Radial Mode Structure Research Articles

Study on filament width of type-I ELM in EAST using VUV imaging system and simulation

The poloidal width of the filaments induced by the type-I edge localized mode has power dependence in EAST. The poloidal widths of the filaments observed by the high-speed vacuum ultraviolet (VUV) imaging system are proportional to the heating power and the ELM size. To understand this power dependence, the BOUT++ nonlinear simulations have been performed with the reconstructed equilibriums from the experimental measurements in this paper. The synthetic filament structures from BOUT++ nonlinear simulation match the experimental observations by the VUV imaging system. The BOUT++ nonlinear simulations also reproduce the power dependence of the filament widths and the ELM size. The filament width and the ELM size are inversely proportional to the toroidal mode number. The low-n mode has a broader radial and poloidal structure, which causes the larger filament width and ELM size. In the high input power case, the mode spectrum shifts to low-n, a result of increasing peeling drive. Besides, we found the β p in a higher input power case leads to a broader pedestal, expanding the radial mode structure of the peeling-ballooning mode.

Alfvén cascade eigenmodes above the TAE-frequency and localization of Alfvén modes in D–3He plasmas on JET

Various types of Alfvén eigenmodes (AEs) have been destabilized by fast ions over a broad frequency range from ∼80 kHz to ∼700 kHz in a series of JET experiments in mixed D–3He plasmas heated with the three-ion ICRF scenario (2020 Nocente et al Nucl. Fusion 60 124006). In this paper, we identify the radial localization of AEs using an X-mode reflectometer, a multiline interferometer and soft x-ray diagnostics. The analysis is focused on the most representative example of these measurements in JET pulse #95691, where two different types of Alfvén cascade (AC) eigenmodes were observed. These modes originate from the presence of a local minimum of the safety factor q min. In addition to ACs with frequencies below the frequency of toroidal Alfvén eigenmodes (TAEs), ACs with frequencies above the TAE frequency were destabilized by energetic ions. Both low- (f ≈ 80–180 kHz) and high-frequency (f ≈ 330–450 kHz) ACs were localized in the central regions of the plasma. The characteristics of the high-frequency ACs are investigated in detail numerically using HELENA, CSCAS and MISHKA codes. The resonant conditions for the mode excitation are found to be determined by passing ions of rather high energy of several hundred keV and similar to those established in JT-60U with negative-ion-based NBI (2005 Takechi et al Phys. Plasmas 12 082509). The computed radial mode structure is found to be consistent with the experimental measurements. In contrast to low-frequency ACs observed most often, the frequency of the high-frequency ACs decreases with time as the value of q min decreases. This feature is in a qualitative agreement with the analytical model of the high-frequency ACs in Breizman et al (2003 Phys. Plasmas 10 3649). The high-frequency AC could be highly relevant for future ITER and fusion reactor plasmas dominated by ∼MeV energetic ions, including a significant population of passing fast ions.

Multiscale Chirping Modes Driven by Thermal Ions in a Plasma with Reactor-Relevant Ion Temperature.

A thermal ion driven bursting instability with rapid frequency chirping, considered as an Alfvénic ion temperature gradient mode, has been observed in plasmas having reactor-relevant temperature in the DIII-D tokamak. The modes are excited over a wide spatial range from macroscopic device size to microturbulence size and the perturbation energy propagates across multiple spatial scales. The radial mode structure is able to expand from local to global in ∼0.1 ms and it causes magnetic topology changes in the plasma edge, which can lead to a minor disruption event. Since the mode is typically observed in the high ion temperature ≳10 keV and high-β plasma regime, the manifestation of the mode in future reactors should be studied with development of mitigation strategies, if needed. This is the first observation of destabilization of the Alfvén continuum caused by the compressibility of ions with reactor-relevant ion temperature.

