Low Toroidal Mode Number Research Articles

Development and validation of a critical gradient energetic particle driven Alfven eigenmode transport model for DIII-D tilted neutral beam experiments

Recent experiments with the DIII-D tilted neutral beam injection (NBI) varying the beam energetic particle (EP) source profiles have provided strong evidence that unstable Alfven eigenmodes (AE) drive stiff EP transport at a critical EP density gradient [Heidbrink et al 2013 Nucl. Fusion 53 093006]. Here the critical gradient is identified by the local AE growth rate being equal to the local ITG/TEM growth rate at the same low toroidal mode number. The growth rates are taken from the gyrokinetic code GYRO. Simulation show that the slowing down beam-like EP distribution has a slightly lower critical gradient than the Maxwellian. The ALPHA EP density transport code [Waltz and Bass 2014 Nucl. Fusion 54 104006], used to validate the model, combines the low-n stiff EP critical density gradient AE mid-core transport with the Angioni et al (2009 Nucl. Fusion 49 055013) energy independent high-n ITG/TEM density transport model controling the central core EP density profile. For the on-axis NBI heated DIII-D shot 146102, while the net loss to the edge is small, about half the birth fast ions are transported from the central core r/a < 0.5 and the central density is about half the slowing down density. These results are in good agreement with experimental fast ion pressure profiles inferred from MSE constrained EFIT equilibria.

Studies of the non-axisymmetric plasma boundary displacement in JET in presence of externally applied magnetic field

Non-axisymmetric plasma boundary displacement is caused by the application of the external magnetic field with low toroidal mode number. Such displacement affects edge stability, power load on the first wall and could affect efficiency of the ICRH coupling in ITER. Studies of the displacement are presented for JET tokamak focusing on the interaction between error field correction coils (EFCCs) and shape control system. First results are shown on the direct measurement of the plasma boundary displacement at different toroidal locations. Both qualitative and quantitative studies of the plasma boundary displacement caused by interaction between EFCCs and shape control system are performed for different toroidal phases of the external field. Axisymmetric plasma boundary displacement caused by the EFCC/shape control system interaction is seen for certain phase values of the external field. The value of axisymmetric plasma boundary displacement caused by interaction can be comparable to the non-axisymmetric plasma boundary displacement value produced by EFCCs.

Magnetic control of magnetohydrodynamic instabilities in tokamaks

Externally applied, non-axisymmetric magnetic fields form the basis of several relatively simple and direct methods to control magnetohydrodynamic (MHD) instabilities in a tokamak, and most present and planned tokamaks now include a set of non-axisymmetric control coils for application of fields with low toroidal mode numbers. Non-axisymmetric applied fields are routinely used to compensate small asymmetries (δB/B∼10−3 to 10−4) of the nominally axisymmetric field, which otherwise can lead to instabilities through braking of plasma rotation and through direct stimulus of tearing modes or kink modes. This compensation may be feedback-controlled, based on the magnetic response of the plasma to the external fields. Non-axisymmetric fields are used for direct magnetic stabilization of the resistive wall mode—a kink instability with a growth rate slow enough that feedback control is practical. Saturated magnetic islands are also manipulated directly with non-axisymmetric fields, in order to unlock them from the wall and spin them to aid stabilization, or position them for suppression by localized current drive. Several recent scientific advances form the foundation of these developments in the control of instabilities. Most fundamental is the understanding that stable kink modes play a crucial role in the coupling of non-axisymmetric fields to the plasma, determining which field configurations couple most strongly, how the coupling depends on plasma conditions, and whether external asymmetries are amplified by the plasma. A major advance for the physics of high-beta plasmas (β = plasma pressure/magnetic field pressure) has been the understanding that drift-kinetic resonances can stabilize the resistive wall mode at pressures well above the ideal-MHD stability limit, but also that such discharges can be very sensitive to external asymmetries. The common physics of stable kink modes has brought significant unification to the topics of static error fields at low beta and resistive wall modes at high beta. These and other scientific advances, and their application to control of MHD instabilities, will be reviewed with emphasis on the most recent results and their applicability to ITER.

