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Nonlinear extended magnetohydrodynamics simulations demonstrating seeding of neoclassical tearing modes (NTMs) via magnetohydrodynamics-transient-induced multimode interactions are presented. Simulations of NTMs are enabled by two recent NIMROD code developments: the implementation of heuristic neoclassical stresses and the application of transient magnetic perturbations (MPs) at the boundary. NTMs are driven unstable by the inherently pressure driven kinetic bootstrap current, which arises due to collisional viscosity between passing and trapped electrons. These simulations use heuristic closures that model the neoclassical electron and ion stresses. NTM growth requires a seed island, which is generated by a transiently applied MP in simulations. The capability is demonstrated using kinetic-based reconstructions with flow of a DIII-D ITER Baseline Scenario discharge (La Haye et al., in Proceedings IAEA FEC, 2020). The applied MP seeds a 2/1 NTM that grows in two phases: a slow growth phase followed by a faster robust growth phase. Additionally, an evolving sequence of higher order core modes are excited at first. Power transfer analysis shows that nonlinear interactions between the core modes and the 2/1 helps drive the initial slow growth. Once the induced 2/1 magnetic island reaches a critical width, the NTM transitions to faster robust growth, which is well described by the nonlinear modified Rutherford equation. This work highlights the role of nonlinear mode coupling in seeding NTMs.

ITER is an international project to design and build an experimental fusion reactor based on the “tokamak” concept. ITER relies upon localized electron cyclotron current drive (ECCD) at the rational safety factor q=2 to suppress or stabilize the expected poloidal mode m=2, toroidal mode n=1 neoclassical tearing mode (NTM) islands. Such islands if unmitigated degrade energy confinement, lock to the resistive wall (stop rotating), cause loss of “H-mode” and induce disruption. The International Tokamak Physics Activity (ITPA) on MHD, Disruptions and Magnetic Control joint experiment group MDC-8 on Current Drive Prevention/Stabilization of Neoclassical Tearing Modes started in 2005, after which assessments were made for the requirements for ECCD needed in ITER, particularly that of rf power and alignment on q=2 [1]. Narrow well-aligned rf current parallel to and of order of one percent of the total plasma current is needed to replace the “missing” current in the island O-points and heal or preempt (avoid destabilization by applying ECCD on q=2 in absence of the mode) the island [2-4]. This paper updates the advances in ECCD stabilization on NTMs learned in DIII-D experiments and modeling during the last 5 to 10 years as applies to stabilization by localized ECCD of tearing modes in ITER. This includes the ECCD (inside the q=1 radius) stabilization of the NTM “seeding” instability known as sawteeth (m/n=1/1) [5]. Recent measurements in DIII-D show that the ITER-similar current profile is classically unstable, curvature stabilization must not be neglected, and the small island width stabilization effect from helical ion polarization currents is stronger than was previously thought [6]. The consequences of updated assumptions in ITER modeling of the minimum well-aligned ECCD power needed are all-in-all favorable (and well-within the ITER 24 gyrotron capability) when all effects are included. However, a “wild card” may be broadening of the localized ECCD by the presence of the island; various theories predict broadening could occur and there is experimental evidence for broadening in DIII-D. Wider than now expected ECCD in ITER would make alignment easier to do but weaken the stabilization and thus require more rf power. In addition to updated modeling for ITER, advances in the ITER-relevant DIII-D ECCD gyrotron launch mirror control system hardware and real-time plasma control system have been made [7] and there are plans for application in DIII-D ITER demonstration discharges.