Linear MHD analyses of locked-mode-like instabilities in LHD

To investigate the driving mechanism of the locked-mode-like instability observed in the large helical device, we reconstruct the magnetohydrodynamic (MHD) equilibria consistent with the measurement and identify a dominant MHD instability in the precursor phase based on linear MHD analyses. From the dependence of the linear growth rate on the magnetic Reynolds number, the radial mode structure of the electrostatic potential fluctuation and other indices, the ideal interchange mode is found to be dominant. Moreover, it is found that the Mercier parameter, D I, becomes much larger than 0.3 during the phase, while the precursor has constant frequency and fluctuation amplitude. Therefore, D I ≫ 0.3 is a good index of the on-set condition of the minor collapse itself. It is also found that the achievement of D I ≫ 0.3 is due to the movement of the resonant surface to the inner plasma region, which corresponds to the larger pressure gradient region.

Systematic simulation studies on the penetration of resonant magnetic perturbations in an Experimental Advanced Superconducting Tokamak

The penetration properties of the n = 1 resonant magnetic perturbations (RMPs) with toroidal rotation are systematically studied by the upgraded three-dimensional toroidal magnetohydrodynamic code CLTx, through both linear and nonlinear simulations. It is found that in the presence of toroidal plasma rotation, the saturation state for high resonant harmonics is obtained in linear simulations due to the mode becoming unlocked from the internal magnetic islands. In nonlinear simulations, nonlinear effects become important when the toroidal plasma rotation is not included. The zonal component resulting from the nonlinear mode coupling is necessary for the saturation of the whole system including the internal kink mode and the m /n = 2/1 tearing mode. The simulations of RMP penetration demonstrate that the mode coupling is associated with the toroidal effect rather than nonlinear effects. With a low resistivity close to the experimental value, the single-harmonic-RMP is hard to penetrate the mode-rational surface because of the plasma screening effects, resulting in a truncation of the radial mode structure. On the other hand, the non-resonant components in the multiple-harmonic-RMP could largely reduce the effect of the plasma shielding, which leads to that the RMP is able to penetrate deeply into the central plasma region through the poloidal harmonic coupling.

Fishbone instability driven by trapped fast ions in a toroidal plasma with reversed magnetic shear

Based on the non-perturbative approach, the hybrid code MARS-K is applied to study fishbone (FB) instabilities driven by trapped fast ions in a toroidal plasma with q profile nearly being flat or non-monotonic. We explore the dependency of the FB with variation in the fast ion distribution, thermal particle kinetic effects, safety factor (q) profile and plasma resistivity. When the safety factor minimum value is larger than unity (i.e. ), the mode can be excited by isotropic or anisotropic fast ions, with the latter strongly enhancing the mode growth rate. The mode frequency increases with increasing , and is more easily triggered in a equilibrium with two q = 1 surfaces, compared with the case with one or no q = 1 surface. Kinetic contributions from transit resonance of passing fast ions and from bounce resonance of trapped fast ions strongly enhance mode instability. The passing thermal ions induced Landau damping has a strong stabilization effect. Furthermore, in such a weak, even reversed magnetic shear plasma, the radial mode structure of FB mode monotonically decreases to zero at q = 1 flux surface instead of a step-like function, and it depends on the kinetic contributions from particles. In addition, the plasma resistivity significantly stabilizes the mode near the marginally unstable point.

Global geodesic acoustic mode in an ideal magnetohydrodynamic tokamak plasma

A concise and transparent second order ordinary differential equation (ODE) describing the radial structure of the global geodesic acoustic mode (GAM) is analytically presented in a low-β tokamak plasma. The large-aspect-ratio and circular cross section are assumed to linearize the ideal magnetohydrodynamic equations. We show clearly how finite β-dependent terms affect the global GAM frequency and radial mode structure. A typical Wentzel–Kramers–Brillouin form of solution is found for some reversed shear equilibria. For some other equilibria with lower β, even also in a reversed shear tokamak, the GAM continuum is upraised by the high order β-dependent terms so that its maximum is beyond ωG, where ωG is the classical local frequency of GAM. As a result, no self-consistent solution to the ODE can be found.