Characterization of peeling modes in a low aspect ratio tokamak

Peeling modes are observed at the plasma edge in the Pegasus Toroidal Experiment under conditions of high edge current density (Jedge ∼ 0.1 MA m−2) and low magnetic field (B ∼ 0.1 T) present at near-unity aspect ratio. Their macroscopic properties are measured using external Mirnov coil arrays, Langmuir probes and high-speed visible imaging. The modest edge parameters and short pulse lengths of Pegasus discharges permit direct measurement of the internal magnetic field structure with an insertable array of Hall-effect sensors, providing the current profile and its temporal evolution. Peeling modes generate coherent, edge-localized electromagnetic activity with low toroidal mode numbers n ⩽ 3 and high poloidal mode numbers, in agreement with theoretical expectations of a low-n external kink structure. Coherent MHD fluctuation amplitudes are found to be strongly dependent on the experimentally measured Jedge/B peeling instability drive, consistent with theory. Peeling modes nonlinearly generate ELM-like, field-aligned filamentary structures that detach from the edge and propagate radially outward. The KFIT equilibrium code is extended with an Akima spline profile parameterization and an improved model for induced toroidal wall current estimation to obtain a reconstruction during peeling activity with its current profile constrained by internal Hall measurements. It is used to test the analytic peeling stability criterion and numerically evaluate ideal MHD stability. Both approaches predict instability, in agreement with experiment, with the latter identifying an unstable external kink.

Rapid shutdown experiments with one and two gas jets on Alcator C-Mod

Massive gas injection rapid shutdown experiments have been conducted on the Alcator C-Mod tokamak using two toroidally separated gas injectors, in order to investigate the effect of multiple gas injection locations on the toroidal asymmetry in the radiated power. Toroidal radiation asymmetry is diagnosed by an array of six single-channel photodiodes mounted on the vessel wall. The presence of magnetohydrodynamic (MHD) activity is diagnosed using an array of magnetic pickup (Mirnov) coils, mounted on stalks on the vessel wall. Scans were conducted of the relative timing between the two jets, of the 95th percentile safety factor, and of the plasma elongation. It is observed that firing the two gas jets so that the injected impurities arrive at the plasma at nearly the same time produced an increase in the toroidal radiation asymmetry. In addition, the radiation asymmetry in the thermal quench phase correlates with the growth rate of low toroidal mode number MHD modes, indicating that these mode(s) are playing a role in setting the radiation asymmetry.

Stability analysis of high-beta plasmas in the Joint European Torus

The linear stability of ideal instabilities with low toroidal mode numbers has been assessed for various high-beta plasmas in JET including steady-state and hybrid scenarios. Results of detailed stability analysis of discharges with the minimum in safety factor near 1, 3/2 and 2 are presented. In all cases, the plasmas are found to become unstable to global ideal kink-ballooning modes as the minimum safety factor decreases with the current diffusion. The plasmas are found to exhibit continuous modes experimentally which degrade performance, with the mode onset being extremely well correlated with the crossing of the numerically predicted stability boundaries. The most favorable profiles for global stability have also been assessed.

Measurement of Peeling Mode Edge Current Profile Dynamics

Peeling modes, an instability mechanism underlying deleterious edge localized mode (ELM) activity in fusion-grade plasmas, are observed at the edge of limited plasmas in a low aspect ratio tokamak under conditions of high edge current density (J(edge) ∼ 0.1 MA/m2) and low magnetic field (B ∼ 0.1 T). They generate edge-localized, electromagnetic activity with low toroidal mode numbers n≤3 and amplitudes that scale strongly with measured J(edge)/B instability drive, consistent with theory. ELM-like field-aligned, current-carrying filaments form from an initial current-hole J(edge) perturbation that detach and propagate outward.

Active excitation and damping rate measurement of intermediate-n toroidal Alfvén eigenmodes in JET, C-Mod and MAST plasmas

The stability properties of Alfvén eigenmodes (AEs) are investigated directly using external antenna excitation and detection of stable modes in a variety of plasma configurations in different devices. Dedicated methods to measure the AE damping rate separately from the fast ion drive have been pioneered at JET, using low toroidal mode number internal saddle coil antennas. Other experiments have since installed localized in-vessel antennas to drive and detect MHD modes in the Alfvén frequency range, first on C-Mod, then on MAST. Experiments on C-Mod proved for the first time that intermediate-n toroidal AEs can be driven and detected, and point out significant differences with respect to the low-n regime on JET in the values and scaling of the damping rate with plasma parameters, e.g. the edge shape. On JET, a new antenna system, comprising two assemblies of four toroidally spaced coils each, was developed to replace the low-n saddle coil structure and excite AEs in the toroidal mode number range that is expected to be most unstable in ITER, with n up to ∼10. Experiments with the new JET antennas confirm that excitation is possible in a large volume plasma, together with real-time tracking of core modes throughout the limiter and divertor phases of high performance discharges, with significant additional heating. The similarities and differences between the active MHD antenna systems as well as a comparison of the results on C-Mod, JET and MAST are illustrated. Both C-Mod and JET results underline the fact that a precise reconstruction of the mode structure and its spectrum, important for a quantitative comparison with theoretical models, represents a significant challenge in the intermediate-n range and in the presence of several modes.