Neoclassical tearing modes (NTMs) will be the principal limit on performance in ITER in the standard scenario, which has beta well below the ideal kink limit. Measurements of island size from ASDEX Upgrade, DIII-D and JET in beta rampdown experiments are used to determine the marginal size for m/n = 3/2 NTM removal. This is compared with data from ASDEX Upgrade, DIII-D and JT-60U with removal of the 3/2 NTM by electron cyclotron current drive (ECCD) at near constant beta. The empirical marginal island size is consistent in both sets of removal experiments and is found to be about twice the ion banana width. A common methodology is developed for fitting the saturated m/n = 3/2 island before (or without) ECCD in all four experimental devices, ASDEX Upgrade, DIII-D, JET and JT-60U. To this is added (and model tested to experiments) the effect of un-modulated co-ECCD on the island width due to replacing the missing bootstrap current and making the tearing stability parameter Δ' more negative. The common model is then used to evaluate the ITER ECCD system, with or without modulation, for both the m/n = 3/2 mode, which is benchmarked here, as well as the m/n = 2/1 NTM. The ITER ECCD top launch system with 20 MW of power is found to be effective in greatly reducing the size of the islands. An m/n = 2/1 mode locking model is used to show that the rotation in ITER should be sufficient for the island reduction by ECCD to avoid locking that causes loss of H-mode and disruption.

The advanced tokamak programme on DIII-D is to develop the scientific basis for steady state, high performance operation in future devices. We report on experiments attempting to demonstrate sustainment of 100% noninductive current for several seconds at high beta, using up to 2.5 MW of off-axis electron cyclotron current drive and up to 15 MW of neutral beam injection with q95 ≈ 5. A 100% noninductive condition was achieved with βT = 3.6%, βN = 3.5, H89 = 2.4 and improved current drive alignment. However, the duration of this phase was limited by the pressure profile evolution leading to magnetohydrodynamic instabilities after about 0.7 s. In a separate discharge, a nearly (~90%) noninductive, stationary condition was maintained for one current relaxation time (1.8 s) only limited by the duration of the hardware system. These experiments have achieved normalized fusion performance with bootstrap current fraction fBS ≈ 60%, consistent with requirements for the ITER Q = 5 steady-state scenarios. The modelling tools that were successfully employed to devise experiments in DIII-D are applied to ITER, indicating that full noninductive operation is plausible for an ITER steady-state scenario with Q ≈ 5.

A potential new standard in stationary tokamak performance is emerging from experiments on DIII-D. These experiments have demonstrated the ability to operate near the free boundary, n = 1 stability limit with good confinement quality under stationary conditions. The normalized fusion performance is at or above that projected for Qfus = 10 operation in the International Thermonuclear Experimental Reactor (ITER) design over a wide operating range in both edge safety factor (2.8–4.7) and plasma density (35–70% of the Greenwald density). Projections to ITER based on this data are uniformly positive and indicate that a wide range of operating options may be available on ITER, including the possibility of sustained ignition. Recent experiments have demonstrated the importance of a small m = 3, n = 2 neoclassical tearing mode in avoiding sawteeth and the effect of edge localized modes on tearing mode stability at an edge safety factor near 3. Transport studies using the GLF23 turbulence transport code suggest that E × B shear stabilization is important in reproducing the measured profiles in the simulation. Yet, even in cases in which the toroidal rotation is moderate, confinement quality is robustly better than the standard H-mode confinement scalings.

Tokamaks designed for burning plasma operation have significant free energy in the poloidal magnetic field and in the thermal stored energy. Protection of the first wall and the vacuum vessel from the effects of a rapid release of this energy (a disruption) is required. While mitigation of a disruption is feasible, avoidance of the disruption is preferable. Suppression of tearing modes that lead to disruption is a key method of avoidance. Electron cyclotron current drive is a demonstrated technique for suppression of tearing modes. The location of the current drive relative to the tearing mode is the critical parameter for successful suppression. Incorporation of this suppression technique in a machine protection system requires continuous aiming of the electron cyclotron waves (for rapid application to island) and a closed-loop optimization of the effect of the current drive on the mode (for maximum effectiveness). Real-time methods to accomplish both of these tasks have been demonstrated successfully in the DIII-D tokamak.