Electron temperature profile collapse induced by double-odd-parity MHD mode in the Large Helical Device

In this paper, we report new results of a beam switching experiment aiming at a reversed magnetic shear profile formation for the study of an MHD-mode-induced profile collapse event. A transient MHD mode, whose oscillation frequency chirps down, is observed. The electron temperature profile collapse is induced by the mode activity, leading to the flattening of the central electron temperature profile. The radial mode structure is the double-odd-parity at the beginning, but it transits to the even-parity in its final stage. The central electron temperature profile recovers after the radial mode structure changes to the even-parity, even though the mode itself does not disappear.

Recent Doppler backscattering applications in Globus-M tokamak

Recently, a four-frequency Doppler backscattering (DBS) system was installed on the Globus-M tokamak. In addition to the classical DBS application for determining the mean plasma rotational velocities, DBS was used for the investigation of different plasma oscillatory processes in the spherical Globus-M tokamak. Application of various DBS data processing allowed us to reveal and investigate plasma oscillations, such as geodesic acoustic mode, limit cycle oscillations and Alfvén modes. It has been shown that DBS also allows registering filament like structures, which manifest as quasi-coherent oscillations in signals of various DBS channels. The multi-frequency DBS system makes it possible to localize plasma oscillations, their poloidal and radial sizes and mode structure. The main results of the DBS application for the study of these oscillations are presented. A comparison of the DBS data with the data of other diagnostics is also given.

Two-fluid MHD regime of resistive drift-wave instability

Drift instabilities contribute to the formation of edge turbulence and zonal flows and thus the anomalous transport in tokamaks. Experiments often found micro-scale turbulence strongly coupled with large-scale magnetohydrodynamic (MHD) processes, whereas a general framework has been lacking that can cover both regimes, in particular, their coupling. In this paper, the linear resistive drift wave instability is investigated using a full 2-fluid MHD model, as well as its numerical implementation in the NIMROD code. Both analytical and numerical analyses reveal a macro-scale global drift wave eigenmode coupled with MHD dynamics and illustrate a non-monotonic dispersion relation with respect to both perpendicular and parallel wavenumbers. NIMROD results also reveal an edge-localized behavior in the radial mode structure as the azimuthal mode number increases, implying the dependence of the 2-fluid effects due to the inhomogeneous density profile. The edge-localization introduces a non-trivial dependence of the effective perpendicular wavenumber to the perpendicular mode number, which may explain the quantitative difference between the global dispersion relation and its local approximation from the conventional local theory.

Linear radial structure of reactive energetic geodesic acoustic modes

In this paper we have developed a fluid model to study the radial mode structure of the reactive energetic geodesic acoustic modes (reactive EGAMs), a branch of GAM that becomes unstable in the presence of a cold fast ion beam. We have solved the resulting dispersion relationship, a second order ODE, both analytically in restricted cases and numerically in general. It is found that the reactive EGAM global mode structure is formed with the inclusion of fast ion finite drift orbit effects. In two cases with typical DIII-D parameters but different q profiles, the global EGAM frequency is slightly higher than the local EGAM extremum, located either on axis with a monotonic shear or at mid-radius with a reversed shear. The mode wavelength roughly scales with in the core and at the edge, though the dependency is more complicated for the reversed shear case when ( is the fast ion drift orbit width and a the minor radius). Finally, the growth rate of the global mode is boosted by 50% to 100% when switching from co-beam to counter-beam, depending on the fast ion density, which may help to explain the more frequent occurrence of EGAMs with counter-injection in experiments.

