Transition from fishbone mode to β-induced Alfvén eigenmode on HL-2A tokamak

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-2 A. When the safety factor at magnetic axis is well below one, typical kink-fishbone transition occurs as the EP fraction increases. When q0 is raised to approaching one, the fishbone mode is replaced with BAE for sufficient amount of EPs. When q0 is slightly above one, the toroidicity-induced Alfvén eigenmode dominates at lower EP pressure, whereas BAE dominates at higher EP pressure.     

Nonlinear excitation of a geodesic acoustic mode by reversed shear Alfvén eignemodes

The parametric decay process of a reversed shear Alfvén eigenmeode (RSAE) into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory. The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold, which could be readily satisfied in burning plasmas operated in steady-state advanced scenario. This decay process can contribute to thermal plasma heating and confinement improvement.     

Alfvén eigenmode stability analysis and energetic particle transport prediction for CFETR hybrid scenario

The hybrid scenario is a projection for CFETR operation with high plasma current and density. Therefore, the energetic particles (EPs) generated by fusion reactions can destabilize Alfvén eigenmodes (AEs), which could result in significant EPs loss and redistribution. Both the eigenvalue code NOVA-K and the wrapped local stability code TGLFEP are used to analyze AE stability. The simulation indicates the beta-induced Alfvén eigenmodes with n>5 in the core region are the most unstable. The NOVA-K code is used to benchmark the critical density gradient calculated by TGLFEP. In addition, the EPtran code is employed to predict EP transport induced by unstable AEs and turbulence, which reduce EP density in the core and drive approximately 30% EP transport from the core to the edge, thus the EP density profile flattens and EPs with lower energy deposit near the edge.     

Effects of the Hot Electron Interchange Instability on Plasma Confined in a Dipolar Magnetic Field

The Levitated Dipole Experiment (LDX) explores confinement and stability of plasma created within the dipole field of a strong superconducting magnet. During initial experiments, long-pulse, quasi-steady state discharges that last more than 10 s and have peak beta of more than 20% are studied. The plasma is created by multi-frequency electron cyclotron resonance heating (ECRH) at 2.45 and 6.4 GHz. A population of energetic electrons, with mean energies above 50 keV, dominates the plasma pressure. Creation of high pressure, high beta plasma is possible only when intense hot electron interchange (HEI) instabilities are stabilized by sufficient neutral gas fueling. The instabilities resonate with the magnetic drift motion of the energetic electrons and can cause rapid radial transport. Measurements of the electrostatic and magnetic fluctuations of the HEI instability are described along with observations of the instability’s spectral characteristics. Fluctuations of the outer poloidal field induced by the HEI show a rapid evolution of the perturbed pressure profile.      

Linear gyrokinetic simulations of reversed shear Alfven eigenmodes and ion temperature gradient modes in DIII-D tokamak

Global linear gyrokinetic simulations using realistic DIII-D tokamak geometry and plasma profiles find co-existence of unstable reversed shear Alfvén eigenmodes(RSAE)with low toroidal mode number n and electromagnetic ion temperature gradient(ITG)instabilities with higher toroidal mode number n.For intermediate n =[10,12],RSAE and ITG co-exist and overlap weakly in the radial domain with similar growth rates but different real frequencies.Both RSAE and ITG growth rates decrease less than 5％when compressible magnetic perturbations are neglected in the simulations.The ITG growth rates increase less than 7％when fast ions are not included in the simulations.Finally,the effects of trapped electrons on the RSAE are negligible.     

Kinetic micro-instabilities in the presence of impurities in toroidal magnetized plasmas

The theoretical and numerical studies on kinetic micro-instabilities,including ion temperature gradient(ITG) driven modes,trapped electron modes(TEMs) in the presence of impurity ions as well as impurity modes(IMs),induced by impurity density gradient alone,in toroidal magnetized plasmas,such as tokamak and reversed-field pinch(RFP) are reviewed briefly.The basic theory for IMs,the electrostatic instabilities in tokamak and RFP plasmas are discussed.The observations of hybrid and coexistence of the instabilities are categorized systematically.The effects of impurity ions on electromagnetic instabilities such as ITG modes,the kinetic ballooning modes(KBMs) and kinetic shear Alfvén modes induced by impurity ions in tokamak plasmas of finite β(=plasma pressure/magnetic pressure) are analyzed.The interesting topics for future investigation are suggested.     