Advanced tokamak (AT) research in DIII-D seeks to provide a scientific basis for steady-state high performance operation in future devices. These regimes require high toroidal beta to maximize fusion output and high poloidal beta to maximize the self-driven bootstrap current. Achieving these conditions requires integrated, simultaneous control of the current and pressure profiles and active magnetohydrodynamic stability control. The building blocks for AT operation are in hand. Resistive wall mode stabilization by plasma rotation and active feedback with non-axisymmetric coils allows routine operation above the no-wall beta limit. Neoclassical tearing modes are stabilized by active feedback control of localized electron cyclotron current drive (ECCD). Plasma shaping and profile control provide further improvements. Under these conditions, bootstrap supplies most of the current. Steady-state operation requires replacing the remaining inductively driven current, mostly located near the half radius, with non-inductive external sources. In DIII-D this current is provided by ECCD, and nearly stationary AT discharges have been sustained with little remaining inductive current. Fast wave current drive is being developed to control the central magnetic shear. Density control, with divertor cryopumps, of AT discharges with ELMing H-mode edges facilitates high current drive efficiency at reactor relevant collisionalities. An advanced plasma control system allows integrated control of these elements. Close coupling between modelling and experiment is key to understanding the separate elements, their complex nonlinear interactions, and their integration into self-consistent high performance scenarios. This approach has resulted in fully non-inductively driven plasmas with ?N ? 3.5 and ?T ? 3.6% sustained for up to 1?s, which is approximately equal to one current relaxation time. Progress in this area, and its implications for next-step devices, will be illustrated by results of these and other recent experiment and simulation efforts.

Advanced Tokamak (AT) research in DIII-D [K. H. Burrell for the DIII-D Team, in Proceedings of the 19th Fusion Energy Conference, Lyon, France, 2002 (International Atomic Energy Agency, Vienna, 2002) published on CD-ROM] seeks to provide a scientific basis for steady-state high performance operation in future devices. These regimes require high toroidal beta to maximize fusion output and poloidal beta to maximize the self-driven bootstrap current. Achieving these conditions requires integrated, simultaneous control of the current and pressure profiles, and active magnetohydrodynamic stability control. The building blocks for AT operation are in hand. Resistive wall mode stabilization via plasma rotation and active feedback with nonaxisymmetric coils allows routine operation above the no-wall beta limit. Neoclassical tearing modes are stabilized by active feedback control of localized electron cyclotron current drive (ECCD). Plasma shaping and profile control provide further improvements. Under these condi...

A review of magnetohydrodynamic limits to tokamak operation in terms of current, density and pressure is given. Although the current and density limits in a tokamak usually lead to disruptive termination of the discharge, it is argued that these can be avoided by staying away from the respective limits. This is especially true since operation close to these limits is not really desirable, due to the decreased confinement at very high density and the high disruptivity at low q. On the other hand, the limit to plasma pressure set by neoclassical tearing modes (NTMs) and resistive wall modes (RWMs) is too low to guarantee economic operation of future fusion reactors. Therefore, active control of these two instabilities is now being studied. Noticeable progress has been made by NTM stabilization with ECCD. Avoidance of NTMs and RWMs by tailoring sawteeth and spinning the plasma, shows promising results. Also, experiments on direct RWM stabilization by active coils are showing their first encouraging results.

