Nonlinear dynamics of the reversed shear Alfvén eigenmode in burning plasmas

In a tokamak fusion reactor operated at steady state,the equilibrium magnetic field is likely to have reversed shear in the core region,as the noninductive bootstrap current profile generally peaks off-axis.The reversed shear Alfvén eigenmode(RSAE)as a unique branch of the shear Alfvén wave in this equilibrium,can exist with a broad spectrum in wavenumber and frequency,and be resonantly driven unstable by energetic particles(EP).After briefly discussing the RSAE linear properties in burning plasma condition,we review several key topics of the nonlinear dynamics for the RSAE through both wave-EP resonance and wave-wave coupling channels,and illustrate their potentially important role in reactor-scale fusion plasmas.By means of simplified hybrid MHD-kinetic simulations,the RSAEs are shown to have typically broad phase space resonance structure with both circulating and trapped EP,as results of weak/vanishing magnetic shear and relatively low frequency.Through the route of wave-EP nonlinearity,the dominant saturation mechanism is mainly due to the transported resonant EP radially decoupling with the localized RSAE mode structure,and the resultant EP transport generally has a convective feature.The saturated RSAEs also undergo various nonlinear couplings with other collective oscillations.Two typical routes as parametric decay and modulational instability are studied using nonlinear gyrokinetic theory,and applied to the scenario of spontaneous excitation by a finite amplitude pump RSAE.Multiple RSAEs could naturally couple and induce the spectral energy cascade into a low frequency Alfvénic mode,which may effectively transfer the EP energy to fuel ions via collisionless Landau damping.Moreover,zero frequency zonal field structure could be spontaneously excited by modulation of the pump RSAE envelope,and may also lead to saturation of the pump RSAE by both scattering into stable domain and local distortion of the continuum structure.

Gyrokinetic simulation of low-n Alfvénic modes in tokamak HL-2A plasmas

The turbulence characteristics of plasmas with internal transport barriers in the HL-2A tokamak are analyzed by means of linear gyrokinetic simulations. It is found that turbulence is dominated by the ion temperature gradient(ITG)mode together with large-scale modes characterized by high-frequency electromagnetic fluctuation, which are destabilized by the steep ion temperature gradient in the weak magnetic shear regime. Comparison with solutions of analytical dispersion relations shows that their linear features match well with the beta-induced Alfvén eigenmode branch of the shear Alfvénic spectrum. It is further clarified that the large population of fast ions in these plasmas plays a stabilization role through the dilution mechanism in high-n ITG mode regimes.

Discrete Alfvén eigenmodes in the CFETR steady-state scenario

The stability features of discrete Alfvén eigenmodes(αTAEs) trapped by α-induced potential wells are explored in the China Fusion Engineering Test Reactor(CFETR) advanced steady-state operation environment, where α denotes a measure of the pressure gradient. For the reversed magnetic shear(RS) H-mode scenario with an enhanced internal transport barrier(ITB), the αTAEs are trapped in the electron cyclotron(EC) power deposition region and the effects of different pedestals on αTAEs are analyzed. For the negative off-axis magnetic shear scenario, the αTAEs are discussed, and the effect of different magnetic shears on the α TAEs is presented. Finally, the effects of beam energies and pitch-angle distributions onαTAE stability are also presented.

Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas

Nonlinear evolution of multiple toroidal Alfvén eigenmodes(TAEs)driven by fast ions is self-consistently investigated by kinetic simulations in toroidal plasmas.To clearly identify the effect of nonlinear coupling on the beam ion loss,simulations over single-n modes are also carried out and compared with those over multiple-n modes,and the wave-particle resonance and particle trajectory of lost ions in phase space are analyzed in detail.It is found that in the multiple-n case,the resonance overlap occurs so that the fast ion loss level is rather higher than the sum loss level that represents the summation of loss over all single-n modes in the single-n case.Moreover,increasing fast ion betaβh can not only significantly increase the loss level in the multiple-n case but also significantly increase the loss level increment between the single-n and multiple-n cases.For example,the loss level in the multiple-n case forβh=6.0%can even reach 13%of the beam ions and is 44%higher than the sum loss level calculated from all individual single-n modes in the single-n case.On the other hand,when the closely spaced resonance overlap occurs in the multiple-n case,the release of mode energy is increased so that the widely spaced resonances can also take place.In addition,phase space characterization is obtained in both single-n and multiple-n cases.

