Toroidal Alfven Eigenmodes Research Articles

PFPO plasma scenarios for exploration of long pulse operation in ITER

Long Pulse Scenarios (LPS) in ITER foreseen during the Pre-Fusion Power Operation (PFPO) phase of the ITER Research Plan (IRP) are assessed using 1.5D transport simulations within the ASTRA framework. Such assessment is required to predict the operational space for LPS operation in PFPO, as well as to evaluate which physics processes for LPS operation during Fusion Power Operation (FPO) could be studied during PFPO. An important aspect in the development of LPSs in PFPO is to minimize lifetime consumption of the Central Solenoid (CS) for these scenarios. The maximum pulse length achievable for LPSs in PFPO with no consumption of CS lifetime (currents in CS coils ⩽30 kA per turn) has been assessed for a range of heating schemes and heating mixes, confinement regimes (L-mode and H-mode) and for helium and hydrogen plasmas. The operational space of LPS and pulse length has been explored through density scans with the Heating and Current Drive mix required for the FPO Q ⩾ 5 steady-state plasma scenario (namely Neutral Beam Injection and Electron Cyclotron Heating) including acceptable shine through losses on the first wall for both helium and hydrogen plasmas. Fast particle physics aspects that are common between FPO plasmas and LPS PFPO H-mode plasmas at low densities are studied including MHD stability analysis with the KINX code and non-perturbative critical gradient model based on high-n Toroidal Alfven Eigenmodes (TAE) stability kinetic ballooning code HINST calculations.

Simulation of the TAEs’ saturation phase in the Large Helical Device: MHD burst

The aim of the present study is to analyze the saturation regime of the toroidal Alfven eigenmodes (TAE) in the Large Helical Device plasma, particularly the MHD burst. The linear and nonlinear evolution of the TAEs are simulated by the FAR3d code that uses a reduced MHD model for the thermal plasma coupled with a gyrofluid model for the energetic particle (EP) species. The linear simulations indicate the overlapping of 1/2 − 1/1, 2/3–2/4 and 3/5–3/6 TAEs in the inner-middle plasma region and frequency range of 45–75 kHz, triggered by EPs with an energy of T f = 45 keV and EP β = 0.022. The nonlinear simulations show that 2/3–2/4 and 3/4–3/5 TAEs are further destabilized due to the energy transfer from the 1/1–1/2 TAE, leading to broad TAE radial overlapping and triggering of the MHD burst. The energy of the 1/1–1/2 TAE is also nonlinearly transferred to the thermal plasma destabilizing the 0/0 and 0/1 modes, inducing the generation of shear flows and zonal currents, as well as large deformations in the thermal pressure and EP density radial profiles. The nonlinear simulation reproduces the same succession of instabilities and the same frequency range with respect to the experiment. The instability propagates outward during the bursting phase, showing a large decrease of the EP density profile between the middle-outer plasma, indicating the loss of part of the EP population that explains the decrease in the plasma heating efficiency observed during the MHD burst.

Анализ потерь быстрых ионов, вызванных распространением тороидальных альфвеновских мод в плазме сферического токамака Глобус-М2

With an increase of magnetic field up to 0.8 T and plasma current to 400 kA, fast ion losses rate in the discharges with toroidal Alfven eigenmodes decreased in tokamak Globus-M2 comparing with Globus-M tokamak discharges. Taking into account the data on the discharges with increased magnetic field and plasma current, the regression fit of neutral particle analyzer flux drop in energy channel close to neutral beam energy on relative eigenmode magnitude, the value of magnetic field and plasma current was analyzed. The power of flux drop dependence on TAE magnitude was found to be ~0.5 and inverse proportional on the value of product of magnetic field and plasma current, which is highly likely is determined only by plasma current due to weak dependence on magnetic field. The result obtained indicates that fast ion losses in Globus-M2, stimulated by toroidal Alfven eigenmodes are mostly determined by the shift of passing orbits to the plasma edge. With the increase of plasma current and magnetic field, neutron flux drops arising in the moments of toroidal mode bursts have also decreased.

