Experimental studies of plasma-antenna coupling with the JET Alfven Eigenmode Active Diagnostic
R. A. Tinguely, P. G. Puglia, N. Fil, S. Dowson, M. Porkolab, A. Dvornova, A. Fasoli, M. Fitzgerald, V. Guillemot, G. T. A. Huysmans, M. Maslov, S. Sharapov, D.… 展开作者
R. A. Tinguely, P. G. Puglia, N. Fil, S. Dowson, M. Porkolab, A. Dvornova, A. Fasoli, M. Fitzgerald, V. Guillemot, G. T. A. Huysmans, M. Maslov, S. Sharapov, D. Testa, JET Contributors
This paper presents a dedicated study of plasma-antenna (PA) coupling with the Alfven Eigenmode Active Diagnostic (AEAD) in JET. Stable AEs and their resonant frequencies f, damping rates $γ$ < 0, and toroidal mode numbers n are measured for various PA separations and limiter versus X-point magnetic configurations. Two stable AEs are observed to be resonantly excited at distinct low and high frequencies in limiter plasmas. The values of f and n do not vary with PA separation. However, $\vertγ\vert$ increases with PA separation for the low-f, but not high-f, mode, yet this may be due to slightly different edge conditions. The high-f AE is detected throughout the transition from limiter to X-point configuration, though its damping rate increases; the low-f mode, on the other hand, becomes unidentifiable. The linear resistive MHD code CASTOR is used to simulate the frequency scan of an AEAD-like external antenna. For the limiter pulses, the high-f mode is determined to be an n = 0 GAE, while the low-f mode is likely an n = 2 TAE. During the transition from limiter to X-point configuration, CASTOR indicates that n = 1 and 2 EAEs are excited in the edge gap. These results extend previous experimental studies in JET and Alcator C-Mod; validate the computational work performed by Dvornova et al 2020 Phys. Plasmas 27 012507; and provide guidance for the optimization of PA coupling in upcoming JET energetic particle experiments, for which the AEAD will aim to identify the contribution of alpha particles to AE drive during the DT campaign.
Two novel nonlinear mode coupling processes for reversed shear Alfven eigenmode (RSAE) nonlinear saturation are proposed and investigated. In the first process, RSAE nonlinearly couples to a co-propagating toroidal Alfven eigenmode (TAE) with the same toroidal and poloidal mode numbers, and generates a geodesic acoustic mode (GAM). In the second process, RSAE couples to a counter-propagating TAE and generates an ion acoustic wave quasi-mode (IAW). The condition for the two processes to occur is favored during current ramp. Both processes contribute to effectively saturate the Alfvenic instabil…
Nonlinear saturation of toroidal Alfven eigenmode (TAE) via ion induced scatterings is investigated in the short-wavelength gyrokinetic regime. It is found that the nonlinear evolution depends on the thermal ion \b{eta} value. Here, \b{eta} is the plasma thermal to magnetic pressure ratio. Both the saturation levels and associated energetic-particle transport coefficients are derived and estimated correspondingly.
We demonstrate analytically that, in toroidal plasmas, scattering by drift wave turbulence could lead to appreciable damping of toroidal Alfven eigenmodes via generation of short-wavelength electron Landau damped kinetic Alfven waves. A corresponding analytic expression of the damping rate is derived, and found to be, typically, comparable to the linear drive by energetic particles. The implications of this novel mechanism on the transport and heating processes in burning plasmas are also discussed.
Gyrokinetic theory of nonlinear mode coupling as a mechanism for toroidal Alfven eigenmode (TAE) saturation in the fusion plasma related parameter regime is presented, including 1) para- metric decay of TAE into lower kinetic TAE (LKTAE) and geodesic acoustic mode (GAM), and 2) enhanced TAE coupling to shear Alfven wave (SAW) continuum via ion induced scattering. Our theory shows that, for TAE saturation in the parameter range of practical interest, several processes with comparable scattering cross sections can be equally important.
