Notes: The maximum normalized beta achieved in long-pulse tokamak discharges at low collisionality falls significantly below both that observed in short pulse discharges and that predicted by the ideal MHD theory. Recent long-pulse experiments, in particular those simulating the International Thermonuclear Experimental Reactor (ITER) [M. Rosenbluth et al., Plasma Physics and Controlled Nuclear Fusion (International Atomic Energy Agency, Vienna, 1995), Vol. 2, p. 517] scenarios with low collisionality νe*, are often limited by low-m/n nonideal magnetohydrodynamic (MHD) modes. The effect of saturated MHD modes is a reduction of the confinement time by 10%–20%, depending on the island size and location, and can lead to a disruption. Recent theories on neoclassical destabilization of tearing modes, including the effects of a perturbed helical bootstrap current, are successful in explaining the qualitative behavior of the resistive modes and recent results are consistent with the size of the saturated islands. Also, a strong correlation is observed between the onset of these low-m/n modes with sawteeth, edge localized modes (ELM), or fishbone events, consistent with the seed island required by the theory. We will focus on a quantitative comparison between both the conventional resistive and neoclassical theories, and the experimental results of several machines, which have all observed these low-m/n nonideal modes. This enables us to single out the key issues in projecting the long-pulse beta limits of ITER-size tokamaks and also to discuss possible plasma control methods that can increase the soft β limit, decrease the seed perturbations, and/or diminish the effects on confinement. © 1997 American Institute of Physics.

Notes: Detailed analysis of recent high beta discharges in the DIII-D [Plasma Physics Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] tokamak demonstrates that the resistive vacuum vessel can provide stabilization of low n magnetohydrodynamic (MHD) modes. The experimental beta values reaching up to βT=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 "resistive wall'' mode are observed. Through slowing of the plasma rotation between the q=2 and q=3 surfaces with the application of a nonaxisymmetric field, it has been determined that the rotation at the outer rational surfaces is most important, and that the critical rotation frequency is of the order of Ω/2π=1 kHz. © 1995 American Institute of Physics.

Notes: 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 wall limit but have little effect at lower beta. The discovery of an error field amplification has led to sustained operation above the no-wall limit through improved magnetic field symmetrization using an external coil set. The required symmetrization is determined both by optimizing the external currents with respect to the plasma rotation and by use of feedback to detect and minimize the plasma response to nonaxisymmetric fields as beta increases. Ideal stability analysis and rotation braking experiments at different beta values show that beta is maintained 50% higher than the no wall stability limit for durations greater than 1 s, and approaches beta twice the no-wall limit in several cases, with steady-state rotation levels. The results suggest that improved magnetic-field symmetry could allow plasmas to be maintained well above no-wall beta limit for as long as sufficient torque is provided. © 2002 American Institute of Physics.

Notes: The development of techniques for neoclassical tearing mode (NTM) suppression or avoidance is crucial for successful high beta/high confinement tokamaks. Neoclassical tearing modes are islands destabilized and maintained by a helically perturbed bootstrap current and represent a significant limit to performance at higher poloidal beta. The confinement-degrading islands can be reduced or completely suppressed by precisely replacing the "missing" bootstrap current in the island O-point or by interfering with the fundamental helical harmonic of the pressure. Implementation of such techniques is being studied in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] in the presence of periodic q=1 sawtooth instabilities, a reactor relevant regime. Radially localized off-axis electron cyclotron current drive (ECCD) must be precisely located on the island. In DIII-D the plasma control system is put into a "search and suppress" mode to make either small rigid radial position shifts of the entire plasma (and thus the island) or small changes in the toroidal field (and, thus, the ECCD location) to find and lock onto the optimum position for complete island suppression by ECCD. This is based on real-time measurements of an m/n=3/2 mode amplitude dBθ/dt. The experiment represents the first use of active feedback control to provide continuous, precise positioning. An alternative to ECCD makes use of the six toroidal section "C-Coil" on DIII-D to provide a large nonresonant static m=1, n=3 helical field to interfere with the fundamental harmonic of an m/n=3/2 NTM. While experiments show success in inhibiting the NTM if a large enough n=3 field is applied before the island onset, there is a considerable plasma rotation decrease due to n=3 "ripple." © 2002 American Institute of Physics.