Linear gyrokinetic simulations of reversed shear Alfvén eigenmodes and ion temperature gradient modes in DIII-D tokamak

Global linear gyrokinetic simulations using realistic DIII-D tokamak geometry and plasma profiles find co-existence of unstable reversed shear Alfvén eigenmodes(RSAE) with low toroidal mode number n and electromagnetic ion temperature gradient(ITG) instabilities with higher toroidal mode number n. For intermediate n?=?[10, 12], RSAE and ITG co-exist and overlap weakly in the radial domain with similar growth rates but different real frequencies. Both RSAE and ITG growth rates decrease less than 5% when compressible magnetic perturbations are neglected in the simulations. The ITG growth rates increase less than 7% when fast ions are not included in the simulations. Finally, the effects of trapped electrons on the RSAE are negligible.     

Suppression and mitigation of inter-ELM high-frequency Alfvén-like mode by resonant magnetic perturbation in EAST

Suppression and mitigation of a high-frequency Alfvén-like mode(HFAM) between type-I edge localized modes(ELMs) during ELM mitigation by resonant magnetic perturbation(RMP) is observed for the first time in the EAST tokamak. This mode is located near the edge pedestal region. The modeling result of the Alfvén continuum shows that the HFAM is located near the elipical Alfvén eigenmode(EAE) gap. During the application of n=1 RMP for ELM mitigation, the HFAM can be fully suppressed when the RMP amplitude exceeds a threshold,below which the HFAM is mitigated. The suppression is caused by a reduction of pedestal height induced by RMP. In the case using n=3 RMP, the mode is localized toroidally at specific phase depending on the phase of applied RMP, i.e. locked in the three-dimensional equilibrium formed by RMP. The dominant toroidal mode number of HFAM is around n=-6 and it reduces to -3 during the application of n=3 RMP, which indicates the existence of possible nonlinear coupling between the HFAM and RMP. Here the negative mode number denotes that the mode rotates in electron diamagnetic drift direction. The observation reported here improves the understanding of pedestal dynamics and its stability in RMP ELM control.     

Mode structure symmetry breaking of reversed shear Alfvén eigenmodes and its impact on the generation of parallel velocity asymmetries in energetic particle distribution

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 is found that the MSSB properties are featured by a finite radial wave phase velocity, and the linear mode structure can be well described by an analytical complex Gaussian expression ${\rm{\Phi }}(s)={{\rm{e}}}^{-\sigma {\left(s-{s}_{0}\right)}^{2}}$ with complex parameters σ and s0, where s is the normalized radial coordinate. The mode structure is distorted in opposite manners when the EP drive shifted from one side of ${q}_{\min }$ to the other side, and specifically, a non-zero average radial wave number 〈ks〉 with opposite signs is generated. The initial EP density profiles and the corresponding mode structures have been used as the input of HAGIS code to study the EP transport. The parallel velocity of EPs is generated in opposite directions, due to different values of the average radial wave number 〈ks〉, corresponding to different initial EP density profiles with EP drive shifted away from the ${q}_{\min }$.     

HL-2A装置中阿尔芬本征模的数值模拟

采用GTAW程序模拟研究了HL-2A装置等离子体中的阿尔芬(Alfvén)本征模,得到了典型放电条件下的本征频率和模结构及等离子体密度分布对本征频率和模结构的影响。计算得到的环形阿尔芬本征模（TAE）间隙中的本征频率99.09、74.90和99.17 kHz与实验观察到的高频Alfvén本征模频率相吻合。计算还发现,等离子体中心电子密度的增大会导致TAE的本征频率减小,但不影响模的径向位置和结构。     

Investigation of ion fishbone stability on HL-2A using NIMROD

Numerical calculations of resistive internal kink mode with effects of energetic particles (EPs) on HL-2A have been performed using the hybrid kinetic-MHD model inplemented in the NIMROD code. The m/n=1/1 resistive internal kink mode is unstable in MHD limit. However, with kinetic effects of energetic ions, a fishbone mode is excited with mode frequency around 10 kHz. We calculate the impact of resistivity on the growth rate and frequency of ion fishbone mode, and the results are in good agreement with the analytic solutions, which are obtained by solving the fishbone dispertion relation including resistivity effect. The effects of β_frac and cut off velocity of EP on fishbone mode are calculated in detail, where β_frac is the ratio of EP pressure to background plasma pressure. This work presents a clear explanation of the stabilizing effect of ECRH on ion fishbone, which is first observed on HL-2A.     

