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electron density profile as a function of normalized poloidal flux: psinorm ne(10^20/m^3) dne/dpsiN Pressure profile as a function of normalized poloidal flux: psinorm ptot(KPa) dptot/dpsiN scaled to oftain beta=5% at magnetic axis Magnetic safety factor profile as a function of normalized poloidal flux: psinorm q_profile All needed to perform the NOVA calculations.
While much about Alfvén eigenmode (AE) stability has been explored in previous and current tokamaks, open questions remain for future burning plasma experiments, especially regarding exact stability threshold conditions and related isotope effects; the latter, of course, requiring good knowledge of the plasma ion composition. In the JET tokamak, eight in-vessel antennas actively excite stable AEs, from which their frequencies, toroidal mode numbers, and net damping rates are assessed. The effective ion mass can also be inferred using measurements of the plasma density and magnetic geometry. Thousands of AE stability measurements have been collected by the Alfvén Eigenmode Active Diagnostic in hundreds of JET plasmas during the recent Hydrogen, Deuterium, Tritium, DT, and Helium-4 campaigns. In this novel AE stability database, spanning all four main ion species, damping is observed to decrease with increasing Hydrogenic mass, but increase for Helium, a trend consistent with radiative damping as the dominant damping mechanism. These data are important for confident predictions of AE stability in both non-nuclear (H/He) and nuclear (D/T) operations in future devices. In particular, if radiative damping plays a significant role in overall stability, some AEs could be more easily destabilized in D/T plasmas than their H/He reference pulses, even before considering fast ion and alpha particle drive. Active MHD spectroscopy is also employed on select HD, HT, and DT plasmas to infer the effective ion mass, thereby closing the loop on isotope analysis and demonstrating a complementary method to typical diagnosis of the isotope ratio.
Alfvén wave instabilities driven by energetic particles are common in fusion devices. Understanding their behavior is essential for the good confinement of fusion plasma. For this purpose, a series of experiments are performed on EAST to investigate the excitation of toroidal Alfvén eigenmodes (TAEs). Experimentally, it was found that AEs with frequencies around 80, 134, 157 kHz are excited by ion cyclotron resonance heating (ICRH) hydrogen minority heating scenario. Moreover, the excitation of AEs is independent of the wall-coating materials, but determined with the generation and confinement of the fast ions. Statistical analysis suggests that the TAEs can only be excited when the ICRH power is larger than 2 MW and the H 98 factor is larger than 1.15. In line with the experiments, a set of simulations using TORIC, ASCOT, and NOVA-C is performed. The simulation results show that with the experimental density profile and safety factor, the measured TAE with frequency of 134 kHz is well reproduced by taking into account the plasma toroidal rotation frequency. However, the appearance of the 80 kHz mode cannot be captured in the simulations. The ICRH-generated fast hydrogen ions mainly have banana orbits and that their perpendicular velocity is much larger than that of the parallel ions. The stability analysis with NOVA-C suggests that the radial gradient of the fast H ion distribution is the only driving source of TAEs. For TAEs locate in the center of Alfvén continuum, the D ion Landau damping is the dominant damping term; For most other TAEs which have intersections with the continuum boundary, the continuum damping becomes the dominant damping mechanism.
Instabilities of Alfvén eigenmodes (AEs) are of significant concern because they can enhance the cross-field transport of fusion-born alpha particles beyond the neoclassical level in magnetic fusion plasmas. The threshold value of alpha-particle pressure for exciting AEs depends critically on the damping rate of AEs. The damping mechanisms include kinetic damping due to interactions with thermal particles, continuum damping due to AE frequency crossing Alfvén continuum, and radiative damping due to emitting kinetic Alfvén waves (KAWs). The radiative damping is substantial and can even prevail in high-temperature burning plasmas [1]. We revisit the radiative damping analytic theory for TAE in plasmas with low positive magnetic shear, considering TAE with an eigenfrequency near the bottom of TAE-gap and with poloidal harmonics of the same sign (even TAE). In contrast to earlier papers, we provide the damping calculations in real space rather than Fourier space. This approach is straightforward technically and more enlightening from a physics standpoint for benchmarking numerical calculations of radiative damping. The parametric dependence of the resulting damping rate agrees with that of Refs. [2-5], but it has a smaller numerical factor in front of it.
