Neoclassical Tearing Mode Seeding by Nonlinear Three-Wave Interactions in Tokamaks.

We report the experimental observation of seed magnetic island formation by nonlinear three-wave coupling of magnetic island triplets. In this experiment, disruptive 2,1 islands are seeded by the coupling of 4,3 and 3,2 tearing modes to a central 1,1 sawtooth precursor. Three-wave interactions between these modes are conclusively identified by bispectral analysis, indicating fixed phase relationships in agreement with theory. This new observation of this seeding mechanism has important implications for future reactors that must operate in stable plasma equilibria, free of disruptive 2,1 islands.

Avoiding Tokamak Disruptions by Applying Static Magnetic Fields That Align Locked Modes with Stabilizing Wave-Driven Currents.

Nonrotating ("locked") magnetic islands often lead to complete losses of confinement in tokamak plasmas, called major disruptions. Here locked islands were suppressed for the first time, by a combination of applied three-dimensional magnetic fields and injected millimeter waves. The applied fields were used to control the phase of locking and so align the island O point with the region where the injected waves generated noninductive currents. This resulted in stabilization of the locked island, disruption avoidance, recovery of high confinement, and high pressure, in accordance with the expected dependencies upon wave power and relative phase between the O point and driven current.

Observation of a multimode plasma response and its relationship to density pumpout and edge-localized mode suppression.

Density pumpout and edge-localized mode (ELM) suppression by applied n=2 magnetic fields in low-collisionality DIII-D plasmas are shown to be correlated with the magnitude of the plasma response driven on the high-field side (HFS) of the magnetic axis but not the low-field side (LFS) midplane. These distinct responses are a direct measurement of a multimodal magnetic plasma response, with each structure preferentially excited by a different n=2 applied spectrum and preferentially detected on the LFS or HFS. Ideal and resistive magneto-hydrodynamic (MHD) calculations find that the LFS measurement is primarily sensitive to the excitation of stable kink modes, while the HFS measurement is primarily sensitive to resonant currents (whether fully shielding or partially penetrated). The resonant currents are themselves strongly modified by kink excitation, with the optimal applied field pitch for pumpout and ELM suppression significantly differing from equilibrium field alignment.

Pedestal bifurcation and resonant field penetration at the threshold of edge-localized mode suppression in the DIII-D Tokamak.

Rapid bifurcations in the plasma response to slowly varying n=2 magnetic fields are observed as the plasma transitions into and out of edge-localized mode (ELM) suppression. The rapid transition to ELM suppression is characterized by an increase in the toroidal rotation and a reduction in the electron pressure gradient at the top of the pedestal that reduces the perpendicular electron flow there to near zero. These events occur simultaneously with an increase in the inner-wall magnetic response. These observations are consistent with strong resonant field penetration of n=2 fields at the onset of ELM suppression, based on extended MHD simulations using measured plasma profiles. Spontaneous transitions into (and out of) ELM suppression with a static applied n=2 field indicate competing mechanisms of screening and penetration of resonant fields near threshold conditions. Magnetic measurements reveal evidence for the unlocking and rotation of tearinglike structures as the plasma transitions out of ELM suppression.

Tokamak operation with safety factor q95 < 2 via control of MHD stability.

Magnetic feedback control of the resistive-wall mode has enabled the DIII-D tokamak to access stable operation at safety factor q(95) = 1.9 in divertor plasmas for 150 instability growth times. Magnetohydrodynamic stability sets a hard, disruptive limit on the minimum edge safety factor achievable in a tokamak, or on the maximum plasma current at a given toroidal magnetic field. In tokamaks with a divertor, the limit occurs at q(95) = 2, as confirmed in DIII-D. Since the energy confinement time scales linearly with current, this also bounds the performance of a fusion reactor. DIII-D has overcome this limit, opening a whole new high-current regime not accessible before. This result brings significant possible benefits in terms of fusion performance, but it also extends resistive-wall mode physics and its control to conditions never explored before. In present experiments, the q(95) < 2 operation is eventually halted by voltage limits reached in the feedback power supplies, not by intrinsic physics issues. Improvements to power supplies and to control algorithms have the potential to further extend this regime.

Reduction of edge-localized mode intensity using high-repetition-rate pellet injection in tokamak H-mode plasmas.