Spectra of magnetic perturbations triggered by pellets in JET plasmas

Aiming at investigating edge localised mode (ELM) pacing for future application on ITER, experiments have been conducted on JET injecting pellets in different plasma configurations, including high confinement regimes with type-I and type-III ELMs, low confinement regimes and Ohmically heated plasmas. The magnetic perturbations spectra and the toroidal mode number, n, of triggered events are compared with those of spontaneous ELMs using a wavelet analysis to provide good time resolution of short-lived coherent modes. It is found that—in all these configurations—triggered events have a coherent mode structure, indicating that pellets can trigger an MHD event basically in every background plasma. Two components have been found in the magnetic perturbations induced by pellets, with distinct frequencies and toroidal mode numbers. In high confinement regimes triggered events have similarities with spontaneous ELMs: both are seen to start from low toroidal mode numbers, then the maximum measured n increases up to about 10 within 0.3 ms before the ELM burst.

Excitation of stable Alfvén eigenmodes by application of alternating magnetic field perturbations in the Compact Helical System

Stable toroidicity-induced Alfvén eigenmodes (TAEs) with low toroidal mode number (n=1 and n=2) were excited by application of alternating magnetic field perturbations generated with a set of electrodes inserted into the edge region of neutral beam injection heated plasmas on the Compact Helical System [K. Nishimura, K. Matsuoka, M. Fujiwara et al., Fusion Technol. 17, 86 (1990)]. The gap locations of TAEs excited by the electrodes are in the plasma peripheral region of ρ&amp;gt;0.7 (ρ is the normalized minor radius) where energetic ion drive is negligibly small, while some AEs are excited by energetic ions in the plasma core region of ρ&amp;lt;0.4. The damping rate of these stable TAEs derived from plasma responses to applied perturbations is fairly large, that is, ∼9% to ∼12% of the angular eigenfrequency. This large damping rate is thought to be dominantly caused by continuum damping and radiative damping.

Contribution of the Large Helical Device Plasmas to Alfvén Eigenmode Physics in Toroidal Plasmas

In the large helical device (LHD) having three dimensional configuration, Alfvén eigenmodes (AEs) destabilized by energetic ions are widely investigated using neutral beam heated plasmas with monotonic and non-monotonic rotational transform (ι/2π) profiles. In a plasma with monotonic ι/2π-profile, core-localized toroidicity-induced Alfvén eigenmode (TAE) as well as global one are often observed. With the increase in the averaged toroidal beta value, defined as the ratio of total plasma pressure to toroidal magnetic pressure, core-localized TAE with low toroidal mode number becomes global. In a relatively high beta plasma with monotonic ι/2π-profile, two TAEs with different toroidal mode number often interact nonlinearly and generate another modes through three wave coupling. In a plasma with non-monotonic ι/2π-profile generated by intense counter neutral beam current drive, reversed shear Alfvén eigenmode (RSAE) and geodesic acoustic mode (GAM) excited by energetic ions were observed for the first time in a helical plasma. Nonlinear coupling was also observed between RSAE and GAM.

Active control of edge localized modes with a low n perturbation fields in the JET tokamak

Active control of edge localized modes (ELMs) by using static external magnetic perturbation fields with low toroidal mode number, n, has been demonstrated for both, ITER baseline ( q 95 ∼ 3 ) and high beta advanced tokamak scenarios at the JET tokamak. During the application of the low n field the ELM frequency increased by a factor up to ∼4–5. Reduction in carbon erosion and ELM peak heat fluxes on the divertor target by roughly the same factor as the increase of the ELM frequency has been observed. The frequency of the mitigated ELMs using a low n field is found to increase proportional to the total input heating power. Compensation of the density pump-out effect observed when the external low n field is applied has been achieved by gas fueling in low triangularity plasmas.

Edge stability of stationary ELM-suppressed regimes on DIII-D

We discuss the MHD stability of the H-mode pedestal region in two edge localized mode (ELM)-suppressed H-mode regimes on DIII-D, the quiescent (Q)H-mode and resonant magnetic perturbation (RMP) H-mode. The QH-mode is obtained at low density with most of the neutral beam power injected counter to the plasma current, and is characterized by a continuous, low toroidal mode number (n), edge harmonic oscillation (EHO). QH-mode is observed to transition back to ELMing H-mode as the rotational shear is decreased by increasing the co-current neutral beam power fraction or by increasing the plasma to conducting wall distance, consistent with a model for the EHO as a peeling instability with added drive from rotational shear, which saturates through self transport of momentum or damping of rotation through drag of the mode on the conducting wall. In RMP H-mode, an n = 3 coil provides the non-axisymmetric perturbation. Two regimes of RMP ELM suppression are observed. At low collisionality with large resonant field perturbation, the pedestal pressure gradient and current density are reduced below the peeling-ballooning mode stability limit; while at higher collisionality with large non-resonant perturbation there is little change in the pedestal parameters and type II ELMs are enhanced.