Alfvén continuum in the presence of a magnetic island in a cylinder configuration

In this work, the effect of a magnetic island on Alfvén waves is studied. A physical model is established wherein Alfvén waves propagate in the presence of a magnetic island in a cylindrical geometry. The structure of the Alfvén wave continuum is calculated by considering only the coupling caused by the periodicity in the helical angle of the magnetic island. The results show that the magnetic island can induce an upshift in the Alfvén continuum. Moreover, the coupling between different branches of the continuous spectrum becomes more significant with increasing continuum mode numbers near the boundary of the magnetic island.     

Frequency multiplication with toroidal mode number of kink/fishbone modes on a static HL-2A-like tokamak

In the presence of energetic particles (EPs), the long-lived mode (LLM) frequency multiplication with n = 1, 2, 3, or higher is often observed on HL-2A, where n is the toroidal mode number. Hybrid kinetic-MHD model simulations of the energetic particle (EP) driven kink/fishbone modes on a static HL-2A-like tokamak using NIMROD code find that when the background plasma pressure is relatively high, and the EP pressure and the beam energy are relatively low, the mode frequency increases almost linearly with EP pressure, and the frequency is proportional to n ('frequency multiplication'), even in the absence of any equilibrium plasma rotation. In addition, the frequency multiplication persists as the safety factor at the magnetic axis q0 varies. In the absence of EPs, the growth rate of the 1/1 mode is the largest; however, as the EP pressure increases, the growth rate of 2/2 modes or 3/3 modes becomes dominant, suggesting that higher-n modes are more vulnerable to EPs. These results may shed light on the understanding of the toroidal mode number dependence of kink/fishbone modes in the advanced scenarios of tokamaks with weak or reversed central magnetic shear.     

Stability analysis of Alfvén eigenmodes in China Fusion Engineering Test Reactor fully non-inductive and hybrid mode scenarios

In this paper, NOVA/NOVA-K codes are used to investigate the stability of Alfvén eigenmodes(AEs) in the China Fusion Engineering Test Reactor(CFETR). Firstly, the stability of AEs excited by energetic alpha particles is investigated. For the fully non-inductive scenario, it is found that all AEs are stable, and the least stable toroidal mode number is n= 8. However, for the hybrid mode scenario, it is found that many AEs are unstable, and the least stable toroidal mode numbers are n= 7, 8. Secondly, the effect of energetic alpha-particle parameters and beam ions on AE stability is also presented. The threshold of the least stable AE is about β_(crit,α) = 1.12%,crit,less than the value of alpha-particle beta(β_α=1.34%). The result demonstrates that the AEs excited by alpha particles are weakly unstable. The effect of the beam ions on AE stability is found to be very weak in CFETR.     

Investigation of the fast magnetosonic wave excited by the Alfvén wave phase mixing by using the Hall–MHD model in inhomogeneous plasma

The inhomogeneity is introduced by a nonzero density gradient which separates the plasma into two different regions where plasma density are constant. The Alfvén waves, the phase mixing and the fast magnetosonic wave are excited by the boundary condition in inhomogeneous magnetized plasma. By using the Hall–magnetohydrodynamics(MHD) model, it is found that there are Alfvén waves in the homogeneous regions, while the phase mixing appears in the inhomogeneous region. The interesting result is that a fast magnetosonic wave is excited in a different direction which has a nonzero angle between the wave propagation direction and the direction of the background magnetic field. The dependence of the propagation direction of the excited fast magnetosonic wave and its strength of the magnetic field on the plasma parameters are given numerically. The results show that increasing both the driving frequency and the ratio of magnetic pressure to thermal pressure will increase the acceleration of the electrons. The electron acceleration also depends on the inhomogeneity parameters.     