High repetition rate injection of deuterium pellets from the low-field side (LFS) of the DIII-D tokamak is shown to trigger high-frequency edge-localized modes (ELMs) at up to 12× the low natural ELM frequency in H-mode deuterium plasmas designed to match the ITER baseline configuration in shape, normalized beta, and input power just above the H-mode threshold. The pellet size, velocity, and injection location were chosen to limit penetration to the outer 10% of the plasma. The resulting perturbations to the plasma density and energy confinement time are thus minimal (<10%). The triggered ELMs occur at much lower normalized pedestal pressure than the natural ELMs, suggesting that the pellet injection excites a localized high-n instability. Triggered ELMs produce up to 12× lower energy and particle fluxes to the divertor, and result in a strong decrease in plasma core impurity density. These results show for the first time that shallow, LFS pellet injection can dramatically accelerate the ELM cycle and reduce ELM energy fluxes on plasma facing components, and is a viable technique for real-time control of ELMs in ITER.

AC compensation of 3D magnetic diagnostic signals in DIII-D and National Spherical Torus Experiment-Upgrade (NSTX-U) for real-time application.

A time domain algorithm has been developed to remove the vacuum pickup generated by both coil current (DC) and induced vessel current (AC) in real time from three dimensional (3D) magnetic diagnostic signals in the National Spherical Torus Experiment-Upgrade (NSTX-U) and DIII-D tokamaks. The possibility of detecting 3D plasma perturbations in real time is essential in modern and future tokamaks to avoid and control MHD instabilities. The presence of vacuum field pickup, due to toroidally asymmetric (3D) coils or to misalignment between sensors and axisymmetric (2D) coils, pollutes the measured plasma 3D field, making the detection of the magnetic field produced by the plasma challenging. Although the DC coupling between coils and sensors can be easily calculated and removed, the AC part is more difficult. An algorithm based on a layered low-pass filter approach for the AC compensation and its application for DIII-D and NSTX-U data is presented, showing that this method reduces the vacuum pickup to the noise level. Comparison of plasma response measurements with and without vacuum compensation shows that accurate mode locking detection and plasma response identification require precise AC and DC compensations.

Evidence for the importance of trapped particle resonances for resistive wall mode stability in high beta tokamak plasmas.

Active measurements of the plasma stability in tokamak plasmas reveal the importance of kinetic resonances for resistive wall mode stability. The rotation dependence of the magnetic plasma response to externally applied quasistatic n=1 magnetic fields clearly shows the signatures of an interaction between the resistive wall mode and the precession and bounce motions of trapped thermal ions, as predicted by a perturbative model of plasma stability including kinetic effects. The identification of the stabilization mechanism is an essential step towards quantitative predictions for the prospects of "passive" resistive wall mode stabilization, i.e., without the use of an "active" feedback system, in fusion-alpha heated plasmas.

Optimizing the differential connection schemes for detecting 3D magnetic perturbations in DIII-D.

Optimizing the differential pair connection scheme (i.e., the set of pairs) of a toroidal array of magnetic sensors dedicated to measuring slowly rotating asymmetric fields can enhance the mode number detection capability and failure-resilience. In this work, the condition number obtained from singular value decomposition of the design matrix is used as a metric to evaluate the quality of a connection scheme. A large number of possible pair connections are usually available, so evaluating all of them may require extensive use of computational resources and can be very time-consuming. Alternative methods to reduce the number of pairs evaluated without losing the capabilities of toroidal mode detection are presented in this paper. Three examples of the applications of such analysis for the 3D magnetic diagnostic system of DIII-D are also presented: the addition of two new toroidal arrays with n > 3 detection capabilities, the modification of an existing toroidal array in the low field side of the machine to accommodate the addition of a helicon antenna, and the design of changes in several toroidal arrays in the high field side to accommodate the addition of a lower hybrid current drive antenna on the center post.

Electromagnetic torque measurements in DIII-D using internal/external magnetic field decomposition.