Modelling of ELM dynamics for DIII-D and ITER

A model for integrated modelling studies of edge localized modes (ELMs) in ITER is discussed in this paper. Stability analyses are carried out for ITER and DIII-D equilibria that are generated with the TEQ and TOQ equilibrium codes. The H-mode pedestal pressure and parallel current density are varied in a systematic way in order to span the relevant parameter space for specific ITER plasma parameters. The ideal MHD stability codes, DCON, ELITE and BALOO, are employed to determine whether or not each ITER equilibrium profile is unstable to peeling or ballooning modes in the pedestal region. Several equilibria that are close to the marginal stability boundary for peeling and ballooning modes are tested with the NIMROD non-ideal MHD code. When the effects of finite resistivity are studied in a series of linear NIMROD computations, it is found that the peeling–ballooning stability threshold is very sensitive to the resistivity and viscosity profiles, which vary dramatically over a wide range near the separatrix. When two-fluid gyro-viscous and Hall effects are included in NIMROD computations, it is found that harmonics with high toroidal mode numbers are stabilized while the growth rate of harmonics with low toroidal mode numbers are only moderately reduced. When flow shear across the H-mode pedestal is included, it is found that linear growth rates are increased, particularly for harmonics with high toroidal mode numbers. In nonlinear NIMROD simulations, ELM crashes produce filaments that extend out to the wall in the absence of flow shear. When flow shear is included, the filaments are dragged by the fluid and sheared off before they extend to the wall.

Energetic Particle Physics Studies on Alcator C-Mod

Energetic particle physics is studied in Alcator C-Mod in reactor relevant regimes with high density and equilibrated electron and ion temperatures. Stable Alfvén eigenmodes are excited with low-power active magnetohydrodynamic antennas in the absence of a significant energetic particle tail to directly measure the damping rate of the modes. Stable toroidal Alfvén eigenmode (TAE) damping rates between 0.5% < γ/Ω < 4.5% have been observed in diverted and limited plasmas. Alfvén eigenmodes are destabilized with high-power hydrogen minority ion cyclotron radio frequency (ICRF) heating (PICRF < 6 MW) in lower-density plasmas in the current rise and in relatively high-density ([bar]ne < 2.5 × 1020 m-3) H-mode plasmas, which creates an energetic hydrogen ion tail with calculated energies up to 400 keV. Low toroidal mode number (n < 4) unstable modes are observed in the current rise with magnetic pickup coils at the wall and phase contrast imaging density fluctuation measurements in the core. Observations of energetic particle modes or TAEs that decrease in frequency and mode number with time up to a large sawtooth collapse indicate that fast particles play a role in stabilizing sawteeth. Alfvén eigenmodes can also be used as diagnostics to precisely constrain the q profile and provide a qualitative measure of the fast particle distribution time evolution.

Numerical Method for the Stability Analysis of Ideal MHD Modes with a Wide Range of Toroidal Mode Numbers in Tokamaks

A numerical method for the stability analysis of ideal MHD modes is devised by using a physical model based on the two-dimensional Newcomb equation in combination with the conventional ideal MHD model. The MARG2D code based on this numerical method is able to analyze the stability of ideal MHD modes with a wide range of toroidal mode numbers. The validity of the MARG2D code has been confirmed through benchmarking tests using the DCON code for the low toroidal mode number MHD mode analysis, and tests using the ELITE code for intermediate to high toroidal mode number mode analysis. By using the MARG2D code, the MHD stability property of JT-60SA, the complemental device of ITER, is investigated with a focus on the effect of the plasma shape.