Linear and nonlinear modelling of Alfvénic instabilities, most notably toroidal Alfvén eigenmodes (TAEs), obtained by using the global nonlinear electromagnetic gyrokinetic model of the code ORB5 are presented for the 15 MA scenario of the ITER tokamak. Linear simulations show that elliptic Alfvén eigenmodes and odd-parity TAEs are only weakly damped but not excited by alpha particles, whose drive favours even-parity TAEs. Low mode number TAEs are found to be global, requiring global treatment. Nonlinearly, even with double the nominal EP density, single mode simulations lead to saturation wit…
General nonlinear equations describing reversed shear Alfven eigenmode (RSAE) self-modulation via zero frequency zonal structure (ZFZS) generation are derived using nonlinear gyrokinetic theory, which are then applied to study the spontaneous ZFZS excitation as well as RSAE nonlinear saturation. It is found that both electrostatic zonal flow (ZF) and electromagnetic zonal current (ZC) can be preferentially excited by finite amplitude RSAE, depending on specific plasma parameters. The modification to local shear Alfven wave continuum is evaluated using the derived saturation level of ZC, which …
In the presence of energetic particles (EPs) from auxiliary heating and burning plasmas, fishbone instability and Alfvén modes can be excited and their transition can take place in certain overlapping regimes. Using the hybrid kinetic-magnetohydrodynamic model in the NIMROD code, we have identified such a transition between the fishbone instability and the $β$-induced Alfvén Eigenmode (BAE) for the NBI heated plasmas on HL-2A. When the safety factor at magnetic axis is well below one, typical kink-fishbone transition occurs as the EP fraction increases. When $q_0$ is raised to approaching one,…
Nonlinear excitation of low frequency zonal structure (LFZS) by beta-induced Alfven eigenmode (BAE) is investigated using nonlinear gyrokinetic theory. It is found that electrostatic zonal flow (ZF), rather than zonal current, is preferentially excited by finite amplitude BAE. In addition to the well-known meso-scale radial envelope structure, ZF is also found to exhibit fine radial structure due to the localization of BAE with respect to mode rational surfaces. Specifically, the zonal electric field has an even mode structure at the rational surface where radial envelope peaks.
Nonlinear generation of high frequency mode (HFM) by toroidal Alfven eigenmode (TAE) observed in HL-2A tokamak is analyzed using nonlinear gyrokinetic theory. It is found that, the HFM can be dominated by $|nq-m|=1$ perturbations with predominantly ideal magnetohydrodynamic if the two primary TAEs are co-propagating; while the HFM can be characterized by $nq-m=0$ electrostatic perturbations if the two primary TAEs are counter-propagating. Here, $n$ and $m$ are respectively the toroidal and poloidal mode numbers, and $q$ is the safety factor. The nonlinear process is sensitive to the equilibriu…
The set of equations describing nonlinear evolution of a single toroidal Alfven eigenmode are derived, including both zero frequency zonal structure (ZFZS) generation and wave-particle phase space nonlinearities. The simplified case of neglecting wave-particle phase space nonlinearity is then investigated to focus on different roles of energetic particles and bulk plasmas on ZFZS generation. It is shown that energetic particles and bulk plasma play dominant roles in ZFZS generation in different nonlinear stages, and the corresponding processes are qualitatively different. Several properties of…
Spontaneous nonlinear excitation of geodesic acoustic mode (GAM) by toroidal Alfvén eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that, the nonlinear decay process depends on thermal ion βvalue. Here, βis the plasma thermal to magnetic pressure ratio. In the low-βlimit, TAE decays into a GAM and a lower TAE sideband in the toroidicity induced shear Alfvén wave continuous spectrum gap; while in the high-βlimit, TAE decays into a GAM and a propagating kinetic TAE in the continuum. Both cases are investigated for the spontaneous decay conditions. The nonlinear sa…
Generation of zonal ow (ZF) by energetic particle (EP) driven toroidal Alfven eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that, nonlinear resonant EP contri- bution dominates over the usual Reynolds and Maxwell stresses due to thermal plasma nonlinear response. ZF can be forced driven in the linear growth stage of TAE, with the growth rate being twice the TAE growth rate. The ZF generation mechanism is shown to be related to polarization induced by resonant EP nonlinearity. The generated ZF has both the usual meso-scale and micro- scale radial structures. Po…
Toroidal Alfven eigenmodes (TAEs) excited in purely ohmically heated plasmas without any auxiliary heating have been identified for the first time in the SUNIST spherical tokamak. The TAE modes are observed during minor disruptions and have a frequency range of 150-500 kHz. The mode structure analysis indicates the existence of both m/n=-3/-1 and -4/-1 harmonics, propagating in the electron diamagnetic direction in the laboratory frame of reference. These TAEs appear simultaneously with the generation of runaway electrons in the current quench phase, accompanying with the density sweeping duri…
