-mode to H-mode transition in the DIII-D tokamak is associated with the sudden reduction in anomalous, fluctuation-connected transport across the outer midplane of the plasma. In addition to the reduction in edge density and magnetic fluctuations observed at the transition, the edge radial electric field becomes more negative after the transition. They have determined the scaling of the H-mode power threshold with various plasma parameters; the roughly linear increase with plasma density and toroidal field are particularly significant. Control of the ELM frequency and duration by adjusting neutral beam input power has allowed us to produce H-mode plasmas with constant impurity levels and durations up to 5 s. Energy confinement time in ohmic H-mode plasmas and in deuterium H-mode plasmas with deuterium beam injection can exceed saturated ohmic confinement times by at least a factor of two. Energy confinement times above 0.3 s have been achieved in these beam-heated plasmas with plasma currents in the range of 2.0 to 2.5 MA. Local transport studies have shown that electron and ion thermal diffusivities and angular momentum diffusivity are comparable in magnitude and all decrease with increasing plasma current.

Wall stabilization of high beta plasmas in DIII-D

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.

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 approximate analytic expression for neoclassical toroidal plasma viscosity in tokamaks

An approximate analytic expression for neoclassical toroidal plasma viscosity in tokamaks that have error fields or magnetohydrodynamic activities is presented. The expression smoothly joins transport fluxes or plasma viscosity in all the known collisionality regimes derived from the solution of the bounce averaged drift kinetic equation and should be useful in modelling results of existing and future tokamak experiments. It also incorporates some of the extensions of the known expressions to include the effects of finite ∇B drift in the non-resonant transport processes. Here, B is the magnitude of the magnetic field. The toroidal momentum balance equation is a nonlinear function of the radial electric field when the neoclassical plasma viscosity is dominant. It can have bifurcated solutions for the radial electric field and may lead to better plasma confinement as a result.

Resistive wall stabilized operation in rotating high beta NSTX plasmas

The National Spherical Torus Experiment (NSTX) has demonstrated the advantages of low aspect ratio geometry in accessing high toroidal and normalized plasma beta, and βN ≡ 10 8〈βt〉 aB0/Ip. Experiments have reached βt = 39% and βN = 7.2 through boundary and profile optimization. High βN plasmas can exceed the ideal no-wall stability limit, βNno-wall, for periods much greater than the wall eddy current decay time. Resistive wall mode (RWM) physics is studied to understand mode stabilization in these plasmas. The toroidal mode spectrum of unstable RWMs has been measured with mode number n up to 3. The critical rotation frequency of Bondeson-Chu, Ωcrit = ωA/(4q2), describes well the RWM stability of NSTX plasmas when applied over the entire rotation profile and in conjunction with the ideal stability criterion. Rotation damping and global rotation collapse observed in plasmas exceeding βNno-wall differs from the damping observed during tearing mode activity and can be described qualitatively by drag due to neoclassical toroidal viscosity in the helically perturbed field of an ideal displacement. Resonant field amplification of an applied n = 1 field perturbation has been measured and increases with increasing βN. Equilibria are reconstructed including measured ion and electron pressure, toroidal rotation and flux isotherm constraint in plasmas with core rotation ω/ωA up to 0.48. Peak pressure shifts of 18% of the minor radius from the magnetic axis have been reconstructed.

Resistive wall mode dynamics and active feedback control in DIII-D

Recent DIII-D experiments have shown that the growth of the n = 1 resistive wall mode (RWM) can be influenced by an external magnetic field applied in closed loop feedback using a six element error field correction coil (C coil). The RWM constitutes the primary limitation to normalized beta in recent DIII-D advanced tokamak plasma experiments. The toroidal rotation of DIII-D plasmas does not seem sufficient to completely suppress the RWM: a very slowly growing (growth rate γ<<1/τw) or saturated RWM is often observed at normalized beta above the no wall limit and this small RWM slows the rotation. As the rotation decreases, there is a transition to more rapid growth (γ~1/τw, where τw is the resistive time constant of the wall). The application of magnetic feedback is able to hold the RWM to a very small amplitude, prolonging the plasma duration above the no wall limit for times much longer than τw. These initial experimental results are being used to compare control algorithms, to benchmark models of the feedback stabilization process and to guide the design of an upgraded coil sensor system for stabilization of the RWM at normalized beta values closer to the ideal wall limit.

Validation of the linear ideal magnetohydrodynamic model of three-dimensional tokamak equilibria

The first quantitative comparison of linear ideal magnetohydrodynamic (MHD) theory with external magnetic measurements of the nonaxisymmetric plasma perturbation driven by external long-wavelength magnetic fields in high-temperature tokamak plasmas is presented. The comparison yields good (within 20%) agreement for plasma pressures up to ∼75% of the ideal stability limit calculated without a conducting wall. For higher plasma pressures, the ideal MHD model tends to overestimate the perturbed field indicating the increasing importance of stabilizing nonideal effects.

Control of the resistive wall mode with internal coils in the DIII-D tokamak

Internal coils, I-Coils, were installed inside the vacuum vessel of the DIII-D device to generate non-axisymmetric magnetic fields to act directly on the plasma. These fields are predicted to stabilize the resistive wall mode (RWM) branch of the long-wavelength external kink mode with plasma beta close to the ideal wall limit. Feedback using these I-Coils was found to be more effective as compared to using external coils located outside the vacuum vessel. Locating the coils inside the vessel allows for a faster response and the coil geometry also allows for better coupling to the helical mode structure. Initial results were reported previously (Strait E.J. et al 2004 Phys. Plasmas 11 2505). This paper reports on results from extended feedback stabilization operations, achieving plasma parameters up to the regime of Cβ ≈ 1.0 and open loop growth rates of γopenτw ≳ 25 where the RWM was predicted to be unstable with only the rotational viscous stabilization mechanism. Here Cβ ≈ (β - βno-wall.limit)/(βideal.wall.limit - βno-wall.limit) is a measure of the beta relative to the stability limits without a wall and with a perfectly conducting wall, and τw is the resistive flux penetration time of the wall. These feedback experimental results clarified the processes of dynamic error field correction and direct RWM stabilization, both of which took place simultaneously during RWM feedback stabilization operation. MARS-F modelling provides a critical rotation velocity in reasonable agreement with the experiment and predicts that the growth rate increases rapidly as rotation decreases below the critical. The MARS-F code also predicted that for successful RWM magnetic feedback, the characteristic time of the power supply should be limited to a fraction of the growth time of the targeted RWM. The possibility of further improvements in the presently achievable range of operation of feedback gain values is also discussed.