Mechanisms of destabilization of toroidal Alfvén eigenmodes (TAEs) in tokamaks are analyzed with the aim to reveal those leading to modes propagating in the direction opposite to plasma current, i.e. counter-propagating modes (ctr-TAE). Plasmas with fast-ions sources [such as neutral beam injection (NBI), ion cyclotron resonance heating, fusion reactions] and without them (Ohmic discharges) are considered. A particular NSTX-U experiment with NBI, where co- and counter-propagating TAEs were observed simultaneously (Podestà et al 2018 Nucl. Fusion 58 082023), is considered. It is concluded that both types of TAEs occurred because their destabilization was caused by the velocity anisotropy of beam ions, which overrode effects of spatial inhomogeneity of these ions.
Alfvén eigenmodes have been suppressed and excited in tokamak plasmas by (just) modifying the poloidal spectra of externally applied static magnetic perturbations. This effect is observed experimentally when toroidal spectra of n = 2, n = 4 as well as a mixed spectrum of n = 2 and n = 4 is applied. Under the n = 2 magnetic perturbations, the modes are excited or suppressed by modifying the coil phasing between the upper and the lower set of coils. Regardless of the absolute rotation, an even parity for the n = 4 perturbation is observed to reduce the amplitude of the Alfvénic instabilities, while an odd parity amplifies it. To combine the stabilizing (and destabilizing) effect of n = 2 and n = 4, a mixed spectrum is applied, finding similar reduction (and amplification) trends. However, the impact on the mode amplitude is more subtle, due to the reduced coil current required for a mixed spectrum. The signal level on the fast-ion loss detector is sensitive to the applied poloidal spectrum, which is consistent with Hamiltonian full-orbit modelling of an edge resonant transport layer activated by the 3D perturbative fields. An internal redistribution of the fast-ion population is induced, modifying the phase-space gradients driving the Alfvénic instabilities, and ultimately determining their existence. The calculated edge resonant layers for both n = 2 and n = 4 toroidal spectra are consistent with the observed suppressed and excited phases. Moreover, hybrid kinetic-magnetohydrodynamic (MHD) simulations reveal that this edge resonant transport layer overlaps in phase-space with the population responsible for the fast-ion drive. The results presented here may help to control fast-ion driven Alfvénic instabilities in future burning plasmas with a significant fusion born alpha particle population.
In magnetic confinement fusion, toroidicity-induced Alfvén eigenmodes (TAEs) are well-studied, weakly stable solutions of the linearized ideal magnetohydrodynamic equations. Driven unstable by suprathermal populations of energetic particles, TAE pose a key vulnerability to the confinement of high-energy alpha particles generated by fusion reactions. Hence, it is paramount to understand TAE dynamics if a working reactor is to be realized. In this work, we detect and characterize signatures of nonstationary nonlinear coupling between TAE using a novel, time-resolved bispectral analysis; results are supported by analytic signal of band-passed data. Crucially, a stationary phase relationship between two TAE and a nascent low frequency fluctuation is observed precisely when the triple product of magnetic fluctuation amplitudes is enhanced. Local mode number and frequency spectrum, gleaned from beam-emission spectroscopy, corroborates simultaneous satisfaction of nonlinear matching conditions, and provides a tool to identify theorized pathways of energy transfer, e.g. TAE parametric instability.
Vertical Displacement Oscillatory Modes (VDOM), with frequency in the Alfvén range, are natural modes of oscillation of magnetically confined laboratory plasmas with elongated cross-section. These axisymmetric modes arise from the interaction between the plasma current, which is in equilibrium with currents flowing in external coils, and perturbed currents induced on a nearby conducting wall. The restoring force exerted by these perturbed currents on the vertical motion of the plasma column leads to its oscillatory behavior. An analytic model for VDOM was proposed based on an idealized 'straight tokamak' equilibrium with uniform equilibrium current density. This article introduces the first numerical simulations of VDOM in a realistic JET tokamak configuration, using the extended-MHD code NIMROD and drawing comparisons with Global Alfvén Eigenmodes (GAE). The results show qualitative agreement with analytic predictions regarding mode frequency and radial structure, supporting the identification of VDOM as a fundamental oscillation mode in tokamak plasmas. VDOM and GAE are modeled in a representative JET discharge, where axisymmetric perturbations with toroidal mode number n = 0 driven unstable by fast ions were observed. The two modes are examined separately using a forced oscillator within the NIMROD code, which enables a comparison of their characteristics and helps identify the experimentally observed mode possibly as a GAE.