Given spatially resolved measurements of normal and tangential components of the magnetic field just outside the surface of a magnetically confined plasma, the field at the measurement location can be uniquely decomposed into contributions from the plasma and from external sources. This principle allows direct measurement of the electromagnetic torque on the plasma without knowledge of the distribution of the internal and external currents, similar to the more well-known formalism using the Maxwell stress tensor. The internal/external field decomposition also enables a mixed approach that incorporates any explicitly known current distributions (e.g., from non-axisymmetric coils). We discuss the requirements and limitations of such an approach to torque measurements. Experimental measurements of the torque evolution as a rotating tearing mode locks to the wall in the DIII-D tokamak are consistent with a simple model.

Conceptual design of extended magnetic probe set to improve 3D field detection in NSTX-U.

Adding toroidal arrays of magnetic probes at the top and bottom of NSTX-U would improve both the detection of the multimodal plasma response to applied magnetic perturbations and the identification of the poloidal structure of unstable plasma modes, as well as contribute to the validation of MHD models, improve the understanding of the plasma response to external fields, and improve the error field correction. In this paper, the linear MHD code MARS-F/K has been used to identify poloidal locations that would improve the capability to measure stationary or near-stationary 3D fields that may result from the plasma response to external sources of non-axisymmetric fields. The study highlighted 6 poloidal positions where new arrays of both poloidal and radial magnetic field sensors would improve the poloidal resolution. The proposed set of new arrays combined with the present ones is shown to be capable of measuring the poloidal structure of perturbations with n ≤ 6 and of detecting the multimodal plasma response. Assessment of the trade-off in the poloidal length of the probes leads to an ideal length between 10 cm and 30 cm. A method to configure the probes of a toroidal array based on the singular value decomposition condition number is proposed, and an ideal solution and a low-cost one are presented.

Measurements of DIII-D poloidal field by fiber-optic pulsed polarimetry.

A new technique for measuring the spatial and temporal structure of the poloidal field is presented, whereby the magnetic field causes the polarization of light traveling through an optical fiber to rotate via the Faraday effect by an amount proportional to the strength of the field oriented along the fiber. In fiber optic pulsed polarimetry, changes in the polarization of the backscatter light from the fiber are detected, thereby permitting measurement of the field as a function of position along the fiber. In this proof-of-principle experiment, specially prepared single-mode fibers with weak fiber Bragg gratings were installed in the poloidal direction on the outside of the thermal blanket on DIII-D. Light at 532 nm from a mode-locked Nd:YAG laser was injected into the optical fibers. The laser repetition rate was 895 kHz with a pulse length of <10 ps, resulting in ∼1 µs temporal resolution. A photodetector system measured the Stokes polarization components necessary to determine the amount of polarization rotation. For this experiment, bandwidth limitations of the detectors resulted in a spatial resolution of ≈2 cm. The measured temporal and spatial distributions of the poloidal field are consistent with inductive probe measurements and Elastodynamic Finite Integration Technique reconstructions of the spatial distribution. This demonstrates the ability of this technique to provide real-time detection of the temporal and spatial variations of the poloidal field. Besides revealing more detailed information about the plasma, this new diagnostic capability can also help in detecting instabilities in real time, thereby enabling enhanced machine protection.

Spatial and temporal analysis of DIII-D 3D magnetic diagnostic data.

An extensive set of magnetic diagnostics in DIII-D is aimed at measuring non-axisymmetric "3D" features of tokamak plasmas, with typical amplitudes ∼10-3 to 10-5 of the total magnetic field. We describe hardware and software techniques used at DIII-D to condition the individual signals and analysis to estimate the spatial structure from an ensemble of discrete measurements. Applications of the analysis include detection of non-rotating MHD instabilities, plasma control, and validation of MHD stability and 3D equilibrium models.

An upgrade of the magnetic diagnostic system of the DIII-D tokamak for non-axisymmetric measurements.