Numerical simulation of the multiple reversed shear Alfvén eigenmodes associated with the triangularity Alfvén gap

It was found that there are multiplicity of low shear toroidicity-induced Alfv′en eigenmodes in a zero beta limit if the inverse aspect ratio is larger than the magnetic shear at the mode location(Candy 1996 Phys. Lett. A 215 299). Because the reversed shear Alfv′en eigenmode(RSAE) and even the RSAE associated with the non-circular triangularity-induced Alfv′en eigenmode(NAE) gap(NAE–RSAE) usually reside near the shear-reversal point, the condition that the inverse aspect ratio is larger than the magnetic shear is naturally satisfied. For this reason, we numerically investigate the existence of multiplicity of core-localized NAE–RSAEs and mode characteristics in the present work. We firstly verify the existence of the multiplicity for zero beta plasma by using a D-shaped equilibrium. It is pointed out that, for a given toroidal mode number, the Alfv′en cascade spectrum accommodates down-sweeping and up-sweeping modes above and below the NAE range of frequencies. An analytical model for the existence of multiple RSAE modes is in good agreement with the simulation results. One notices that the triangularity has a greater effect on the odd-type modes than that on the even-type modes: the odd-type modes come into existence because of the plasma triangularity.

Observation of Multiple Broadband Alfvénic Chirping Modes in HL-2A NBI Plasmas

Multiple broadband Alfvenic chirping modes(CMs),with frequencies in the wide range of f-35-150 kHz and chirping down rapidly,are found in HL-2A neutral beam injection plasmas,and the CMs can even coexist.The frequency chirping down process can be completed within-1 ms,and the frequency shift can reach 30-50 kHz.The CMs propagate in ion diamagnetic drift directions poloidally.The toroidal mode number is confirmed to be n=1,2,3 and 4 for the f-35-65,55-90,70-120 and 100-150 kHz CMs,respectively.The CMs are more like to be energetic-particle continuum modes(EPMs),since the modes almost locate on the Alfven continuum.

Study of nonlinear mode–mode couplings between Alfvénic modes by the Fourier bicoherence and Lissajous-curve technique in HL-2A

Nonlinear couplings of various Alfvén modes driven by energetic particles in HL-2 A are addressed by employing the Fourier bicoherence and Lissajous-curve technique. Long-lived modes and high-frequency coherent modes are presented. Then the squared bicoherence of three waves establishes the existence of three-wave coupling. Lissajous-curves of those waves manifest that their phases are locked, which again confirms that they are nonlinearly coupled to each other. Moreover, coupled modes triggered by supersonic molecular beam injection are investigated. The phase evolution of them is given by the Lissajous-curve. Further details of phase-flip and phase-slip are presented and discussed.

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.

Simulation of Modes of Ionosphere Alfven Resonator with High Quality Factors in the Case of Oblique Geomagnetic Field

The properties of the ionosphere Alfvén resonator (IAR) in the general case of an oblique geomagnetic field are investigated. The modes at the frequencies f = 0.2 - 10 Hz well localized within the ionosphere are considered, which are important for the lithosphere—ionosphere coupling. An attention is paid to the modes with quite high quality factors , where . A proper selection of calculated eigenfrequencies has been realized. Two independent simulation algorithms have been proposed. The resonant frequencies and the profiles of magnetic field components of the modes have been calculated. The modulation of electron and ion concentrations at the heights 170 - 230 km leads to essential shifting the resonant frequencies.

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 ASDEXUpgrade 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 expressionФ(s)=e^(-σ(s-s_(0))^(2))with complex parametersσand s_(0),where s is the normalized radial coordinate.The mode structure is distorted in opposite manners when the EP drive shifted from one side of qminto the other side,and specifically,a non-zero average radial wave number 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,corresponding to different initial EP density profiles with EP drive shifted away from the qmin.

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.

探讨基于核心指标集构建中医特色的射血分数保留心力衰竭1+N模式疗效评价体系

核心指标集是就某一特定研究领域达成的所有临床研究都应该测量和报告的最少的临床结局,核心指标集可以提高临床疗效评价的规范性和可比性,是循证医学发展的必然、是中医药临床疗效评价的重要抓手、是推动中医药疗效评价与国际接轨的关键。如何运用核心指标集实现临床疗效国际化、标准化的同时,又能遵循中医诊疗特点体现自身优势是中医临床疗效评价的难点。针对这一难点,项目组创新性地提出了1+N模式的射血分数保留心衰(heart failure with preserved ejection fraction, HFpEF)疗效评价体系,即通用的核心指标集“1”+个性化指标集“N”,以满足循证医学和中医学疗效评价的双重需求。本文初探HFpEF疗效评价构建模式,主张在规范化基础上体现多样化和个性化的研究目的需求。结合HFpEF临床疗效评价的现状,综合业内专家意见,探讨了HFpEF 1+N模式疗效评价构建中核心指标集“1”的取舍以及“N”体系的构建思路,以期最大程度的形成符合中医药特色的临床评价体系新范式,推动中医药国际化进程。