The prevention of neoclassical tearing modes (NTMs) in tokamak plasmas is a major challenge for fusion. Ideal modes can seed NTMs through forced reconnection, yet in sawtoothing discharges it is not well understood why a particular sawtooth crash seeds a NTM after several preceding sawteeth did not. Also, tearing modes sometimes appear and grow without an obvious ideal mode causing a seed island. Based on theoretical and experimental results a new mechanism for tearing mode onset is proposed and tested which explains these puzzling observations. Tearing stability calculations based on experimental equilibria from the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] indicate that tearing modes can be driven unstable by a rapid increase in the linear tearing stability index Δ′ just before onset. Near the ideal kink limit in βN≡β/(I/aBT), Δ′ becomes large and positive as it approaches a pole discontinuity. The relative time scales of the change in Δ′ vs the effects of finite island width will determine the evolution of the island, and the eventual nonlinear state. Theoretical predictions of the onset point, the βN at a specified small island width, and the early evolution characteristics are compared with results from new DIII-D experiments designed specifically to test this hypothesis. Time integration of the island evolution equation shows that these predictions are consistent with the experimental observations. The nonlinear 3D resistive magnetohydrodynamic code NIMROD [A. H. Glasser et al., Plasma Phys. Control. Fusion 41, A747 (1999)] is used to evolve equilibria reconstructed from these experiments in time to provide a more comprehensive prediction of the island evolution during the early nonlinear phase. The simulations are also consistent with the proposed mechanism.

Suppression of the resistive wall mode (RWM) has been successfully demonstrated in the DIII–D tokamak by using rotational stabilization in conjunction with a close-fitting vacuum vessel wall. The duration of the high-pressure discharge was extended to hundreds of times the wall skin time. Frequently, the plasma pressure reached the ideal-wall magnetohydrodynamic (MHD) kink limit. The confined pressure is up to twice as high as the no-wall ideal MHD kink limit. Near its marginal stability point, the RWM is found to resonate with residual non-axisymmetric fields (e.g. components of the error field). A magnetic feedback system has been used to identify and compensate for the residual non-axisymmetric fields. This is to the best of our knowledge, the first demonstration of the sustainment of a stable plasma with pressure at levels well above the no-wall pressure limit. This technique is expected to be applicable to other toroidal devices.

Neoclassical tearing modes are one of the most serious concerns for operation on a next-step tokamak device. The modes occur on present tokamaks at normalized pressure (beta (N)) values comparable to those envisaged For baseline scenarios in future devices, such as ITER-FEAT. Further, empirical scalings based on data from many of the present machines point to much lower thresholds on a larger device. However, physics-based models indicate an important role for the seed island mechanisms, which may in fact give rise to increased stability on larger devices-i.e. if the seed island width (required to trigger the NTM) falls below the critical levels required. Fits based on these models suggest this is the case, bur are too badly constrained at present to make reliable predictions, and the physics is complex, making quantitative theoretical calculation difficult. Further experiments are required to examine the scaling of the seed, as well as to identify the role and relative sizes of the stabilizing terms that set the critical size for mode growth. In the event that the modes are unavoidable, promising feedback stabilization techniques are being developed with the use of localized RF current drive to change the stability properties of the plasma. Further work is needed to demonstrate sustained access to higher beta (N) and provide data to refine models. This paper reviews the underlying physics and key issues, commenting on the present status of understanding and further work required.

The islands from tearing modes driven unstable and sustained by the helically perturbed neoclassical bootstrap current often provide the practical limit to long-pulse, high confinement tokamak operation. The destabilization of such “metastable” plasmas depends on a “seed” island exceeding a threshold. A database from similar regimes [high confinement H-mode with periodic edge localized modes (ELMs) and periodic central sawteeth] was compiled from the tokamaks ASDEX Upgrade (AUG) [Plasma Phys. Controlled Fusion 41, 767 (1999)], DIII-D [Nucl. Fusion 38, 987 (1998)], and JET (Joint European Torus) [Plasma Phys. Controlled Fusion 41, B1 (1999)]. A comparison is made of the measured critical beta for onset of the m/n=3/2 mode (m and n being the poloidal and toroidal Fourier harmonics, respectively) to a model in terms of dimensionless parameters for the seed and threshold islands. This modeling is then used for extrapolation to a reactor-grade tokamak design such as ITER/FDR (International Thermonuclear Experi...