A careful theoretical analysis of the excitation of Alfvén eigenmodes (AEs), such as TAE (toroidicity-induced AE) and RSAE (reversed shear AE), by superalfvenic energetic particles is required for reliable predictions of energetic ion relaxation in present day fusion experiments. This includes the evaluation of different AE damping mechanisms including radiative and continuum dampings which are the focus of this study. A recent comprehensive benchmark of different eigenmode solvers including gyrokinetic, gyrofluid and hybrid magenetohydrodynamics (MHD) has shown that employed models may have deficiencies when addressing some of them (Taimourzadeh et al., Nucl. Fusion, vol. 59, 2019, 066006). Here, in this paper, we are studying the radiative and continuum dampings of RSAEs in details which were missing in hybrid NOVA/NOVA-C calculations to prepare a NOVA-C package with a substantial upgrade. Both dampings require the finite Larmor radius (FLR) corrections to AE mode structures to be accounted for. Accurately calculating different damping rates and understanding their parametric dependencies, we resolve the limitation coming out of the perturbative approach. In particular, here, the radiative damping is included perturbatively, whereas the continuum damping is computed non-perturbatively. Our comparison leads to the conclusion that the non-perturbative treatment of the unstable RSAE modes is needed to find the agreement with the gyrokinetic calculations. We expect that the RSAE mode structure modification plays a dominant role in determining the RSAE stability.
Fast-ion-driven Alfvén eigenmodes (AEs) are observed during ICRF-heated high-β p plasmas on EAST. Multiple high frequency modes are observed for shot 112670 at f TAE1 ~ 145 kHz, δB/B ~ 4 × 10 –4 and f TAE2 ~ 175 kHz, δB/B ~ 1.2 × 10 –5 measured by high-frequency Mirnov coils, at B 0 ~ 2.45 T, I p ~ 350kA, n e ramp-up from 3.5 × 10 19 to 4 × 10 19 m −3 at P ECRH ~ 2 MW, PLHW ~ 2 MW, and P ICRH ~ 2.1 MW. Here, 37 MHz ICRF minority hydrogen heating scheme, located at plasma core, creates fast ion population which drives TAEs unstable from TORIC + SFFPQL. In the experiment, it is observed that the evolution of mode frequency depends on electron density, following the theoretical TAE frequency characteristic $f_{{{\text{th}}}} = V_{{\text{a}}} /(4\pi qR) \propto \sqrt {n_{{\text{e}}} }$. As the electron density increases, the amplitude of the AE mode progressively diminishes. Higher plasma density shortens the fast-ion slowing-down time, reduces the heating efficiency of minority hydrogen, weakens the high-energy tail, and consequently decreases the fast-ion beta. Based on the diagnostic results from the microwave reflectometer and electron cyclotron emission (ECE) diagnostics, the TAE is located within the plasma core, consistent with the narrower core region of the TAE gap observed in the continuous spectrum.
A first of its kind fully data-driven system has been developed and implemented into the DIII-D plasma control system to detect and control Alfvén eigenmodes (AE) in real-time. Susceptibility to fast ion-induced AE is a challenge in fully non-inductive tokamak operation, which significantly reduces fast-particle confinement and results in degraded fusion gain. Controlling AEs in real-time to improve fast-ion confinement is, hence, important for future advanced tokamak fusion reactors. The models were implemented and tested in experiments which showed that neural networks (NN) are highly effective in detecting 5 types of AE (BAE, EAE, LFM, RSAE, TAE) using high resolution ECE. To estimate the neutron deficit, a NN has been trained that outputs the classical neutron rate using similar inputs to NUBEAM. Also a preliminary ML-based proportional control has been designed and gone through initial testing in experiment to use feedback-control on the neutral beam power to achieve desired amplitude of AE modes and neutron deficits. The effect of AEs on fast-ion confinement is measured by analysing the gap in classical neutron rate from the proposed NN-based NUBEAM and the measured neutron rate.
