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.

Scalings for the Alfvén-cyclotron instability in a bi-kappa plasma

The particle velocity distribution in space plasma usually exhibits a non-Maxwellian high-energy tail that can be well modeled by kappa distributions.In this study,we focus on the growth rates of the Alfvén-cyclotron instability driven by ion temperature anisotropy in a kappa plasma.By solving the kinetic linear dispersion equation,we explore the sensitivity of growth rates to the spectral indexκof a bi-kappa distribution under different plasma conditions,including a variety of plasma beta β_(hp) and temperature anisotropy A_(hp) values of hot protons.Furthermore,a concise,analytic scaling formula is derived that relates the dimensionless maximum growth rate to three independent variables:the spectral index and the plasma beta and temperature anisotropy of hot protons.Our results show that as theκ-value increases,the instability bandwidth narrows and the maximum growth rate increases significantly.For higherβ_(hp)and A_(hp)′the maximum instability undergoes a sharp increase as well.When our fits of dimensionless maximum growth rates are compared with solutions to kinetic linear dispersion theory,the results generally exhibit good agreement between them.Especially under the circumstances of largeκ-values and highβ_(hp)and A_(hp)′the scalings of maximum growth rates primarily accurately model the numerical solutions.Our analytic expressions can readily be used in large-scale models of the Earth’s magnetosphere to understand wave generation due to the Alfvén-cyclotron instability.

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.

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.

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.

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.

扭转Alfvén波共振的数学描述

提出完备正交函数基(OFSE)展开方法,求解冕环中无耗散扭转Alfvn波。每个基函数对应冕环中每根磁力线的一个固有角频率ω_n,当冕环足点驱动频率等于磁力线的固有频率时,Alfvn波将在这根磁力线处发生共振。采用OFSE方法求解了双足点驱动时冕环Alfvn波的时变演化问题,给出了时变解析解的新形式,其中包含共振项,从共振项可以发现,在共振角频率为ω的共振磁力线附近,在时间t为π/ω的整数倍时,出现δ型间断;在t为π/(2ω)的奇数倍时,出现1/x间断。共振磁力线振幅随时间线性增加,增加的斜率正比于Alfvn波速,反比于冕环长度,与驱动频率无关。

惯性区低-β等离子体中的动力学Alfvén孤波

运用双流体MHD方程描述电子和离子的行为 ,采用非扰动理论 ,把孤子看作经典粒子 ,通过推导的赝势 (也称Sagdeev势 )方程 ,结合数值计算来研究惯性区低 - β等离子体中动力学Alfv啨ｎ孤波的特性 .结果表明离子热效应对Alfv啨ｎ孤波特性的影响不可忽略 ,且在惯性区稀疏型孤波和压缩型孤波均存在 .此结论与Freja卫星在极区上空所观测结果吻合很好 .Alfv啨ｎ孤波携带有平行电场 ,它对带电粒子的加速有重要作用 ,这给极光粒子加速提供了一种可能的物理机制 .

低频Alfvén波谱与冷等离子体的非共振作用研究

本文讨论了低频率Alfvén波谱与冷等离子体的非线性相互作用。研究表明,对于多个低频Alfvén波,在波的振幅相对于背景磁场较小时,随着时间的增加,粒子动理学温度的各向异性会降低;随着振幅的增加,平行方向的动理学温度不断升高,且在A2=0.1处,平行方向的动理学温度将超过垂直方向的动理学温度。

低频Alfvén波对等离子体非共振加热与随机加热的粒子模拟

采用粒子模拟方法,研究沿背景磁场方向传播的低频Alfvén波对磁化等离子体加热的物理过程.模拟结果表明:离子在垂直和平行于背景磁场的方向都得到明显的加热,在非共振加热阶段,垂直方向比平行方向的加热效果更加显著,形成温度各向异性;在随机加热阶段,垂直和平行方向的温度最终达到饱和且趋于一致.加热过程中,离子所获得动力学温度的最大值由外加磁场能量密度与等离子体密度的比值决定,与Alfvén波的频率及振幅无关;离子在平行于背景磁场方向上被加速,并最终获得相当于Alfvén波相速度大小的流速.