Analysis of toroidal Alfven eigenmode-induced fast ion losses in Globus-M2 spherical tokamak

With an increase of magnetic field up to 0.8 T and plasma currentto 400 kA, fast ion losses rate in the discharges with toroidal Alfveneigenmodes decreased in tokamak Globus-M2 comparing with Globus-M tokamakdischarges. Taking into account the data on the discharges with increasedmagnetic field and plasma current, the regression fit of neutral particleanalyzer flux drop in energy channel close to neutral beam energy onrelative eigenmode magnitude, the value of magnetic field and plasma currentwas analyzed. The power of flux drop dependence on TAE magnitude was foundto be ~0.5 and inverse proportional on the value of product of magneticfield and plasma current, which is highly likely is determined only byplasma current due to weak dependence on magnetic field. The resultobtained indicates that fast ion losses in Globus-M2, stimulated by toroidalAlfven eigenmodes are mostly determined by the shift of passing orbits tothe plasma edge. With the increase of plasma current and magnetic field,neutron flux drops arising in the moments of toroidal mode bursts have alsodecreased. Keywords: TAE, NPA, spherical tokamak, fast ion losses\

Multi-scale interactions between turbulence and magnetohydrodynamic instability driven by energetic particles

In order to realize high performance burning plasmas in magnetic-confinement fusion devices, such as tokamaks, both bulk plasma transport and that of energetic fusion alpha-particles, which result from different scale fluctuations with different free energy sources, have to be reduced simultaneously. Utilizing the advantage of global toroidal non-linear simulations covering a whole torus, here, we found a new coupling mechanism between the low-frequency micro-scale electromagnetic drift-wave fluctuations regulating the former, while the high-frequency macro-scale toroidal Alfven eigenmode (TAE) regulates the latter. This results from the dual spread of micro-scale turbulence due to the macro-scale TAE not only in wavenumber space representing local eddy size but also in configuration space with global profile variations. Consequently, a new class of turbulent state is found to be established, where the turbulence is homogenized on the poloidal cross-section with exhibiting large-scale structure, which increases fluctuation levels and then both transports, leading to deterioration in the fusion performance.

Noise suppression for MHD characterization with electron cyclotron emission imaging 1D technique

Significant noise suppression for magnetohydrodynamics (MHD) mode characterization in the spatial and spectral domain is achieved by processing two-dimensional (2D) electron cyclotron emission imaging (ECEI) data with a one-dimensional (1D) ECEI technique using a short time window (). The technique is applied to detect toroidal Alfven eigenmodes (TAEs) in the temporal spectrum and fit their radial envelope using the data from the DIII-D tokamak W-band 2D ECEI system. Using the data length (time window) of only 1 , the 1D ECEI can clearly detect the TAEs (∼100 ) on the spectrum, while similar spectrum quality requires ∼10 data length with the cross power spectrum between two midplane ECEI channels. The 1D ECEI technique also effectively avoids biased fitting when resolving the fine structure of the TAE’s radial envelope. The radially spatial resolution of 1D ECEI is constrained by the finite ECE radiation volume of the ECEI receiver. With forward radiation modeling, we find the DIII-D ECEI system can sensitively measure the even parity MHD activities, for which the mode width is >15 mm, and tearing modes (odd parity MHD activities), for which the island full width is >30 mm.

Study of the Alfven eigenmodes stability in CFQS plasma using a Landau closure model