At sufficiently high poloidal beta beta(theta) and low collisionality, m/n = 3/2 tearing modes are excited in the DIII-D tokamak by a q = 1 sawtooth crash perturbation. The resulting islands of full radial width w are long lived and reduce global confinement (and beta(theta)) by up to 30%. These are tearing modes produced by the perturbed neoclassical bootstrap current destabilization of a seed island arising from the m/n = 2/2 sawtooth precursor. The tearing modes are metastable. Even if the modes are conventionally stable, i.e. Delta' < 0, far sufficiently high beta(theta), there is a range of island widths zu above some threshold value over which the modified Rutherford equation predicts island growth. This threshold value increases with collisionality. Both 'transport' and 'polarization' threshold models are compared with experiment. The transport model gives the correct scaling with experiment, but the threshold island w(d) is 3 to 9 times too small, depending on whether ion or electron parallel heat transport is used. The polarization model threshold island w(g) gives good agreement with experiment, utilizing an approximately hyperbolic tangent transition from collisionless to collisional regimes.

The High performance H-mode regime on DIII-D has been extended to both low q and high q (high {Beta}p) and low q operation. In high current operation, VH-mode discharges were obtained for the first time with I{sub P}(MA)/B{sub T} (T) > 1. These discharges had q{sub 95}= 3.4, H = 2.9, {Beta}{sub N}= 3, and {Beta}{sub T}{Tau}{sub E}=3%-sec. {Beta}{sub T}{Tau}{sub E} was improved by approximately 50% over previous results. These discharges were obtained with neutral beam injection during the plasma current ramp up which maintained the axial q above 1. In low current operation, neutral beam heated discharges with 100% of the plasma current from non-inductive sources were obtained at high q, q{sub 95}=15, with {Beta}{sub N}=3.9, H=3.1, and {Beta}{sub p}=4.9. These discharges represent an extension of the high performance regime to q{sub 95} > 7.2, which was made possible by reduction in the locked mode low density limit, as the result of improvements in the magnetic field error correcting coils. These low current discharges do not exhibit some of the standard signatures of VH-mode, but appear to represent a new regime of improved H-mode confinement. Similar, non-VH-mode, high energy confinement discharges were obtained at low density and moderate q.

Small (o.d. = 1.8 mm, t = 0.37 mm) polystyrene shells filled with either pressurized argon gas or boron powder have been fired into DIII‐D plasmas for disruption mitigation experiments. The pellet shells were observed to burn up at ρ≈0.5, roughly consistent with ablation rate calculations. Pellet slowing from 350 m/s down to 100 m/s was observed, which is not well‐understood at present. Negligible plasma current contraction or MHD onset were seen as a result of the shell burn‐up in the plasma edge, consistent with calculations. The pellet payloads were observed to ionize rapidly in the pellet vicinity (

Resistive neoclassical tearing modes (NTMs) will be the principal limit on stability and performance in the ITER standard scenario as the resulting islands break up the magnetic surfaces that confine the plasma. Drag from rotating island‐induced eddy current in the resistive wall can also slow the plasma rotation, produce locking to the wall, and cause loss of high confinement H‐mode and disruption. The NTMs are maintained by helical perturbations to the pressure‐gradient driven “bootstrap” current. Thus, this is a high beta instability even at the modest beta for ITER. A major line of research on NTM stabilization is the use of radio frequency (rf) current drive at the island rational surface. While large, broad current drive from lower hybrid waves has been shown to be stabilizing (COMPASS‐D), most research is directed to small, narrow current drive from electron cyclotron waves (ECCD); ECCD stabilization and/or preemptive prevention is successful in ASDEX Upgrade, DIII‐D and JT‐60U, for example, with a...