The non-perturbative MHD-kinetic hybrid code MARS-K (Liu et al 2014 Phys. Plasmas 21 056105) is updated to include relativistic effects for kinetic fast particles, enabling the code to model excitation of Alfvén eigenmodes (AEs) by runaway electrons (REs) in post-disruption tokamak plasmas. Applying the updated code to RE beams in both DIII-D and ITER, a zoo of AE modes triggered by trapped REs due to precessional drift-kinetic resonances is computed while scanning the RE energy. At fixed RE energy, multiple unstable roots are also excited. These AE modes possess radially different eigenmode structures, ranging from global modes to core-localized ones. The computed mode frequency is in the Alfvén frequency range, increasing with the assumed RE energy in a staircase fashion and quantitatively matching the experimental measurement (in DIII-D). At the (more relevant) high-frequency range (above 1 MHz), the modeled eigenmodes are identified as compressional AEs (CAEs) in DIII-D and a mixture of CAE and shear Alfvén waves in ITER.
Mitigation and suppression of low-𝑘 turbulence are observed during the nonlinear evolution of toroidicity-induced Alfvén eigenmodes (TAEs) in DIII-D experiments. Turbulence mitigation begins when the dominant TAE starts to depart from the typical shear Alfvén wave polarization. TAE activity then evolves into a new state, characterized by more discrete coherent modes, increased total amplitude, and more localized radial structures. During this transition, a narrow shear flow layer forms, driven by an enhanced Reynolds stress force, with a shearing rate that exceeds the local turbulence decorrelation rate, leading to a full turbulence suppression. Furthermore, these observations indicate the imbalance between Reynolds and Maxwell stress forces during the nonlinear evolution of the TAE and their important roles in shear flow generation and turbulence reduction.
Abstract This paper reports global nonlinear gyrokinetic simulations that couple meso-scale reversed shear Alfvén eigenmodes (RSAEs) driven by energetic particles (EPs) and ion temperature gradient (ITG) microturbulence driven by thermal plasma, using equilibrium and profiles from DIII-D discharge #159243. In simulations focusing only on the ITG, electrostatic ITG drives a huge thermal ion heat transport, which is reduced by a factor of 10 to a level close to the experimental value in electromagnetic simulation due to finite β effect. In the simulations coupling the RSAE and ITG, ITG can scatter the resonant EP nonlinearly trapped by the RSAE and damp the zonal flows generated by the RSAE. The regulation of the RSAE by the ITG greatly reduces the initial saturation amplitude of the RSAE but increases the RSAE amplitude and associated EP transport to experimental levels in the quasi-steady state. The RSAE effects on the ITG, specifically the stronger zonal flows generated by the RSAE and the RSAE frequency modulation of the ITG-induced thermal ion heat transport, in turn, leads to a reduction of the thermal ion heat transport by more than a factor of 2 . For a stronger background ITG, the regulation of the RSAE by the ITG is stronger, while the RSAE effects on the ITG are weaker. This work highlights the importance of cross-scale coupling in the dynamics of the AE turbulence and EP transport.