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 a given closure relation. The simulation results indicate the destabilization of n = 1 to 4 AEs by EP during the slowing down process, particularly n = 1 and n = 2 toroidal AEs (TAE), n = 3 elliptical AE (EAE) and n = 4 non circular AE (NAE). If the resonance is caused by EPs with an energy above 17 keV (weakly thermalized EP), n = 2 EAEs and n = 3 NAEs are unstable. On the other hand, EPs with an energy below 17 keV (late thermalization stage) lead to the destabilization of n = 3 and n = 4 TAEs. The simulations for an off-axis NBI injection indicate the further destabilization of n = 2 to 4 AEs although the growth rate of the n = 1 AEs slightly decreases, so no clear optimization trend with respect to the NBI deposition region is identified. In addition, n = 2, 4 helical AE (HAE) are unstable above an EP β threshold. Also, if the thermal β of the simulation increases (higher thermal plasma density) the AE stability of the plasma improves. The simulations including the effect of the finite Larmor radius and electron-ion Landau damping show the stabilization of the n = 1 to 4 EAE/NAEs as well as a decrease of the growth rate and frequency of the n = 1 to 4 BAE/TAEs.

Application of Doppler Backscattering for Alfvén Mode Study on the Globus-M Spherical Tokamak

The Alfven oscillations were studied using the multifrequency Doppler backscattering (DBS) method on the Globus-M spherical tokamak during the neutral deuterium injection. The principles of Alfven mode registration by the DBS method are discussed. Microwave schemes of multifrequency probing are described. It is shown that the observed plasma rotation velocity oscillations are due to the oscillations of the drift velocity in crossed radial electric field of the Alfven wave and the magnetic field. The absolute values of the magnetic field perturbations of the toroidal Alfven eigenmode (TAE) in the internal regions of the tokamak discharge are determined. The obtained data are compared with the results of the magnetic field oscillations measurements obtained by a magnetic probe located outside the plasma region. The use of multifrequency probing in the DBS method made it possible to determine the radial distributions of the amplitude of magnetic field oscillations. These data were obtained for oscillations at the TAE fundamental frequency and at harmonic frequencies, which were found to correspond to different toroidal mode numbers. In general, the data obtained can be compared with the results of numerical modeling of the Alfven spectrum in the Globus-M tokamak. The prospects for the further use of the DBS method for studying Alfven oscillations in toroidal installations are discussed.

Progress of Experimental Studies in the HL-2A Tokamak

During the last several years, the HL-2A experiment has made significant progress in the following areas: (1) lower-hybrid wave (LHW) heating and current drive, (2) plasma confinement and turbulent transport, (3) magnetohydrodynamic (MHD) instabilities and energetic particle physics and (4) H-mode and edge localized mode (ELM) control. The results show that the LHW system working in the co-current mode can reach higher driving efficiency and full non-inductive lower-hybrid current drive (LHCD) has been achieved. The intrinsic poloidal torque characterized by the divergence of the residual stress is deduced from synthesis for the first time. The dynamics of spectral symmetry breaking in drift wave turbulence is in good agreement with the development of the poloidal torque to drive the edge poloidal flow. The influence of the cross-phase dynamics on turbulent stress was also investigated. The ion internal transport barrier has been observed in the NBI-heated plasma, and inside the barrier the ion thermal transport is reduced to the neoclassical level. Besides, micro-turbulence is modulated by the rotation frequency of the magnetic island, and this modulation effect is related to a critical island width. Strong E × B shear is found at the island boundary. Three kinds of axisymmetric modes, beta-induced Alfven eigenmode (BAE), toroidal Alfven eigenmode (TAE) and the ellipticity-induced Alfven eigenmode (EAE), are found to be driven unstable by nonlinear mode coupling between Alfven eigenmodes and tearing mode which is well explained by the nonlinear gyrokinetic theory. The fishbone and tearing modes were actively controlled by the electron cyclotron resonance heating (ECRH). The dynamics of the edge plasma flows and turbulence during the L–I–H transition have been dedicatedly investigated. The geodesic acoustic mode (GAM) and limit cycle oscillation (LCO) coexist for a short time and disappear in the H-mode plasma with the increasing of E × B shear flow before the I–H transition, which plays an important role in the turbulence suppression. Different techniques, such as LHW, ECRH, resonant magnetic perturbation (RMP), and impurity seeding by the laser blow-off (LBO) and supersonic molecular beam injection (SMBI), have been successfully applied to control the large ELMs. It has been found that pedestal turbulence enhancement might be responsible for the observed mitigation effect.