Neoclassical tearing modes (NTMs) are MHD modes which can become destabilized in a tokamak by a helical pressure perturbation. The NTM is particularly well suited to control since the mode is linearly stable although nonlinearly unstable, so if the island amplitude can be decreased below a threshold size the mode will decay and vanish. One means of shrinking the island is the replacement of the ''missing'' bootstrap current by a localized current generated by electron cyclotron current drive (ECCD). This method has been applied to the m=3/n=2 and the 2/1 tearing modes in DIII-D, in H-mode plasmas with ongoing ELMs and sawteeth, both of which generate seed islands periodically. In the case of the 3/2 mode, full suppression was obtained robustly by applying about 1.5 MW of ECCD very near the flux surface of maximum mode amplitude. When the mode first appears in the plasma the stored energy decreases by 30%, but when the mode is stabilized by the ECCD the beta may be raised above the initial threshold pressure by 20% by additional neutral beam heating, thereby effecting an improvement in the limiting beta of nearly a factor 2. An innovative automated search algorithm was implemented to find andmore » retain the optimum location for the ECCD in the presence of the mode. Only partial success has been obtained in stabilizing the 2/1 mode by ECCD, but calculations indicate that ECCD power near 3 MW should be adequate for complete suppression of this mode.« less

Complete suppression of the m=2/n=1 neoclassical tearing mode (NTM) is reported for the first time using electron cyclotron current drive (ECCD) to noninductively generate current at the radius of the island O‐point. Experiments on the DIII‐D tokamak show that the maximum shrinkage of the m=2/n=1 island amplitude occurs when the ECCD location coincides with the q=2 surface. Estimates of the ECCD radial profile width from the island shrinkage are consistent with ray tracing calculations but may allow for a factor‐of‐1.5 broadening from electron radial transport.

A271 ELECTRON CYCLOTRON CURRENT DRIVE IN DIII-D: EXPERIMENT AND THEORY. Experiments on the DIII-D tokamak in which the measured off-axis electron cyclotron current drive has been compared systematically to theory over a broad range of parameters have shown that the Fokker-Planck code CQL3D provides an excellent model of the relevant current drive physics. This physics understanding has been critical in optimizing the application of ECCD to high performance discharges, supporting such applications as suppression of neoclassical tearing modes and control and sustainment of the current profile.

Tearing modes have been shown to limit β and confinement in conventional ELMing H-mode tokamak regimes. The tearing modes grow from a “seed” island due to the destabilizing effect of pressure flattening in the island leading to a reduction in the local bootstrap current. Recent experiments on the DIII-D tokamak have demonstrated stabilization of m=3/n=2 tearing modes in the presence of sawteeth through localized electron cyclotron current drive (ECCD). Variation of the deposition location indicates the ECCD remains localized despite the beam traversing an ELMing edge. The effect of the ECCD on the mode is consistent with predictions that the ECCD must be within the island for stabilization. The calculated EC current density (JEC) is greater than the calculated local bootstrap current density (JBS) also in accord with predictions. A closed-loop feedback scheme has been successfully operated for the first time using position control and magnetic signals as the actuator and sensor, respectively.

Neoclassical tearing modes are found to limit the achievable beta in many high performance discharges in DIII-D. Electron cyclotron current drive within the magnetic islands formed as the tearing mode grows has been proposed as a means of stabilizing these modes or reducing their amplitude, thereby increasing the beta limit by a factor around 1.5. Some experimental success has been obtained previously on Asdex-U. Here we examine the parameter range in DIII-D in which this effect can best be studied.

13MW of electron cyclotron current drive (ECCD) power deposited inside the q = 1 surface is likely to reduce the sawtooth period in ITER baseline scenario below the level empirically predicted to trigger neo-classical tearing modes (NTMs). However, since the ECCD control scheme is solely predicated upon changing the local magnetic shear, it is prudent to plan to use a complementary scheme which directly decreases the potential energy of the kink mode in order to reduce the sawtooth period. In the event that the natural sawtooth period is longer than expected, due to enhanced alpha particle stabilisation for instance, this ancillary sawtooth control can be provided from > 10MW of ion cyclotron resonance heating (ICRH) power with a resonance just inside the q = 1 surface. Both ECCD and ICRH control schemes would benefit greatly from active feedback of the deposition with respect to the rational surface. If the q = 1 surface can be maintained closer to the magnetic axis, the efficacy of ECCD and ICRH schemes significantly increases, the negative effect on the fusion gain is reduced, and off-axis negative-ion neutral beam injection (NNBI) can also be considered for sawtooth control. Consequently, schemes to reduce the q = 1 radius are highly desirable, such as early heating to delay the current penetration and, of course, active sawtooth destabilisation to mediate small frequent sawteeth and retain a small q = 1 radius., 29 pages, 16 figures