Decay of geodesic acoustic modes due to the combined action of phase mixing and Landau damping

Geodesic acoustic modes (GAMs) are oscillations of the electric field whose importance in tokamak plasmas is due to their role in the regulation of turbulence. The linear collisionless damping of GAMs is investigated here by means of analytical theory and numerical simulations with the global gyrokinetic particle-in-cell code ORB5. The combined effect of the phase mixing and Landau damping is found to quickly redistribute the GAM energy in phase-space, due to the synergy of the finite orbit width of the passing ions and the cascade in wave number given by the phase mixing. When plasma parameters characteristic of realistic tokamak profiles are considered, the GAM decay time is found to be an order of magnitude lower than the decay due to the Landau damping alone, and in some cases of the same order of magnitude of the characteristic GAM drive time due to the nonlinear interaction with an ion-temperature-gradient (ITG) mode. In particular, the radial mode structure evolution in time is investigated here and reproduced quantitatively by means of a dedicated initial value code and diagnostics.

Impact of pressure anisotropy on magnetic configuration and stability

A number of tools have recently been developed to study equilibrium and stability in tokamaks with pressure anisotropy. Here we apply these tools to a Mega Ampere Spherical Tokamak (MAST) discharge to calculate equilibrium, Alfvén continua and eigenmodes, through to linear growth and nonlinear saturation of a toroidal Alfvén eigenmode (TAE); this is the first study of wave growth and saturation for anisotropic equilibria. Comparisons with the standard tools which assume an isotropic pressure reveal various differences in equilibrium and modes: the safety factor profile in the isotropic reconstruction is reversed shear while the anisotropic reconstruction gives normal shear; the isotropic TAE gap is much narrower than the anisotropic gap; and the TAE radial mode structure is wider in the anisotropic case. These lead to a modification in the resonant regions of fast-ion phase space, and produce a 35% larger linear growth rate and an 18% smaller saturation amplitude for the TAE in the anisotropic analysis compared to the isotropic analysis.

Non-resonant fishbone-like modes in tokamak plasmas with reversed magnetic shear

Energetic ion excited non-resonant fishbone-like modes (FLMs) of m / n > 1 is investigated for reversed magnetic shear configurations. It is found that the mode can be destabilized by trapped fast ions with a similar excitation mechanism as m / n = 1 fishbones but with a local interchange-like mode structure, which is in agreement with previous experiments (Toi et al 1999 Nucl. Fusion 39 1929). The dispersion relation of the mode is derived for m / n > 1. The radial mode structure is then studied by numerically solving the eigenvalue equation. Effects of on/off-axis heating, the width of the particle distribution, the beam energy and the energy distribution on the mode are discussed in detail. Nonlinear analysis of the mode is also carried out by a modified predator–prey model.

Resistive interchange mode destabilized by helically trapped energetic ions and its effects on energetic ions and bulk plasma in a helical plasma

A resistive interchange mode of the structure (, : poloidal and toroidal mode numbers, respectively) with a bursting character and rapid frequency chirping in the range less than 10 kHz is observed for the first time in the edge region of the net current-free, low beta LHD (Large Helical Device) plasmas during high power injection of perpendicular neutral beams. The mode resonates with the precession motion of helically trapped energetic ions (EPs), following the resonant condition. The radial mode structure is recognized to be similar to that of the pressure-driven resistive interchange mode, of which radial displacement eigenfunction quite localizes around the mode rational surface, and evolves into an odd-type (or island-type) during the late of frequency chirping phase. This beam driven mode is excited when the beta value of helically trapped EPs exceeds a certain threshold. This instability is thought to be a new branch of resistive interchange mode destabilized by the trapped energetic ions. The radial transport, i.e. redistribution and losses, of helically trapped energetic ions induced by the mode transiently generates significant radial electric field near the plasma peripheral region. The large shear of thus generated radial electric field is thought to contribute to the observed suppression of micro-turbulence and transient increases of the temperature of fully ionized carbon impurity ions and electron density, suggesting improvement of bulk plasma confinement.