Modeling of the ECCD injection effect on the Heliotron J and LHD plasma stability

The aim of the study is to analyze the stability of the energetic particle modes (EPM) and Alfven Eigenmodes (AE) in Helitron J and LHD plasma if the electron cyclotron current drive (ECCD) is applied. The analysis is performed using the code FAR3d that solves the reduced MHD equations describing 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 particle (EP) species, including the effect of the acoustic modes. The Landau damping and resonant destabilization effects are added via the closure relation. The simulation results show that the n = 1 EPM and n = 2 global AE (GAE) in Heliotron J plasma can be stabilized if the magnetic shear is enhanced at the plasma periphery by an increase (co-ECCD injection) or decrease (ctr-ECCD injection) of the rotational transform at the magnetic axis (). In the ctr-ECCD simulations, the EPM/AE growth rate decreases only below a given , similar to the ECCD intensity threshold observed in the experiments. In addition, ctr-ECCD simulations show an enhancement of the continuum damping. The simulations of the LHD discharges with ctr-ECCD injection indicate the stabilization of the n = 1 EPM, n = 2 toroidal AE (TAE) and n = 3 TAE, caused by an enhancement of the continuum damping in the inner plasma leading to a higher EP β threshold with respect to the co- and no-ECCD simulations.

Implementation of cross-phase analysis for study of MHD instabilities arising on TUMAN-3M and Globus-M tokamaks

Following paper represents a method to resolve spatial mode structure of plasma MHD instabilities employing cross-phase correlation analysis applied to signals of magnetic probes, mounted on Globus-M and Tuman-3M tokamaks. The data on observations of toroidal Alfven eigenmodes (TAEs), which were formerly identified in Globus-M tokamak discharges, has been analyzed. Possible interpretation of the phase plot, acquired from analysis of NBI-stimulated ion-cyclotron emission (ICE) on Tuman-3M is given as well. The method described below turns out to be useful instrument for resolution of spatial structure of plasma instabilities, especially in D-shaped tokamaks with low aspect ratio.

Numerical study of transition between even and odd toroidal Alfvén eigenmodes on EAST

Linear simulations of toroidal Alfvén eigenmodes (TAEs) driven by energetic particles (EPs) on EAST (Experimental Advanced Superconducting Tokamak) are performed using the hybrid-kinetic MHD model implemented in NIMROD code. The EAST equilibrium is reconstructed using the EFIT code based on the 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/RSAE (Reverse Shear Alfvén Eigenmode)/EPM (energetic particle mode) modes are consistent between the eigenvalue analysis and the NIMROD simulation. As the β fraction of EP increases, a transition between even and odd TAEs occurs, along with that between the ballooning and antiballooning mode structures. When the β fraction of EP is close to the transition threshold, both types of TAEs coexist.

Toroidal Alfvén Modes in the Plasma of the Globus-M Spherical Tokamak

Results of experimental studies of toroidal Alfven eigenmodes (TAEs) in the Globus-M spherical tokamak (R = 36 cm, a = 24 cm) are reported. The experiments were carried out in a wide range of plasma parameters at a magnetic field of up to 0.5 T and plasma current of up to 250 kA. Auxiliary plasma heating was performed by tangential injection of a deuterium beam with a power of Pb= 0.75 MW and particle energy of Eb = 28 keV into deuterium plasma. The experiments have shown that the TAE-induced loss of fast particles decreases with increasing plasma current and magnetic field. Using multifrequency Doppler backscattering diagnostics, it is established that the TAEs are localized at the plasma periphery. Results of simulations of the Alfven continuum and TAE structure by means of the modified KINX and CAXE codes agree satisfactory with the experimental data on the TAE frequencies and localization.