Compressional Alfvén eigenmodes (CAE) driven by energetic ions have been observed in magnetic fusion experiments. In this paper, we show that the modes can also be driven by runaway electrons formed in post-disruption plasma, which may explain kinetic instabilities observed in DIII-D disruption experiments with massive gas injection. The mode-structure is calculated, as are the frequencies which are in agreement with experimental observations. Using a runaway electron distribution function obtained from a kinetic simulation, the mode growth rates are calculated and found to exceed the collisio…
Alfven Eigenmodes (AE) can be destabilized by energetic particles in neutral beam injection (NBI) heated plasmas through inverse Landau damping and couplings with gap modes in the shear Alfven continua. We describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system using the reduced MHD equations, density and parallel velocity moments for the energetic particles as well as the geodesic acoustic wave dynamics. A closure relation adds the Landau damping and resonant destabilization effects in the model. We apply the model to study the Alfven…
Alfvénic modes in the current quench (CQ) stage of the tokamak disruption have been observed in experiments. In DIII-D the excitation of these modes is associated with the presence of high-energy runaway electrons, and a strong mode excitation is often associated with the failure of RE plateau formation. In this work we present results of self-consistent kinetic-MHD simulations of RE-driven compressional Alfvén eigenmodes (CAEs) in DIII-D disruption scenarios, providing an explanation of the CQ modes. Simulation results reveal that high energy trapped REs can have resonance with the Alfvén mod…
A perturbative hybrid ideal-MHD/drift-kinetic approach to assess the stability of alpha-particle-driven Alfven eigenmodes in burning plasmas is used to show that certain foreseen ITER scenarios, namely the Ip = 15 MA baseline scenario with very low and broad core magnetic shear, are sensitive to small changes in the background magnetic equilibrium. Slight variations (of the order of 1%) of the safety-factor value on axis are seen to cause large changes in the growth rate, toroidal mode number, and radial location of the most unstable eigenmodes found. The observed sensitivity is shown to proce…
This paper presents results of extensive analysis of mode excitation observed during the operation of the Alfvén Eigenmode Active Diagnostic (AEAD) in the JET tokamak during the 2019-2020 deuterium campaign. Six of eight toroidally spaced antennas, each with independent power and phasing, were successful in actively exciting stable MHD modes in 479 plasmas. In total, 4768 magnetic resonances were detected with up to fourteen fast magnetic probes. In this work, we present the calculations of resonant frequencies $f_0$, damping rates $γ< 0$, and toroidal mode numbers $n$, spanning the parameter …
The resonant and non-resonant effects of core plasma on the excitation of low frequency modes with $ω< ω_{BAE}$, such as Beta-induced Alfvén Acoustic Eigenmodes (BAAEs) and Kinetic Ballooning Modes (KBMs) are examined in the framework of the generalized fishbone-like dispersion relation. The formalism of the fishbone-like equation contains all the necessary ingredients to describe the features of these low frequency fluctuations, and explain experimental findings. Core plasma properties (diamagnetic frequency and precession resonance with trapped ions) strongly affect the excitation of the mod…
Alfven Eigenmodes are destabilized at the DIII-D pedestal during transient beta drops in high poloidal beta discharges with internal transport barriers (ITBs), driven by n=1 external kink modes, leading to energetic particle losses. There are two different scenarios in the thermal beta recovery phase: with bifurcation (two instability branches with different frequencies) or without bifurcation (single instability branch). We use the reduced MHD equations in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles as well as the geodesic acou…
In this paper, we report the novel experimental observation of both unstable and stable Toroidicity-induced Alfvén Eigenmodes (TAEs) measured simultaneously in a JET tokamak plasma. The three-ion-heating scheme (D-DNBI-3He) is employed to accelerate deuterons to MeV energies, thereby destabilizing TAEs with toroidal mode numbers n = 3-5, each decreasing in mode amplitude. At the same time, the Alfvén Eigenmode Active Diagnostic resonantly excites a stable n = 6 TAE with total normalized damping rate $-γ/ω_0 \approx$ 1%-4%. Hybrid kinetic-MHD modeling with codes NOVA-K and MEGA both find eigenm…
Linear simulations of toriodal Alfvén eigenmodes (TAEs) driven by energetic particles (EPs) on EAST (Experimental Advanced Superconducting Tokamak) are performed using the hybrid-kinetic MHD (HK-MHD) model implemented in NIMROD code. The EAST equilibrium is reconstructed using the EFIT code based on experimental measurement. The "slowing down" distribution is adopted for modeling the equilibrium distribution of the energetic ions from the deuterium neutral beam injection on EAST. The frequency, the dominant poloidal mode number, the radial location and the detailed 2D mode structure of the TAE…