A Field Study on Effects of Nitrogen Fertilization Modes on Nutrient Uptake,Crop Yield and Soil Biological Properties in Rice-Wheat Rotation System

Rational application of nitrogen （N） fertilizers is an important measure to raise N fertilizer recovery rate and reduce N loss.A two-year field experiment of rice-wheat rotation was employed to study the effects of N fertilization modes including a N fertilizer reduction and an organic manure replacement on crop yield,nutrient uptake,soil enzyme activity,and number of microbes as well as diversity of microbes.The result showed that 20% reduction of traditional N fertilizer dose of local farmers did not significantly change crop yield,N uptake,soil enzyme activity,and the number of microbes （bacteria,actinomycetes,and fungi）.On the basis of 20% reduction of N fertilizer,50% replacement of N fertilizer by organic manure increased the activity of sucrose,protease,urease,and phosphatase by 46-62,27-89,33-46,and 35-74%,respectively,and the number of microbes,i.e.,bacteria,actinomycetes,and fungi by 36-150,11-153,and 43-56%,respectively.Further,organic fertilizer replacement had a Shannon＇s diversity index （H） of 2.18,which was higher than that of other modes of single N fertilizer application.The results suggested that reducing N fertilizer by 20% and applying organic manure in the experimental areas could effectively lower the production costs and significantly improve soil fertility and biological properties.

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.

Large-scale inverted-V channels of upflowing oxygen ions pumped by Alfvén waves

Large-scale inverted-V channels of upflowing oxygen ions are frequently identified in data collected by Cluster,at all local times,near the open-closed field line boundary over Earth’s high-latitude ionosphere-occur with downward propagating MHD Alfvén waves which have cascaded into kinetic regimes of plasma.The transverse acceleration of the oxygen ions in the center of these structures is interpreted as the integrated energization by these waves along the channels.Also observed within the channels are upward parallel electric fields,a key characteristic of kinetic Alfvén waves,which may contribute not only to lifting the ions but also to precipitating aurora electrons that might initiate ion upflow in the ionosphere below.Statistics on five-year observations of Cluster show that the channels typically form during geomagnetic perturbations,particularly when solar-wind dynamic pressure is high or highly fluctuated.Near the open-closed field line boundary,the stronger the wave power,the higher the upward oxygen flux and the higher the beam energy,indicating that these waves provide a simple but efficient way to drive oxygen upflows.

Transition from fishbone mode toβ-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 theβ-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.

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.

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.

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.

Preliminary computation of the gap eigenmode of shear Alfvén waves on the LAPD

Characterizing the gap eigenmode of shear Alfv′en waves(SAWs) and its interaction with energetic ions is important to the success of magnetically confined fusion. Previous studies have reported an experimental observation of the spectral gap of SAW on the on Large Plasma Device(LAPD)(Zhang et al. 2008 Phys. Plasmas 15 012103), a linear large plasma device(Gekelman et al. 1991 Rev. Sci. Instrum. 62 2875) possessing easier diagnostic access and lower cost compared with traditional fusion devices, and analytical theory and numerical gap eigenmode using ideal conditions(Chang 2014 Ph.D Thesis at Australian National University). To guide experimental implementation, the present work models the gap eigenmode of SAWs using exact LAPD parameters. A full picture of the wave field for previous experiment reveals that the previously observed spectral gap is not global but an axially local result. To form a global spectral gap, the number of magnetic mirrors has to be increased and stronger static magnetic field makes it clearer. Such a spectral gap is obtained for the magnetic field of B0(z) = 1.2 + 0.6 cos[2π(z-33.68)/3.63] with 7.74-m magnetic beach. By introducing two types of local defects(corresponding to Eθ(z0) = 0 and E’θ(z0) = 0 respectively), odd-parity and even-parity discrete eigenmodes are formed clearly inside the gap. The strength of these gap eigenmodes decreases significantly with collision frequency, which is consistent with previous studies. Parameter scans show that these gap eigenmodes can be even formed successfully for the field strength of B0(z) = 0.2 + 0.1 cos[2π(z-33.68)/3.63] and with only four magnetic mirrors, which are achievable by the LAPD at its present status. This work can serve as a strong motivation and direct reference for the experimental implementation of the gap eigenmode of SAWs on the LAPD and other linear plasma devices.