Theory of Alfvén-slow frequency gaps and discovery of Alfvén-slow eigenmodes in tokamaks

An analytical theory based on the MHD model is presented for understanding the coupling between the shear Alfvén wave and the slow magnetosonic wave (or the so called slow mode) in the frequency range below the Toroidal Alfvén Eigenmode (TAE) continuum spectrum gap. In tokamak plasmas, coupling of the Alfvén m poloidal harmonic and the slow mode m ± 1 harmonics causes the Alfvén m harmonic continuous spectrum to be uplifted from the uncoupled Alfvén spectrum by an amount related to the plasma pressure and the geodesic magnetic field curvature. However, the frequency of one of the slow mode m ± 1 harmonics is reduced by the same pressure-curvature coupling effect. But the frequency of the other slow mode harmonic is relatively unaffected. As a result, the Alfvén-slow (AS) mode continuous spectrum is broken up into two Alfvén-Slow (AS) gaps below the TAE continuum gap. Coupling of the Alfvén m harmonic with the slow mode m ± 2 harmonics also creates additional AS gaps if their frequencies cross each other. The AS gap widths increase with the plasma pressure. The creation of AS gaps allows the existence of several new types of Alfvén-Slow Eigenmodes (ASEs). The radial structure of these new ASEs does not intersect with the continuous spectrum and thus does not suffer from continuum damping. The Beta-induced Alfvén-Acoustic Eigenmode (BAAE) is one type of ASEs with frequency in the lowest AS frequency gap. However, the BAAE usually interacts with the Alfvén-Slow continuum and suffers from continuum damping. The existence of ASEs is ubiquitous for normal and reserve safety factor profiles, broad range of plasma β values, different plasma shapes, and many different toroidal mode numbers. The newly discovered ASEs provide explanation for the experimentally observed Beta-induced Alfvén Eigenmodes destabilized by fast ions with frequencies below the TAE frequency gap.

Overview of HL-2A recent experiments

The mission of HL-2A is to explore the key physical topics relevant to ITER and to the advanced tokamak operation (e.g. the operation of future HL-2M), such as the access of H-mode, energetic particle physics, edge-localized mode (ELM) mitigation/suppression and disruption mitigation. Since the 2016 Fusion Energy Conference, the HL-2A team has focused on the investigations on the following areas: (i) pedestal dynamics and L–H transition, (ii) techniques of ELM control, (iii) turbulence and transport, (iv) energetic particle physics. The HL-2A results demonstrated that the increase of mean shear flow plays a key role in triggering L–I and I–H transitions, while the change of flow is mainly induced by the ion pressure gradient. Both mitigation and suppression of ELMs were realized by laser blow-off seeded impurity (Al, Fe, W). The 30% Ne mixture supersonic molecular beam injection seeding also robustly induced ELM mitigation. The ELMs were mitigated by low-hybrid current drive. The stabilization of m/n = 1/1 ion fishbone activities by electron cyclotron resonance heating was found on the HL-2A. A new m/n = 2/1 ion fishbone activity was observed recently, and the modelling indicated that passing fast ions dominantly contribute to the driving of 2/1 fishbone. The non-linear coupling between the toroidal Alfven eigenmode and tearing mode (TM) led to the generation of a high frequency mode with the toroidal mode number n = 0. The turbulence was modulated by TM when the island width exceeds a threshold and the modulation is localized merely in the inner area of the islands. Meanwhile, turbulence radial spread took place across the island region.

Anomalous Fast-Ion Transport During Neutral Beam Injection on EAST

The fast-ion transport during neutral beam injection on the Experimental Advanced Superconducting Tokamak (EAST) is studied. Based on the NUBEAM and TRANSP codes, it is found that fast-ion transport is anomalous when the minimum safety factor (qmin) is about 2, while it is neoclassical when qmin is around 1. Neutral beam injection heating efficiency, plasma stored energy, and the total heating power are reduced when the fast ion transport is anomalous. The Alfven continuum spectrum and the mode structures of toroidal Alfven eigenmodes (AEs) are also calculated for comparison between neoclassical fast-ion transport and anomalous fast-ion transport. High-qmin discharge with anomalous fast-ion transport has more AE activity than that of lower qmin discharge with neoclassical fast-ion transport.