High-order plasma shaping (mainly elongation and shift, as opposed to low-order toroidicity) is shown, under certain conditions, to open gaps in the coupled shear-Alfvén and acoustic continua at frequencies significantly above the values predicted by previous theories. Global eigenmodes in these gaps, which lie between those of geodesic acoustic modes (GAMs) and toroidicity-induced Alfvén eigenmodes (TAEs), are found unstable to hot-ion populations typical of tokamak operation, whilst their fundamental resonances with circulating particles are shown to take place at velocities near the geometr…
Linear and nonlinear benchmark of gyrokinetic simulation of energetic particle driven toroidal Alfven eigenmodes in ITPA TAE benchmark case
Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Science（中国科学院合肥物质科学研究院等离子体物理研究所）；Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系）
To guide the experimental design of a linear plasma device for studying the interaction between energetic ions and Alfvénic gap eigenmode (AGE), this work computes AGE referring to fusion conditions in a ultra-long large plasma cylinder ended with strong magnetic throats for axial confinement of charged particles. It is shown that: (i) for uniform equilibrium field between the ending throats, the dispersion relation of computed wave field agrees well with a simple analytical model for shear Alfvénic mode; (ii) for periodic equilibrium field with local defect, clear AGE is formed inside spectra…
Fully self-consistent hybrid MHD/particle simulations reveal strong energetic particle modifications to sub-cyclotron global Alfvén eigenmodes (GAE) in low-aspect ratio, NSTX-like conditions. Key parameters defining the fast ion distribution function -- the normalized injection velocity $v_0/v_A$ and central pitch -- are varied in order to study their influence on the characteristics of the excited modes. It is found that the frequency of the most unstable mode changes significantly and continuously with beam parameters, in accordance with the Doppler-shifted cyclotron resonances which drive t…
Recently-proposed tokamak concepts use magnetic fields up to 12 T, far higher than in conventional devices, to reduce size and cost. Theoretical and computational study of trends in plasma behavior with increasing field strength is critical to such proposed devices. This paper considers trends in Alfvén eigenmode (AE) stability. Energetic particles, including alphas from D-T fusion, can destabilize AEs, possibly causing loss of alpha heat and damage to the device. AEs are sensitive to device magnetic field via the field dependence of resonances, alpha particle beta, and alpha orbit width. We d…
It is found that the presence of the so-called non-axisymmetric resonances of wave-particle interaction in stellarators [which are associated with the lack of axial symmetry of the magnetic configuration, Kolesnichenko et al., Phys. Plasmas 9 (2002) 517] may have a strong stabilizing influence through Landau mechanism on the Toroidicity-induced Alfvén Eigenmodes (TAE) and isomon modes (Alfvénic modes with equal poloidal and toroidal mode numbers and frequencies in the continuum region) destabilized by the energetic ions. These resonances involve largest harmonics of the equilibrium magnetic fi…
A theoretical framework has been developed for an NBI scenario to model the hard nonlinear evolution of Global Alfven Eigenmodes (GAEs) where the adiabatic motion of phase-space sturctures (holes and clumps), associated with the frequency chirping, occurs in generalized phase-space of slowing down energetic particles. The radial profile of the GAE is expanded using finite elements which allows update of the mode structure as the mode frequency chirps. Constants of motion are introduced to track the dynamics of energetic particles during frequency chirping by implementing proper Action-Angle va…
Global electromagnetic gyrokinetic simulations are performed with the Particle-in-Cell code ORB5 for an ITER Pre-Fusion-Power-Operation (PFPO) plasma scenario, with half-field (2.65 T) and half-current (7.5 MA). We report on a 'multi-scale' analysis of the discharge, considering eigenmodes and instabilies across three scale-lengths. Although the scenario will nominally have neutral beam heating with particles injected with 1 MeV, Alfvén eigenmodes are investigated in the absence of such source, and Reversed Shear (RSAE), Toroidal (TAE) and Elliptical (EAE) Alfvén eigenmodes are found with weak…
Recent upgrades in H-1 power supplies have enabled the operation of the H-1 experiment at higher heating powers than previously attainable. A heating power scan in mixed hydrogen/helium plasmas reveals a change in mode activity with increasing heating power. At low power (<50 kW) modes with beta-induced Alfven eigenmode (BAE) frequency scaling are observed. At higher power modes consistent with an analysis of nonconventional Global Alfven Eigenmodes (GAEs) are observed, the subject of this work. We have computed the mode continuum, and identified GAE structures using the ideal MHD solver CKA a…