Orbit-based analysis of resonant excitations of Alfvén waves in tokamaks

The exponential growth phase of fast-ion-driven Alfvénic instabilities is simulated and the resonant wave-particle interactions are analyzed numerically. The simulations are carried out in realistic magnetic geometry and with a realistic particle distribution for a JT-60U plasma driven by negative-ion-based neutral beams. In order to deal with the large magnetic drifts of the fast ions, two new mapping methods are developed and applied. The first mapping yields the radii and pitch angles at the points, where the unperturbed orbit of a particle intersects the mid-plane. These canonical coordinates allow to express analysis results (e.g., drive profiles and resonance widths) in a form that is easy to understand and directly comparable to the radial mode structure. The second mapping yields the structure of the wave field along the particle trajectory. This allows us to unify resonance conditions for trapped and passing particles, determine which harmonics are driven, and which orders of the resonance are involved. This orbit-based resonance analysis (ORA) method is applied to fast-ion-driven instabilities with toroidal mode numbers n = 1-3. After determining the order and width of each resonance, the kinetic compression of resonant particles and the effect of linear resonance overlap are examined. On the basis of the ORA results, implications for the fully nonlinear regime, for the long-time evolution of the system in the presence of a fast ion source, and for the interpretation of experimental observations are discussed.

A current-driven electromagnetic mode in sheared and toroidal configurations

The induced electric field in a tokamak drives a parallel electron current flow. In an inhomogeneous, finite beta plasma, when this electron flow is comparable to the ion thermal speed, the Alfvén mode wave solutions of the electromagnetic gyrokinetic equation can become nearly purely growing kink modes. Using the new ‘low-flow’ version of the gyrokinetic code GS2 developed for momentum transport studies (Barnes et al 2013 Phys. Rev. Lett. 111 055005), we are able to model the effect of the induced parallel electric field on the electron distribution to study the destabilizing influence of current on stability. We identify high mode number kink modes in GS2 simulations and make comparisons to analytical theory in sheared magnetic geometry. We demonstrate reassuring agreement with analytical results both in terms of parametric dependences of mode frequencies and growth rates, and regarding the radial mode structure.

The mechanism of particles transport induced by electrostatic perturbation in tokamak

Particle transport in tokamak devices due to wave-particle resonance induced diffusion is studied. The diffusion coefficient is derived both analytically using quasilinear theory, and numerically using a test particle code, and the obtained diffusion coefficient agrees with each other in its validity regime. Dependence of the diffusion coefficient on turbulence intensity, turbulence radial mode structures, and particle energy is investigated. It is found that the diffusion coefficient is proportional to the turbulence intensity, and the diffusion is maximized for Et≃Ti, and krΔ0≃1. Here, Et is the test particle energy, Ti is the thermal ion temperature, Δ0 is the distance between neighboring mode rational surfaces, and 1/kr is the half width of the fine radial mode structure on each rational surface.

Properties of Alfvén eigenmodes in the Toroidal Alfvén Eigenmode range on the National Spherical Torus Experiment-Upgrade

A second Neutral Beam (NB) injection line is being installed on the NSTX Upgrade device, resulting in six NB sources with different tangency radii that will be available for heating and current drive. This work explores the properties of instabilities in the frequency range of the Toroidal Alfvén Eigenmode (TAE) for NSTX-U scenarios with various NB injection geometries, from more perpendicular to more tangential, and with increased toroidal magnetic field with respect to previous NSTX scenarios. Predictions are based on analysis through the ideal MHD code NOVA-K. For the scenarios considered in this work, modifications of the Alfvén continuum result in a frequency up-shift and a broadening of the radial mode structure. The latter effect may have consequences for fast ion transport and loss. Preliminary stability considerations indicate that TAEs are potentially unstable with ion Landau damping representing the dominant damping mechanism.

Nonlinear dynamics of beta-induced Alfvén eigenmode driven by energetic particles

Nonlinear saturation of a beta-induced Alfvén eigenmode, driven by slowing down energetic particles via transit resonance, is investigated by the nonlinear hybrid magnetohyrodynamic gyrokinetic code. Saturation is characterized by frequency chirping and symmetry breaking between co- and counter-passing particles, which can be understood as the evidence of resonance detuning. The scaling of the saturation amplitude with the growth rate is also demonstrated to be consistent with radial resonance detuning due to the radial nonuniformity and mode structure.