The DIII-D tokamak magnetic diagnostic system [E. J. Strait, Rev. Sci. Instrum. 77, 023502 (2006)] has been upgraded to significantly expand the measurement of the plasma response to intrinsic and applied non-axisymmetric "3D" fields. The placement and design of 101 additional sensors allow resolution of toroidal mode numbers 1 ≤ n ≤ 3, and poloidal wavelengths smaller than MARS-F, IPEC, and VMEC magnetohydrodynamic model predictions. Small 3D perturbations, relative to the equilibrium field (10(-5) < δB/B0 < 10(-4)), require sub-millimeter fabrication and installation tolerances. This high precision is achieved using electrical discharge machined components, and alignment techniques employing rotary laser levels and a coordinate measurement machine. A 16-bit data acquisition system is used in conjunction with analog signal-processing to recover non-axisymmetric perturbations. Co-located radial and poloidal field measurements allow up to 14.2 cm spatial resolution of poloidal structures (plasma poloidal circumference is ~500 cm). The function of the new system is verified by comparing the rotating tearing mode structure, measured by 14 BP fluctuation sensors, with that measured by the upgraded B(R) saddle loop sensors after the mode locks to the vessel wall. The result is a nearly identical 2/1 helical eigenstructure in both cases.

Observation of plasma rotation driven by static nonaxisymmetric magnetic fields in a tokamak.

We present the first evidence for the existence of a neoclassical toroidal rotation driven in a direction counter to the plasma current by nonaxisymmetric, nonresonant magnetic fields. At high beta and with large injected neutral beam momentum, the nonresonant field torque slows down the plasma toward the neoclassical "offset" rotation rate. With small injected neutral beam momentum, the toroidal rotation is accelerated toward the offset rotation, with resulting improvement in the global energy confinement time. The observed magnitude, direction, and radial profile of the offset rotation are consistent with neoclassical theory predictions.

Intense geodesic acousticlike modes driven by suprathermal ions in a tokamak plasma.

Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (q_{min}>or=2). Strong bursting and frequency chirping are observed, concomitant with large (10%-15%) drops in the neutron emission. Large electron density fluctuations (n[over ]_{e}/n_{e} approximately 1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode.

Reduced critical rotation for resistive-wall mode stabilization in a near-axisymmetric configuration.

Recent DIII-D experiments with reduced neutral beam torque and minimum nonaxisymmetric perturbations of the magnetic field show a significant reduction of the toroidal plasma rotation required for the stabilization of the resistive-wall mode (RWM) below the threshold values observed in experiments that apply nonaxisymmetric magnetic fields to slow the plasma rotation. A toroidal rotation frequency of less than 10 krad/s at the q=2 surface (measured with charge exchange recombination spectroscopy using C VI) corresponding to 0.3% of the inverse of the toroidal Alfvén time is sufficient to sustain the plasma pressure above the ideal MHD no-wall stability limit. The low-rotation threshold is found to be consistent with predictions by a kinetic model of RWM damping.

Multitude of core-localized shear Alfvén waves in a high-temperature fusion plasma.

Evidence is presented for a multitude of discrete frequency Alfvén waves in the core of magnetically confined high-temperature fusion plasmas. Multiple diagnostic instruments confirm wave excitation over a wide spatial range from the device size at the longest wavelengths down to the thermal ion Larmor radius. At the shortest scales, the poloidal wavelengths are comparable to the scale length of electrostatic drift wave turbulence. Theoretical analysis confirms a dominant interaction of the modes with particles in the thermal ion distribution traveling well below the Alfvén velocity.

Sustained stabilization of the resistive-wall mode by plasma rotation in the DIII-D tokamak.

Values of the normalized plasma pressure up to twice the free-boundary stability limit predicted by ideal magnetohydrodynamic (MHD) theory have been sustained in the DIII-D tokamak. Long-wavelength modes are stabilized by the resistive wall and rapid plasma toroidal rotation. High rotation speed is maintained by minimization of nonaxisymmetric magnetic fields, overcoming a long-standing impediment [E. J. Strait, Phys. Rev. Lett. 74, 2483 (1995)]]. The ideal-MHD pressure limit calculated with an ideal wall is observed as the operational limit to the normalized plasma pressure.

Measurement of the resistive-wall-mode stability in a rotating plasma using active MHD spectroscopy.

The stability of the resistive-wall mode (RWM) in DIII-D plasmas above the conventional pressure limit, where toroidal plasma rotation in the order of a few percent of the Alfve n velocity is sufficient to stabilize the n=1 RWM, has been probed using the technique of active MHD spectroscopy at frequencies of a few Hertz. The measured frequency spectrum of the plasma response to externally applied rotating resonant magnetic fields is well described by a single-mode approach and provides an absolute measurement of the damping rate and the natural mode rotation frequency of the stable RWM.