The shear Alfvén continuum spectrum is studied for a tokamak with a single island chain using the ideal Magnetohydrodynamics (MHD) theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the Mirror-induced Alfvén Eigenmode (MAE) gap and the Helicity-induced Alfvén Eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside Toroidal Alfvén Eigenmode (TAE) gap into t…
Toroidal Alfvén eigenmodes (TAEs) are gap modes induced by the toroidicity of tokamak plasmas in absence of continuum damping. They can be excited by energetic particles (EPs) when the EP drive exceeds other dampings. A TAE benchmark case, which was proposed by the International Tokamak Physics Activity (ITPA) group, is studied in this work. Numerical calculations of linear growth of TAEs driven by EPs in a circular-shaped, large aspect ratio tokamak have been performed using the Hybrid Kinetic-MHD (HK-MHD) model implemented in the NIMROD code. This HK-MHD model couples a delta f particle-in-c…
A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron frequency compressional (CAE) and global (GAE) Alfvén Eigenmodes in low aspect ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam power in NSTX experiments, prompting further examination of the conditions for their excitation. Linear simulations are performed with the hybrid MHD-kinetic initial value code HYM in order to capture the general Doppler-shifted…
On nonlinear saturation of toroidal Alfvén eigenmode due to thermal plasma nonlinearities
Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）；Center for Nonlinear Plasma Science and C.R. ENEA Frascati（非线性等离子体科学中心及恩瑞亚弗拉斯卡蒂研究中心）；Institute for Fusion Theory and Simulation, School of Physics, Zhejiang University（浙江大学物理学院聚变理论与模拟研究所）；Key Laboratory of Frontier Physics in Controlled Nuclear Fusion and Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所及受控核聚变前沿物理重点实验室）；De Vinci Higher Education, De Vinci Research Center（德文奇高等教育机构及德文奇研究中心）
In this work, the gyrokinetic eigenvalue code LIGKA, the drift-kinetic/MHD hybrid code HMGC and the gyrokinetic full-f code TRIMEG-GKX are employed to study the mode structure details of Reversed Shear Alfvén Eigenmodes (RSAEs). Using the parameters from an ASDEX-Upgrade plasma, a benchmark with the three different physical models for RSAE without and with Energetic Particles (EPs) is carried out. Reasonable agreement has been found for the mode frequency and the growth rate. Mode structure symmetry breaking (MSSB) is observed when EPs are included, due to the EPs' non-perturbative effects. It…
Energetic particle populations in nuclear fusion experiments can destabilize Alfv\' en Eigenmodes through inverse Landau damping and couplings with gap modes in the shear Alfv\' en continua. We use the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles. We add the Landau damping and resonant destabilization effects by a closure relation. We apply the model to study the Alfv\' en modes stability in Large Helical Dev…
The interaction of Alfvén Eigenmodes (AEs) and energetic particles is one of many important factors determining the success of future tokamaks. In JET, eight in-vessel antennas were installed to actively probe stable AEs with frequencies ranging 25-250 kHz and toroidal mode numbers $\vert n \vert < 20$. During the 2019-2020 deuterium campaign, almost 7500 resonances and their frequencies $f_0$, net damping rates $γ< 0$, and toroidal mode numbers were measured in almost 800 plasma discharges. From a statistical analysis of this database, continuum and radiative damping are inferred to increase …
Neutral-beam-driven, sub-cyclotron compressional (CAE) and global (GAE) \Alfven eigenmodes are routinely excited in spherical tokamaks such as NSTX(-U) and MAST, have been observed on the conventional aspect ratio tokamak DIII-D, and may be unstable in ITER burning plasmas. Their presence has been experimentally linked to the anomalous flattening of electron temperature profiles at high beam power in NSTX, potentially limiting fusion performance. A detailed understanding of CAE/GAE excitation, therefore, is vital to predicting (and ultimately controlling) their effects on plasma confinement. T…
Alfven Eigenmodes (AE) can be destabilized during ITER discharges driven by neutral beam injection (NBI) energetic particles (EP) and alpha particles. The aim of the present study is to analyze the AE stability of different ITER operation scenarios considering multiple energetic particle species. We use the reduced magneto-hydrodynamic (MHD) equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species including the effect of the…
The aim of this study is to analyze the destabilization of Alfven Eigenmodes (AE) by multiple energetic particles (EP) species in DIII-D and LHD discharges. We use the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species, including the effect of the acoustic modes, diamagnetic currents and helical couplings. We add the Landau damping and resonant destabilization effects using a closure relation. The simulatio…
The aim of this study is to analyze the stability of the Alfven eigenmodes (AE) in the Chinese First Quasi-axisymmetric Stellarator (CFQS). The AE stability is calculated using the code FAR3d that solves the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moment for the energetic particles (EP) species including the effect of the helical couplings and acoustic modes. The Landau damping and resonant destabilization effects are added in the model by…