Linear gyrokinetic (GK) simulations using the Gyrokinetic Toroidal Code (GTC) have been performed to investigate Toroidicity-driven Alfvén Eigenmodes (TAEs) driven by the neutral beam injection (NBI) induced fast ions in the Mega-Amp Spherical Tokamak (MAST) to identify the non-perturbative and kinetic effects of thermal plasma. A specific TAE in MAST discharge 26887, with an on-axis NBI power of approximately 1.5 MW and plasma current around 800 kA, exhibited frequency chirping, and the tangential soft x-ray camera array resolved the radial mode structure peaked near |q|=1.5. Various excitation methods were used in the GTC linear simulations, illustrating this code's capability to realistically represent the mechanisms and behaviors of fast ion-driven TAEs in spherical tokamaks. The radial structures from these GK simulations closely match measurements and calculations performed using the NOVA ideal MHD code, though with the frequencies approximately 10 kHz lower, likely due to various kinetic and non-perturbative effects. The simulations measured the damping rates due to continuum damping, radiative damping, and ion Landau damping, revealing that ion Landau damping has the most significant contribution to the total damping rate of the TAE. A comparison of growth rates of TAEs excited by fast ion Maxwellian and slowing-down distributions shows that the TAEs excited by a fast ion anisotropic pitch distribution (as part of the slowing-down distributions) are more unstable compared to those excited by a Maxwellian distribution with an equivalent fast ion beta. This shows that the use of fast ion anisotropy alters the number of fast ions to be in shear Alfvén resonance, and hence, it can greatly affect the stability of TAEs. These tests can be performed with the GTC but impossible with ideal MHD simulations, highlighting the necessity of kinetic simulations such as the GTC for a precise prediction of the TAE stability.
Orbit-following simulations of fast-ion transport and losses with time-dependent electromagnetic perturbations are performed to clarify the roles of Alfvén eigenmodes (AEs) and the low-frequency magnetohydrodynamic (MHD) mode observed in the kinetic-MHD hybrid simulation of AE bursts in the Large Helical Device. Fast-ion pressure profile flattening in the kinetic-MHD hybrid simulation can be reproduced by an orbit-following simulation with only the primary single AE of the time-dependent amplitude following the kinetic-MHD hybrid simulation result, while orbit-following simulations with constant AE amplitude of average level during AE burst cannot reproduce the fast-ion pressure profile flattening observed. The effects of other modes are negligible on the fast-ion pressure profile flattening. The fast-ion losses in kinetic-MHD hybrid simulation can be reproduced by an orbit-following simulation with time-dependent amplitude when the low-frequency MHD mode is considered in addition to multiple AEs. This indicates the synergetic effect of multiple AEs and the low-frequency MHD mode on fast-ion losses.
In scenarios where a sustained energetic particle source strongly drives toroidal Alfvén eigenmodes (TAE), and phase-space transport is insufficient to saturate TAE, this novel theory of TAE-zonal mode (ZM)-turbulence—self-regulated by cross-scale interactions (including collisionless ZF damping) – merits consideration. Zonal modes are driven by Reynolds and Maxwell stresses, without the onset of modulational instability. TAE evolution in the presence of ZMs conserves energy and closes the system feedback loop. The saturated zonal shears can be sufficient to suppress ambient drift-ion temperature gradient (ITG) turbulence, achieving an enhanced core confinement regime. The saturated state is regulated by linear and turbulent zonal flow drag. This regulation leads to bursty TAE spectral oscillations, which overshoot while approaching saturation. Heating by both collisional and collisionless ZM damping deposits alpha particle energy into the thermal plasma, achieving effective alpha channeling. This theory offers a mechanism for EP-induced transport barrier formation, and predicts a novel thermal ion heating mechanism.
Twisting of the spatial structure of eigenmodes by energy fluxes generated due to the spatial channeling (SC)—the fast-ion energy and momentum transfer across the magnetic field by destabilized modes—is considered. It is revealed that there is a correlation between the direction of the radial wave energy flux, orientation of the mode twist (MT), and the direction of mode rotation. The mode twist parameter is introduced and relations connecting it with the energy flux are established. It is shown the energy flux transforms zeros of the radial profile of the mode amplitude into minima (i.e., zeros disappear). It is found that the radial group velocity and phase velocity of reversed shear Alfvén eigenmodes (RSAEs) have opposite directions. These findings can be used for diagnostics of the energy fluxes during fast-ion driven instabilities and understanding whether the SC degrades or improves plasma performance. Specific calculations are carried out for fast magnetoacoustic modes, FMMs (known also as compressional Alfvén eigenmodes, CAEs), and Alfvén eigenmodes, AEs. A DIII-D experiment where RSAEs were observed is considered. It is concluded that an outward SC took place in this experiment. Peculiarities of various modes are discussed, which may explain why twisting of AEs, but not of FMMs, was observed experimentally in the DIII-D and NSTX tokamaks.