低频Alfvén波多波相干加热粒子模拟

采用粒子模拟方法,考察多支沿背景磁场方向传播的低频Alfvén波对磁化等离子体的加热过程,研究不同频率的多支低频Alfvén波相干加热.结果表明可以通过调整波的频率比实现对非共振加热过程和随机加热过程这两个阶段的强化.符合相干共振条件的多波加热会强化低频Alfvén波对粒子拾取,进而强化非共振加热,明显提高加热效率.在多波加热的过程中,如果多支波之间的频率差足够小,则多波在调制过程中会形成波包.波包的出现标志着粒子各向异性的强化,从而提升随机加热效率.

Nonlinear simulation of multiple toroidal Alfvén eigenmodes in tokamak plasmas

Nonlinear evolution of multiple toroidal Alfven 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 beta β_h 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 for β_h=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.

Spatial Measurement on the Evidence of Ionospheric Alfvén Resonator

Using the data of ULF/ELF electric and magnetic wave field measured on board AUREOL-3 satellite, by the high resolution spectral analyses, one obtained for the first time the spatial measurement on the evidence of ionospheric alfvén resonator. The result of the measurement indicates that there are 7. 8 Hz for fundamental frequency, 14 Hz for second resonant frequency in the electric field component, and also the spectral resonance structure, but not in the magnetic vertical component for the magnetic field components.

Alfvénic Fluctuations in an Interplanetary Coronal Mass Ejection Observed Near 1 AU

As for the present situation of coronal mass ejection （CME） triggering models, the distributions of Alfv@n waves in flux ropes are different from model to model, and thus examining those distributions in interplanetary coronal mass ejection （ICME） is an effective way to connect ICME observations with these theoretical models of CME triggering. However, previous observations of Alfv@nic fluctuations in ICMEs were rare with locations ranging from 0.3 AU to 0.68 AU only, which is usually explained as rapid dissipation of those remnant waves. Here we present an observation of Alfv@n waves in a magnetic cloud （MC） near 1 AU, in situ detected by WIND in February 17,-~20, 2011. The MC was generated by a CME accompanied with the first X-class flare in the 24th solar cycle. The slope of the power spectral densities of magnetic fluctuation in the MC, are similar to those modes in ambient solar wind, but more anisotropic. The results will also be helpful for studies of CME theories and ICME thermodynamics.

Effect of Kinetic Alfvén Waves on Electron Transport in an Ion-Scale Flux Rope

At the Earth＇s magnetopause, the electron transport due to kinetic Alfvén waves（KAWs） is investigated in an ion-scale flux rope by the Magnetospheric Multiscale mission. Clear electron dropout around 90° pitch angle is observed throughout the flux rope, where intense KAWs are identified. The KAWs can effectively trap electrons by the wave parallel electric field and the magnetic mirror force, allowing electrons to undergo Landau resonance and be transported into more field-aligned directions. The pitch angle range for the trapped electrons is estimated from the wave analysis, which is in good agreement with direct pitch angle measurements of the electron distributions. The newly formed beam-like electron distribution is unstable and excites whistler waves,as revealed in the observations. We suggest that KAWs could be responsible for the plasma depletion inside a flux rope by this transport process, and thus be responsible for the formation of a typical flux rope.

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.

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.

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.

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.

低频左旋和右旋Alfvén波加热Kappa分布离子的研究

为了研究非热平衡态下Alfvén波与离子之间相互作用,采用试探粒子模拟的方法,研究低频单支左旋与右旋Alfvén波对Kappa分布离子的加热效果。结果表明:当越小,垂直加热效果越不显著,加热后温度趋于各向同性,左旋波与右旋波加热效果趋于一致;当增大时,在垂直方向加热效果明显提升,呈现各向异性,左旋提升速度快于右旋;当时,加热效果最好且温度异性最大,对于频率为0.1倍回旋频率的Alfvén波,垂直方向温度左旋比右旋约高出22%,左旋温度异性比右旋约高出23%。