Notes: A proof of principle magnetic feedback stabilization experiment has been carried out to suppress the resistive wall mode (RWM), a branch of the ideal magnetohydrodynamic (MHD) kink mode under the influence of a stabilizing resistive wall, on the DIII-D tokamak device [Plasma Phys. Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159; Phys. Plasmas 1, 1415 (1994)]. The RWM was successfully suppressed and the high beta duration above the no-wall limit was extended to more than 50 times the resistive wall flux diffusion time. It was observed that the mode structure was well preserved during the time of the feedback application. Several lumped parameter formulations were used to study the feedback process. The observed feedback characteristics are in good qualitative agreement with the analysis. These results provide encouragement to future efforts towards optimizing the RWM feedback methodology in parallel to what has been successfully developed for the n=0 vertical positional control. Newly developed MHD codes have been extremely useful in guiding the experiments and in providing possible paths for the next step. © 2001 American Institute of Physics.

Notes: The amplitude and frequency of modes driven in the edge region of tokamak high mode (H-mode) discharges [type I edge-localized modes (ELMs)] are shown to depend on the discharge shape. The measured pressure gradient threshold for instability and its scaling with discharge shape are compared with predictions from ideal magnetohydrodynamic theory for low toroidal mode number (n) instabilities driven by pressure gradient and current density and good agreement is found. Reductions in mode amplitude are observed in discharge shapes with either high squareness or low triangularity where the stability threshold in the edge pressure gradient is predicted to be reduced and the most unstable mode is expected to have higher values of n. The importance of access to the ballooning mode second stability regime is demonstrated through the changes in the ELM character that occur when second regime access is not available. An edge stability model is presented that predicts that there is a threshold value of n for second regime access and that the most unstable mode has n near this threshold. © 2000 American Institute of Physics.

Notes: Reliable operation of discharges with negative central magnetic shear has led to significant increases in plasma performance and reactivity in both low confinement, L-mode, and high confinement, H-mode, regimes in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159]. Using neutral beam injection early in the initial current ramp, a large range of negative shear discharges have been produced with durations lasting up to 3.2 s. The total noninductive current (beam plus bootstrap) ranges from 50% to 80% in these discharges. In the region of shear reversal, significant peaking of the toroidal rotation [fφ(0)∼30–60 kHz] and ion temperature [Ti(0)∼15–22 keV] profiles are observed. In high-power discharges with an L-mode edge, peaked density profiles are also observed. Confinement enhancement factors up to H≡τE/τITER-89P∼2.5 with an L-mode edge, and H∼3.3 in an edge localized mode (ELM)-free H mode, are obtained. Transport analysis shows both ion thermal diffusivity and particle diffusivity to be near or below standard neoclassical values in the core. Large pressure peaking in the L mode leads to high disruptivity with βN≡βT/(I/aB)≤2.3, while broader pressure profiles in the H mode gives low disruptivity with βN≤4.2. © 1996 American Institute of Physics.