It is found that flow shear has a stabilizing effect on m/n=3/2 neoclassical tearing mode islands through a more negative classical tearing stability index Δ′ in the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] tokamak. The heating neutral beams are mixed between co- and counter-directions to vary the torque on the plasma and thus the plasma flow (rotation) and flow shear. This is done “shot to shot” in the presence of a saturated m/n=3/2 neoclassical tearing mode (NTM) while slowly raising the plasma beta up to the limit of the onset of an m/n=2/1 mode. A heuristic model for the stabilizing effect of flow shear on Δ′ is shown to explain how flow shear acts to reduce NTM island size and obviate the effect of higher beta and concomitant destabilizing helically perturbed bootstrap current.

The DIII-D Advanced Tokamak (AT) program in the DIII-D tokamak [J. L. Luxon, Plasma Physics and Controlled Fusion Research, 1986, Vol. I (International Atomic Energy Agency, Vienna, 1987), p. 159] is aimed at developing a scientific basis for steady-state, high-performance operation in future devices. This requires simultaneously achieving 100% noninductive operation with high self-driven bootstrap current fraction and toroidal beta. Recent progress in this area includes demonstration of 100% noninductive conditions with toroidal beta, βT=3.6%, normalized beta, βN=3.5, and confinement factor, H89=2.4 with the plasma current driven completely by bootstrap, neutral beam current drive, and electron cyclotron current drive (ECCD). The equilibrium reconstructions indicate that the noninductive current profile is well aligned, with little inductively driven current remaining anywhere in the plasma. The current balance calculation improved with beam ion redistribution that was supported by recent fast ion diagno...

Active control of the resistive wall mode (RWM) for DIII-D [Luxon and Davis, Fusion Technol. 8, 441 (1985)] plasmas is studied using the MARS-F code [Y. Q. Liu, Phys. Plasmas 7, 3681 (2000)]. Control optimization shows that the mode can be stabilized up to the ideal wall beta limit, using the internal control coils (I-coils) and poloidal sensors located at the outboard midplane, in combination with an ideal amplifier. With the present DIII-D power supply model, the stabilization is achieved up to 70% of the range between no-wall and ideal-wall limits. Reasonably good quantitative agreement is achieved between MARS-F simulations and experiments on DIII-D and JET (Joint European Torus) [P. H. Rebut, Nucl. Fusion 25, 1011 (1985)] on critical rotation for the mode stabilization. Dynamics of rotationally stabilized plasmas is well described by a single mode approximation; whilst a strongly unstable plasma requires a multiple mode description. For ITER [R. Aymar, P. Barabaschi, and Y. Shimomura, Plasma Phys. Controlled Fusion 44, 519 (2002)], the MARS-F simulations show the plasma rotation may not provide a robust mechanism for the RWM stabilization in the advanced scenario. With the assumption of ideal amplifiers, and using optimally tuned controllers and sensor signals, the present feedback coil design in ITER allows stabilization of the n=1 RWM for plasma pressures up to 80% of the range between the no-wall and ideal-wall limits.

An electron cyclotron heating experiment is described in which 28 GHz microwave power is launched from the high field side (inside) of a tokamak discharge from a steerable phased array antenna exciting the extraordinary mode. The central temperature was doubled (from 600 eV to 1200 eV) with a power at the antenna approximately two‐thirds the Ohmic input. An oblique launch of the extraordinary mode was found to heat more efficiently and to a higher density than either the perpendicularly launched extraordinary mode or the ordinary mode launched from the outside.