Analysis of resonant fast ion distributions during combined ICRF and NBI heating with transients using neutron emission spectroscopy

ICRF heating at the fundamental cyclotron frequency of a hydrogen minority ion species also gives rise to a partial power absorption by deuterium ions at their second harmonic resonance. This paper studies the deuterium distributions resulting from such 2nd harmonic heating at JET using neutron emission spectroscopy data from the time of flight spectrometer TOFOR. The fast deuterium distributions are obtained over the energy range 100 keV to 2 MeV. Specifically, we study how the fast deuterium distributions vary as ICRF heating is used alone as well as in combination with NBI heating.When comparing the different heating scenarios, we observed both a difference in the shapes of the distributions as well as in their absolute level. The differences are most pronounced below 0.5 MeV. Comparisons are made with corresponding distributions calculated with the code PION. We find a good agreement between the measured distributions and those calculated with PION, both in terms of their shapes as well as their amplitudes.However, we also identified a period with signs of an inverted fast ion distribution, which showed large disagreements between the modeled and measured results. Resonant interactions with tornado modes, i.e. core localized toroidal alfven eigenmodes (TAEs), are put forward as a possible explanation for the inverted distribution.

Optimization of Antenna Current Feeding for the Alfvén Eigenmodes Active Diagnostic System of JET

The possibility of exploring proper phasing of the feeding currents in the existing antenna of the Alfven Eigenmodes Active Diagnostic system of JET, to excite pure toroidal spectra of Toroidal Alfven Eigenmodes, is numerically investigated. Special attention is given to the actual perturbed fields excited in the plasma, which are calculated self-consistently using the antenna version of the CASTOR code. It is found that due to the close spacing of the JET antenna modules and quasi degeneracy of modes with medium to high values of the toroidal mode number n, although a proper choice of the phasing of the feeding currents of the antenna modules indeed leads to an increase of the perturbed fields of the selected mode, modes with nearby values of n are also excited with large amplitudes, so that a scheme to proper select the detected modes remains necessary. A scheme using different antenna position distribution is proposed to achieve successful optimization.

Toroidal Alfvén Eigenmodes in Globus-M Spherical Tokamak Plasma

Conditions of the excitation of toroidal Alfven eigenmodes (TAEs) and their inf luence on the confinement of fast particles into the Globus-M spherical tokamak have been studied by KINX code calculations of the magnetohydrodynamic spectra of reconstructed divertor equilibrium configurations with stability margin q0 > 1 on the magnetic axis. The sensitivity of the frequencies of TAE modes with toroidal wavenumber n = 1 to the type of boundary conditions and choice of boundary surface has been studied. It has been established that the frequencies of modes with dominating poloidal harmonics m = 1 and 2 in the gap of continuum are significantly higher than those observed in the spectra of signals measured in the Mirnov coil probes, especially under the assumption of free plasma boundary with allowance for its compressibility. The TAE modes with lower frequencies and higher poloidal wavenumbers localized near the plasma boundary may be responsible for the oscillations observed in the experiment. However, these modes are characterized by the interaction with continuum and, probably, exhibit related damping.

Discrete Alfvén eigenmodes under the condition <_ufe:lines-br xmlns:_ufe="http://www.arbortext.com/namespace/Styler/UserFormattingElements" xml:base="-7mm"> </_ufe:lines-br>of bootstrap current in EAST

Basing on experimental advanced superconducting Tokamak (EAST), we have researched relation between bootstrap current and α -induced toroidal Alfven eigenmode ( α TAE, α is a measure of plasma pressure gradient), which is investigated, in this paper, for the EAST tokamak operation condition with the bootstrap current. Our results show that the α TAE may exist in a relatively broad region of minor radius, where a large bootstrap current density is observed. In the presence of energetic particles, produced by the NBI experiments, our MHD-gyrokinetic hybrid simulations demonstrate that this quasi-marginally stable α TAE (within MHD description) can be readily destabilized by the kinetic compression upon the wave-particle resonances.