Notes: Stability at high beta (the ratio of plasma pressure to magnetic field pressure) is an important requirement for a compact, economically attractive fusion reactor. It is also important in present large tokamak experiments, where the best performance is now often limited by instabilities rather than by energy transport. The past decade has seen major advances in our understanding of the stability of high beta tokamak plasmas, as well as in the achievement of high values of beta. Ideal magnetohydrodynamic (MHD) theory has been remarkably successful in predicting the stability limits, and the scaling of maximum stable beta with the normalized plasma current predicted by Troyon and others has been confirmed in many experiments, yielding a limit βmax≈3.5 (%-m-T/MA) I/aB (where I is the plasma current, a is the minor radius, and B is the toroidal field). The instabilities which are predicted to limit beta have been observed experimentally, in good agreement with theoretical predictions, including long-wavelength kink modes and short-wavelength ballooning instabilities. Advances in understanding of tokamak stability have opened several paths to higher values of beta. The use of strong discharge shaping, approaching the limits of axisymmetric stability, has allowed beta values as high as 12% to be reached in agreement with Troyon scaling. Recent experimental results and ideal MHD modeling have shown that the beta limit depends on the form of the pressure and current density profiles, and modification of the current density to create a centrally peaked profile has allowed beta values up to 6I/aB to be achieved experimentally.Recent experiments have also begun to explore both local and global access to the predicted second stable regime for ballooning modes, with the potential for very high values of β/(I/aB). Preliminary experimental investigations of wall stabilization and radio-frequency (RF) current profile control hold the promise of further improvements in beta through passive and active control of instabilities. The developing understanding of high beta stability and the application of this understanding to present experiments and future fusion devices hold the potential for production of stable, steady state plasmas at high beta with good confinement.

Notes: High-confinement (H-mode) operation is the choice for next-step tokamak devices based either on conventional or advanced tokamak physics. This choice, however, comes at a significant cost for both the conventional and advanced tokamaks because of the effects of edge localized modes (ELMs). ELMs can produce significant erosion in the divertor and can affect the beta limit and reduced core transport regions needed for advanced tokamak operation. Experimental results from DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] this year have demonstrated a new operating regime, the quiescent H-mode regime, which solves these problems. We have achieved quiescent H-mode operation that is ELM-free and yet has good density and impurity control. In addition, we have demonstrated that an internal transport barrier can be produced and maintained inside the H-mode edge barrier for long periods of time (〉3.5 s or 〉25 energy confinement times τE), yielding a quiescent double barrier regime. By slowly ramping the input power, we have achieved βNH89=7 for up to 5 times the τE of 150 ms. The βNH89 values of 7 substantially exceed the value of 4 routinely achieved in the standard ELMing H mode. The key factors in creating the quiescent H-mode operation are neutral beam injection in the direction opposite to the plasma current (counter injection) plus cryopumping to reduce the density. Density and impurity control in the quiescent H mode is possible because of the presence of an edge magnetohydrodynamic (MHD) oscillation, the edge harmonic oscillation, which enhances the edge particle transport while leaving the energy transport unaffected. © 2001 American Institute of Physics.

Notes: One promising approach to maintaining stability of high beta tokamak plasmas is the use of a conducting wall near the plasma to stabilize low-n ideal magnetohydrodynamic instabilities. However, with a resistive wall, either plasma rotation or active feedback control is required to stabilize the more slowly growing resistive wall modes (RWMs). Previous experiments have demonstrated that plasmas with a nearby conducting wall can remain stable to the n=1 ideal external kink above the beta limit predicted with the wall at infinity. Recently, extension of the wall stabilized lifetime τL to more than 30 times the resistive wall time constant τw and detailed, reproducible observation of the n=1 RWM have been possible in DIII-D [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159] plasmas above the no-wall beta limit. The DIII-D measurements confirm characteristics common to several RWM theories. The mode is destabilized as the plasma rotation at the q=3 surface decreases below a critical frequency of 1–7 kHz (∼1% of the toroidal Alfvén frequency). The measured mode growth times of 2–8 ms agree with measurements and numerical calculations of the dominant DIII-D vessel eigenmode time constant τw. From its onset, the RWM has little or no toroidal rotation (ωmode≤τw−1(very-much-less-than)ωplasma), and rapidly reduces the plasma rotation to zero. These slowly growing RWMs can in principle be destabilized using external coils controlled by a feedback loop. In this paper, the encouraging results from the first open loop experimental tests of active control of the RWM, conducted in DIII-D, are reported. © 1999 American Institute of Physics.