Observation of MHD Instabilities Driven by Energetic Electrons in the Large Helical Device

Coherent magnetic fluctuations in an acoustic range of frequency have been regularly observed in low-density(n_e0.2×10~(19)m~(-3))plasmas with strong second harmonic electron cyclotron resonance heating(ECRH)on the Large Helical Device.Hard X-ray measurements indicated that energetic electrons are generated in these ECRH discharges.The magnetic fluctuations are suppressed in higher density discharges where energetic electrons are not present.The ECRH power modulation experiment indicated that the observed magnetohydrodynamic(MHD)mode has an acoustic nature rather than an Alfvenic nature.     

Influence of Superathermal Electrons on Central Plasma Relaxation oscillations during Localized Electron Cyclotron Heating on the HL—1M Tokamak

During initial studies of ECRH in the HL-1M tokamak,non-standard central MHD activities,such as saturated wawtooth,partially saturated sawtooth,double sawtooth,and the strong m=1 bursts have been observed while changing the heating location,the ECRH power.the plasma density,Complete suppression of sawtooth is achieved for the duration of the ECRH.when the heating power is applied on the high-fiedl side of low-density plasma,and exceeds a threshold value of power .The m=1 bursts riding on the ramp phase of sawtooth can only be excited when the ECRH locaxation activities are produced or suppressed are described.Experimental results imply that the energetic electrons generated during ECRH are responsible for the modification/or stabilization/or excitation of the instability.Near the q=1 surface,the passing electrons play the role of reducing the shear and tending to stabilize the sawtooth activity,while the barely-trapped electrons play the role of enhancing or driving an internal kink instability.     

A simulation study of protons heated by left/right-handed Alfvén waves generated by electromagnetic proton-proton instability

Most protons in the solar wind belong to one of two different populations,the less dense beam protons and the denser core protons.The beam protons,with a velocity of(1-2)VA(VA is the local Alfvén speed),always drift relative to the core protons;this kind of distribution is unstable and stimulates several kinds of wave mode.In this study,using a 2D hybrid simulation model,we find that the original right-handed elliptically polarized Alfvén waves become linearly polarized,and eventually become right-handed and circularly polarized.Given that linearly polarized waves are a superposition of left-handed and right-handed waves,cyclotron resonance in the right-handed/left-handed component heats beam/core protons perpendicularly.The resonance between beam protons and right-handed polarized waves is stronger when the beam relative density is lower,resulting in more dramatic perpendicular heating of beam protons,whereas the situation is reversed when the beam relative density is larger.     

Solitary kinetic Alfvén waves in a dense electron-positron-ion plasma with degenerate electrons and positrons

Through the use of a reductive perturbation technique, solitary kinetic Alfvén waves(KAWs) are investigated in a low but finite b(particle-to-magnetic pressure ratio) dense electron–positron–ion plasma where electrons and positrons are degenerate. The degenerate plasma model considered here permits the existence of sub-Alfvénic compressive solitary KAWs. The influence of r(equilibrium positron-to-ion density ratio), sF(electron-to-positron Fermi temperature ratio), b and obliqueness parameter lzon various characteristics of solitary KAWs are examined through numerical plots. We have shown that there exists a critical value of lzat which a soliton width attains its maximum value which decreases with an increase in r and sF.It is also found that solitons with a higher energy propagate more obliquely in the direction of an ambient magnetic field. The results of the present investigation may be useful for understanding low frequency nonlinear electromagnetic wave propagation in magnetized electron–positron–ion plasmas in dense stars. Specifically, the relevance of our investigation to a pulsar magnetosphere is emphasized.     

A brief review: experimental investigation of zonal flows and geodesic acoustic modes in fusion plasmas

Zonal flows self-generated by turbulence play an important role in regulating turbulence, reducing transport level, and thus improve plasma confinement in fusion plasmas. The zonal flows and geodesic acoustic modes have been identified in various devices. The related issues, such as the poloidal and toroidal symmetries, coupling to turbulence, effects on turbulence and transport, nonlinear energy transfer between turbulence and zonal flows, dependence of the plasma parameters, roles in the confinement regime transitions etc are overviewed briefly in this paper. The interaction between zonal flows and magnetic islands is emphasized.