Optimization of DIII-D advanced tokamak discharges with respect to the β limit

Results are presented from comparisons of modeling and experiment in studies to assess the best choices of safety factor q profile, pressure profile, and discharge shape for high β, steady-state, noninductive advanced tokamak operation in the DIII-D device [J. L. Luxon, Nucl. Fusion 42, 614 (2002)]. These studies are motivated by the need for high qminβN to maximize the self-driven bootstrap current while maintaining high toroidal β to increase fusion gain. Modeling shows that increases in the normalized beta βN stable to ideal, low toroidal mode number (n=1,2), instabilities can be obtained through broadening of the pressure profile and use of a symmetric double-null divertor shape. Experimental results are in agreement with this prediction. The general trend is for qminβN to increase with the minimum q value (qmin) although βN decreases as qmin increases. By broadening the pressure profile, βN≈4 is obtained with qmin≈2. Modeling of equilibria with near 100% bootstrap current indicates that operation with βN≈5 should be possible with a sufficiently broad pressure profile.

The resistive wall mode and feedback control physics design in NSTX

One of the goals of the National Spherical Torus Experiment (NSTX) is to investigate the physics of global mode stabilization in a low aspect ratio device. NSTX has a major radius R0 = 0.86 m, a midplane half-width of 0.7 m, and an on-axis vacuum toroidal field B0 ⩽ 0.6 T and has reached a plasma current Ip = 1.5 MA. Experiments have established the wall-stabilized MHD operating space of the machine. The maximum βt and βN have reached 35% and 6.5%, respectively, with βN reaching 9.5li. Collapses in plasma toroidal rotation and βt have been correlated with violation of the n = 1 ideal MHD beta limit, βN no−wall, computed by the DCON stability code using time-evolving EFIT reconstructions of experimental discharges. The resistive wall mode (RWM) was observed over a wide range of βN when βN no−wall was exceeded. Plasma toroidal rotation damping during the RWM was rapid and global. Damping rates were more than five times larger than caused by low toroidal mode number rotating modes alone, which displayed a slower, diffusive rotation damping away from the rational surface. The rotation damping rate and dynamics depend on the applied toroidal field and the computed minimum value of the safety factor. The computed RWM perturbed field structure from experimental plasma reconstructions has been input to the VALEN feedback analysis code for quantitative comparison of experimental and theoretical RWM growth rates and to analyse the effectiveness of various active feedback stabilization designs. The computed RWM n = 1 mode growth rate, which depends on plasma equilibrium parameters such as βN and pressure profile peaking, agrees well with experimental growth rates in different operating regimes. Increasing βN in the ST initially improves mode coupling to the stabilizing wall; however, at the highest βN values reached, the ideal with-wall beta limit, βN wall, is approached, the effectiveness of the passive stabilizing plates is reduced, and the computed RWM growth rate approaches ideal MHD growth rates. Several active mode control designs were considered and evaluated. The most effective configuration is computed to provide stabilization at βN up to 94% of the ideal with-wall limit.

Edge localized magnetosonic eigenmodes in the ion cyclotron frequency range

Edge localized magnetosonic modes are analyzed in toroidal plasmas. For low and medium high toroidal mode numbers they are found to propagate poloidally around the plasma. A model of these modes is developed and benchmarked against a global wave code. The eigenvalues are found to be almost independent of the aspect ratio for constant minor radius, but sensitive to the ellipticity. Magnetosonic modes localized to an annular region in the poloidal plane have been proposed as an explanation for ion cyclotron emission from the edge and strongly localized mode conversion. The appearance of such modes will also give rise to parasitic absorption at the edge during ion cyclotron resonance heating.

Magnetohydrodynamic Stability of Improved Confinement Plasmas in JT-60U

Progress in the understanding of magnetohydrodynamic (MHD) stability is summarized on JT-60U tokamak discharges with improved confinement such as the (hot-ion) H-mode, high-βp mode, high-βp H-mode, and reversed shear discharges. Transport barriers, which are essential for the improved confinement, play key roles in the local and global MHD stability owing to the local large pressure gradient and the related bootstrap current. Disruptive β limits of these discharges are consistent with theoretical ideal kink-ballooning stability limits with low toroidal mode numbers n. Achievable β limit is improved by broadening of the pressure profile with high plasma internal inductance, plasma shaping, and wall stabilization. Edge localized modes (ELMs) and barrier localized modes (BLMs), which are associated with edge and internal transport barriers, respectively, are analyzed carefully. Resistive interchange modes with n ≤ 3 are excited in the negative shear region in reversed shear discharges with the internal transport barrier and lead to major collapse occasionally through nonlinear coupling with a tearing mode in the positive shear region. MHD characteristics of low m/n (m: poloidal mode number) tearing modes, which are attributed to the neoclassical tearing mode, are investigated. Stabilization of tearing modes and control of sawtooth activity are demonstrated using the fundamental O-mode electron cyclotron wave injection. Resistive wall modes associated with current-driven and pressure-driven low n external kink modes are identified.